Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Infraphylum Vertebrata Lamarck, 1801 - vertebrates
         Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
           Eugnathostomata
             Grade Teleostomi Bonaparte, 1836 see Clade Pan-Osteichthyes Rowe 2004 [Moore & Near 2020]
               Class Osteichthyes Huxley, 1880 - bony fishes and tetrapods see Clade Osteichthyes Huxley 1880 [Moore & Near 2020]
                 Subclass Actinopterygii Woodward, 1891 - ray-finned fishes see Class Actinopterygii Woodward, 1891
                   [stem] [unranked] †subholosteans
                     1 Order †Redfieldiiformes Berg, 1940 [monotypic]
                     2 Order †Ptycholepidiformes Andrews et al., 1967 [monotypic]
                     3 Order †Pholidopleuriformes [monotypic]
                     4 Order †Perleidiformes Berg, 1937 [paraphyletic?]
                     5 Order †Luganoiformes orth. inval. [monotypic] see Order Luganoiiformes Lehman, 1958