After Ivantsov & Fedonkin, 2003, and Leme, Guimarães Simões, Marques & van Iten, 2008

<==o †Conulariina Miller & Gurley, 1896 [Conulata Moore & Harrington, 1956; Conulariida Miller & Gurley, 1896 sensu Moore & Harrington, 1956] (conulariids; kartiomeduusat; konulaarit)
   `--o †Conulariidae Walcott, 1886
      |--+-- †Vendoconularia triradiata Ivantsov & Fedonkin, 2002; Vend. NAs.
      |  `--+--o †Teresconularia Leme et al., 2003; Ord.
      |     |  `-- †T. argentinensis
      |     `--+--o †Eoconularia Sinclair, 1943 [paraphyletic Paraconulariinae]
      |        |  `-- †E. loculata [Conularia loculata] Ord.-Sil.
      |        `--o †Conularina Sinclair, 1942; Ord. [paraphyletic Ctenoconulariinae]
      |           `-- †C. triangulata (Raymond, 1905) [Conularia triangulata (Raymond, 1905)]
      `--+--o †Conulariella Boucek, 1928 [Conulariellidae Kiderlen, 1937; paraphyletic Conulariinae] Camb.-Ord.
         |  |-- †C. robusta
         |  `-- †C. sulca
         `--+--o †Baccaconularia Hughes et al., 2000; Camb.
            |  `-- †B. robinsoni
            `--+--o †Glyptoconularia Sinclair, 1948; Ord. [paraphyletic Conulariinae]
               |  `-- †G. gracilis
               `--+--o †Metaconularia Foerste, 1928; Ord.-Sil. [paraphyletic Conulariinae]
                  |  `-- †M. aspersa [Conularia aspersa]
                  |--+--o †Pseudoconularia Boucek, 1939; Sil. [paraphyletic Conulariinae]
                  |  |  `-- †P. grandissima
                  |  `--+--o †Conularia Miller, in Sowerby, 1821; Ord.-Perm. [paraphyletic Conulariinae]
                  |     |  |-- †C. quadrisulcata
                  |     |  |-- †C. elegantula
                  |     |  `-- †C. quichua
                  |     `--o †Ctenoconularia Sinclair, 1952; Ord. [paraphyletic Ctenoconulariinae]
                  |        `-- †C. obex
                  `--+--o †Archaeoconularia Boucek, 1939; Ord.-Sil. [paraphyletic Conulariinae]
                     |  `-- †A. insignis [Conularia insignis]
                     `--+--o †Notoconularia Thomas, 1969; Perm.
                        |  `-- †N. inornata [Conularia inornata]
                        `--+--o †Climacoconus Sinclair, 1942; Ord. [paraphyletic Ctenoconulariinae]
                           |  `-- †C. quadrata
                           `--+--o †Paraconularia Sinclair, 1940; Dev.-Trias. [paraphyletic Paraconulariinae]
                              |  |-- †P. inaequicostata (DeKoninck, 1883) [Conularia inaequicostata DeKoninck, 1883]
                              |  `-- †P. missouriensis (Swallow)
                              `--o †Reticulaconularia Babcock & Feldmann, 1986a; Dev.
                                 `-- †R. penouili [Conularia penouili]

Conulariina incertae sedis:

Some taxa from Ivantsov & Fedonkin, 2003, with taxa untreated or unmentioned by Leme et al., 2008

    †Carinachitiida [=? Conulariidae]
        †Carinachitidae
            †Carinachites Qian Yi, 1977; Camb.
                † C. spinatus
            †Emeiconularia Qian Yi et al., 1997; Camb.
                †E. trigemme

    †Protoconulariida?? [4 families, 19 genera, 31 species, or 4/6/12]

    †Hexangulaconularida

    †Conulariina Miller & Gurley, 1896
        †Conomedusites
        †Podolimirus Fedonkin, 1983
        †Swartpuntia Narbonne et al., 1997
        †Calyptrina Sokolov
        †Gexagulaconulariidae [=? Conulariidae]
        †Hexaconulariidae [=? Conulariidae]
            †Hexaconularia He Yuanxiang & Yang Xianhe, 1986, Camb.
                †H. sichuanensis
        †Arthrochitiidae [=? Conulariidae]
            †Arthrochites Chen Menge, 1982; Camb.
                † A. emeishanensis
        †Circonulariidae [=? Conulariidae]
            †Circonularia Bischoff, 1978; Sil.-Dev.
                † C. eosilurica
        †Conulariopsidae Sugiyama, 1942 [=? Conulariidae]
            †Conulariopsis Sugiyama, 1942 Trias.
                † C. quadrata
        †Conulariidae Walcott, 1886
                †Adesmoconularia Driscoll, 1963; Carb.
                    †A. byblis
                †Australoconularia Bischoff, 1978; Sil.
                    † A. borenorensis
                †Beijingconularia Xu Gueiyong & Li Fenglin, 1979; Carb.
                    † B. planarea
                †Cathayconularia Xu Gueiyong & Li Fenglin, 1979; Carb.
                    † C. qingshuijianensis
                †Changshaconus Zhu Zhikang, 1985; Dev.
                    † C. carinata
                †Cheliconularia Waterhouse, 1986; Perm.
                    † C. cheliensis
                †Conulariopsiella Xu Gueiyong & Li Fenglin, 1979; Ord.
                    † C. minima
                †Flectoconularia Waterhouse, 1979; Trias.
                    † F. abapertura
                †Garraconularia Bischoff, 1978; Sil.
                    † G. multicostata
                †Gondaconularia Waterhouse, 1986; Perm.-Trias.
                    †C. elviniaria
                †Holoconularia Hergarten, 1985; Dev.
                    †H. hummeli
                †Hunanoconularia Xu Gueiyong & Li Fenglin, 1979; Dev.
                    †H. hunanensis
                †Malvinoconularia Babcock et al., 1987a; Dev.
                    †M. cahuanotensis
                †Pustuloconularia Zhu Zhikang, 1985; Perm.
                    †P. chinensis
                †Sinusconularia Hergarten, 1994; Dev.
                    †S. blasii
                †Tasmanoconularia Parfrey, 1982; Ord.
                    †T. tuberosa
                †Yinoconularia Zhu Zhikang, 1985; Dev.
                    †Y. huaqiaoensis
            †Conulariinae Walcott, 1886 [polyphyletic sensu Leme et al., 2008]
                †Anaconularia Bouc.ek, 1939; Ord.
                    †A. anomala [Conularia anomala]
                †Diconularia Sinclair, 1952; Sil.-Carb.
                    † C. micronema
                †Exoconularia Sinclair, 1952; Ord.
                    † C. exquisita
                †Mesoconularia Boucek, 1939; Dev.-Carb.
                    †C. fragilis
            †Paraconulariinae Sinclair, 1952 [polyphyletic sensu Leme et al., 2008]
                †Calloconularia Sinclair, 1952; Carb.
                    † C. strimplei
                †Neoconularia Sugiyama, 1942; Perm.
                    †N. rectangularis
            †Ctenoconulariinae Sinclair, 1952 [polyphyletic sensu Leme et al., 2008]
                †Sphenothallus Hall, 1847; Ord.
                    †S. angustifolius

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