[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
                 †Pachyosteomorphi Stensiö, 1944 - pachyosteomorphs
                   †Aspinothoracidi Stensiö, 1959
                     1 Family †Dinichthyidae Newberry, 1885
                     2 Family †Brachydeiridae Gross, 1932
                     3 Family †Braunosteidae Stensiö, 1963
                     4 Family †Hadrosteidae Gross, 1932
                     5 Family †Selenosteidae Dean, 1901
                     6 Family †Leiosteidae Stensiö, 1963
                     7 Family †Leptosteidae Gross, 1932
                     8 Family †Titanichthyidae Dean, 1901
                     9 Family †Bulbocanthidae Young & Goujet, 2003