Vertebrata Cuvier, 1812 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
   Gnathostomata
     Teleostomi Bonaparte, 1836
       Class Osteichthyes Huxley, 1880 [paraphyletic] - bony fishes and tetrapods see Clade Osteichthyes Huxley 1880 [Moore & Near 2020]
         Subclass Actinopterygii Woodward, 1891 - ray-finned fishes see Class Actinopterygii Woodward, 1891
           Infraclass Chondrostei Müller, 1844 see Subclass Chondrostei Müller, 1844
             Order †Palaeonisciformes Jarvik, 1961
               Suborder †Palaeoniscoidea see Suborder Palaeoniscoidei
                 01 Family †Cheirolepidae see Family Cheirolepididae Pander, 1860
                 02 Family †Stegotrachelidae Gardiner, 1963, "nom. praeval."
                 03 Family †Tegeolepidae Romer, 1945 see Family Stegotrachelidae Gardiner, 1963, "nom. praeval."
                 04 Family †Rhabdolepidae Gardiner, 1963, nom. illeg. see Family Rhabdolepididae Gardiner, 1963
                 05 Family †Rhadinichthyidae Romer, 1945
                 06 Family †Carbovelidae Romer, 1945
                 07 Family †Canobiidae Aldinger, 1937
                 08 Family †Cornuboniscidae White, 1939
                 09 Family †Styracopteridae Moy-Thomas, 1937
                 10 Family †Cryphiolepidae Moy-Thomas, 1939 see Family Cryphiolepididae Moy-Thomas, 1939, nom. praeval.
                 11 Family †Holuriidae
                 12 Family †Cosmoptychiidae Gardiner, 1963
                 13 Family †Pygopteridae Fitzinger, 1873
                 14 Family †Elonichthyidae Aldinger, 1937
                 15 Family †Acrolepidae Aldinger, 1937 see Family Acrolepididae Aldinger, 1937, nom. praeval.
                 16 Family †Coccocephalichthyidae Fowler, 1951 (1945)
                 17 Family †Amblypteridae Romer, 1945
                 18 Family †Aeduellidae Romer, 1945
                 19 Family †Commentryidae Gardiner, 1963
                 20 Family †Palaeoniscidae Bonaparte, 1846
                 21 Family †Dicellopygidae Romer, 1945
                 22 Family †Boreolepidae Aldinger, 1937 see Family Boreolepididae Aldinger, 1937, nom. praeval.
                 23 Family †Birgeriidae Aldinger, 1937
                 24 Family †Scanilepidae Aldinger, 1937 see Family Scanilepididae Aldinger, 1937, nom. praeval.
                 25 Family †Centrolepidae Gardiner, 1960, nom. illeg. see Family Centrolepididae Gardiner, 1960
                 26 Family †Coccolepidae Berg, 1940