After Carroll, 1988, with species from “Paleobiology Database”

<==o †Luganoiiformes
   |--o †Luganoiidae Brough 1939
   |  |-- †Luganoia lepidosteoides Brough, 1939; M.-L.Trias. Eu. [incl. Luganoia intermedia Brough, 1939; Luganoia macrodentata Brough, 1939]
   |  `--o †Besania Brough, 1939; M.-L.Trias. Eu. 
   |     |-- †B. micrognathus Brough, 1939
   |     `-- †B. schaufelbergeri Herzog & Bürgin, 2005
   |--o †Hadroichthyidae
   |  |-- †Nannolepis elegans Griffith, 1977 L.Trias. Eu. 
   |  `--o †Habroichthys Brough, 1939; L.Trias. Eu.
   |     |-- †H. gregarius Griffith 1977
   |     |-- †H. griffithi Bürgin 1992
   |     `-- †H. minimus Brough, 1939
   `?-o †Thoracopteridae Griffith 1977 sensu Xu, Zhao, Gao & Wu, 2012
      |-- †Thoracopterus niederristi Bronn, 1858 [Pterygopterus] ?E.Trias. NA. M.Trias. Aus. L.Trias. Eu.
      `--+-- †Gigantopterus telleri Abel, 1906; L.Trias. Eu.
         |-- †Potanichthys xingyiensis Xu, Zhao, Gao & Wu, 2012; E.Trias. SEAs.
         `--+-- †“Thoracopterusmartinisi Tintori and Sassi 1992
            `-- †“Thoracopterusmagnificus Tintori and Sassi 1987

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