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]
               Class †Acanthodii Owen, 1846 - acanthodians
                 Order †Acanthodiformes Berg, 1940
                   Family †Cheiracanthidae Bleeker, 1859
                     1 Genus †Carycinacanthus Miles, 1966
                     2 Genus †Cheiracanthus Agassiz, 1835
                     3 Genus †Homalacanthus Russell, 1951