†Placodermi McCoy, 1848
   †Arthrodira Woodward, 1891
     †Brachythoraci Gross, 1932
       †Eubrachythoraci Miles, 1971
         †Pachyosteomorphi Stensiö, 1944
           †Aspinothoracidi Stensiö, 1959
             1 ?Family †Mylostomatidae Woodward, 1891
             2 Family †Leiosteidae Stensiö, 1963
             3 Family †Trematosteidae Gross, 1932
             4 Family †Titanichthyidae Dean, 1901
             5 Family †Bungartiidae Denison, 1975
             6.1 Family †Selenosteidae Dean, 1901
             6.2 Family †Braunosteidae Stensiö, 1959
             7.1 Genus †Gymnotrachelus Dunkle & Bungart, 1939 [monotypic]
             7.2.1 Family †Dinichthyidae Newberry, 1885 [monotypic]
             7.2.2.1 Genus †Heintzichthys Whitley, 1933
             7.2.2.2.1 Family †Hadrosteidae Gross, 1932
             7.2.2.2.2 Genus †Gorgonichthys Claypole, 1892 [monotypic]