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?]
                     1 Family †Haplolepidae Westoll, 1944, incertae sedis
                     2 Order †Palaeonisciformes Jarvik, 1961
                     3.1 Order †Tarrasiiformes
                     3.2 Order †Guildayichthyiformes Lund, 2000
                     4 Order †Phanerorhynchiformes [monotypic]
                     5 Order †Saurichthyiformes Aldinger, 1937 [monotypic]
                     6 Order Acipenseriformes Berg, 1940 - paddlefishes and sturgeons
                     7 Order †Ptycholepiformes Andrews et al., 1967 see Order Ptycholepidiformes Andrews et al., 1967
                     8 Order †Pholidopleuriformes [monotypic]
                     9.1 Order †Peltopleuriformes
                     9.2.1 Order †Perleidiformes Berg, 1937
                     9.2.2.1 Order †Luganoiiformes Lehman, 1958