[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
                   Family †Coccosteidae Asmuss, 1856
                     1 Genus †Coccosteus Agassiz, 1844
                     2 ?Genus †"Solenosteus" nom. nud.
                     3 Genus †Millerosteus Stensiö, 1959