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 †Placodermiomorphi [monotypic]
               Class †Placodermi McCoy, 1848
                 Order †Arthrodiriformes Grande & Eastman, 1986 - arthrodires see [unranked] Arthrodira Woodward, 1891
                   Suborder †Brachythoraci Gross, 1932
                     †Eubrachythoraci Miles, 1971
                       †coccosteomorphs Stensiö, 1944 - coccosteomorphs
                         Family †Coccosteidae Asmuss, 1856
                           1 Genus †Coccosteus Agassiz, 1844