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
             01 Order †Palaeonisciformes Jarvik, 1961
             02 Order †Haplolepiformes [monotypic] see Order Haplolepidiformes
             03 Order †Dorypteriformes Cope, 1871 [monotypic]
             04 Order †Tarrasiiformes [monotypic]
             05 Order †Ptycholepiformes Andrews et al., 1967 [monotypic] see Order Ptycholepidiformes Andrews et al., 1967
             06 Order †Pholidopleuriformes [monotypic]
             07 Order †Luganoiiformes Lehman, 1958
             08 Order †Redfieldiiformes Berg, 1940 [monotypic]
             09 Order †Perleidiformes Berg, 1937
             10 Order †Peltopleuriformes
             11 Order †Phanerorhynchiformes [monotypic]
             12 Order †Saurichthyiformes Aldinger, 1937 [monotypic]
             13 Order Polypteriformes [monotypic] - bichirs
             14 Order Acipenseriformes Berg, 1940 - paddlefishes and sturgeons