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
           Grade †Placodermiomorphi [monotypic]
             Class †Placodermi McCoy, 1848 [paraphyletic?]
               Order †Arthrodiriformes Grande & Eastman, 1986 - arthrodires see [unranked] Arthrodira Woodward, 1891
                 Suborder †Brachythoracoidei - brachythoracoids see Suborder Brachythoraci Gross, 1932
                   †Eubrachythoraci Miles, 1971
                     †coccosteomorphs Stensiö, 1944 - coccosteomorphs
                       01 Family †Buchanosteidae White, 1952
                       02 Family †Camuropiscidae Dennis & Miles, 1979
                       03 Family †Coccosteidae Asmuss, 1856
                       04 Family †Dinichthyidae Newberry, 1885
                       05 Family †Dunkleosteidae Stensiö, 1963, "nom. praeval."
                       06 Family †Mylostomatidae Woodward, 1891
                       07 Family †Panxiosteidae Wang, 1979
                       08 Family †Selenosteidae Dean, 1901
                       09 Family †Titanichthyidae Dean, 1901
                       10 Family †Wuttagoonaspididae Ritchie, 1973, nom. praeval.