Vertebrata Cuvier, 1812 - vertebrates
   Gnathostomata
     Class †Placodermi McCoy, 1848
       Order †Arthrodira Woodward, 1891 see Order Arthrodiriformes Grande & Eastman, 1986
         Suborder †Brachythoraci Gross, 1932
           1 Superfamily †Buchanosteoidea White, 1952
           2 Superfamily †Heterosteoidea Denison, 1984 [monotypic]
           3 Superfamily †Homosteoidea Denison, 1978 [monotypic]
           4 Superfamily †Brachydeiroidea Denison, 1978
           5 Superfamily †Coccosteoidea Traquair, 1888
           6 Superfamily †Dinichthyloidea