Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Vertebrata Lamarck, 1801 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
         Myopterygii Janvier, 1978 - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Teleostomi Bonaparte, 1836 see Clade Pan-Osteichthyes Rowe 2004 [Moore & Near 2020]
               Euteleostomi - bony vertebrates see Clade Osteichthyes Huxley 1880 [Moore & Near 2020]
                 Class Actinopterygii Woodward, 1891 - ray-finned fishes see Clade Actinopterygii Woodward 1891 [Moore & Near 2020]
                   Subclass Chondrostei Müller, 1844 [monophyletic?]
                     Order †Palaeonisciformes Jarvik, 1961
                       1 Genus †Coccolepis Agassiz, 1844, incertae sedis
                       2 Suborder †Palaeoniscoidei see Order Palaeonisciformes Jarvik, 1961
                       3 Suborder †Redfieldioidei (Berg, 1955) [monotypic] see Order Redfieldiiformes Berg, 1940
                       4 Suborder †Platysomoidei Moy-Thomas, 1939 see Order Platysomiformes
                       5 Suborder †Dorypteroidei [monotypic] see Order Dorypteriformes Cope, 1871