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
                 1 ?[Order] †Stensioelliformes
                 2 ?Order †Pseudopetalichthyiformes
                 3 Order †Acanthothoraciformes see Order Acanthothoraci Stensiö, 1944
                 4 Order †Rhenaniformes see Order Rhenanida Broili, 1930
                 5 Order †Antiarchiformes Grande & Eastman, 1986 - antiarchs see [unranked] Antiarchi Cope, 1885
                 6 Order †Petalichthyiformes see Order Macropetalichthyiformes
                 7 Order †Ptyctodontiformes [monotypic]
                 8 Order †Arthrodiriformes Grande & Eastman, 1986 - arthrodires see [unranked] Arthrodira Woodward, 1891