[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
         Class †Placodermi McCoy, 1848
           †Arthrodira Woodward, 1891
             Order †Phlyctaeniiformes
               Suborder †Brachythoraci Gross, 1932
                 †Coccosteomorphi Stensiö, 1944 - coccosteomorphs
                   1 Family †Coccosteidae Asmuss, 1856
                   2 Family †Torosteidae Gardiner & Miles, 1990
                   3 Family †Trematosteidae Gross, 1932
                   4 Family †Camuropiscidae Dennis & Miles, 1979
                   5 Family †Mylostomatidae Woodward, 1891
                   6 Family †Bungartiidae Denison, 1975