Class †Placodermi McCoy, 1848
   Order †Arthrodira Woodward, 1891 see [unranked] Arthrodira Woodward, 1891
     †coccosteids Asmuss, 1856
       1.1 Genus †Coccosteus Agassiz, 1844
       1.2.1 Genus †Watsonosteus Miles & Westoll, 1963
       1.2.2 Genus †Millerosteus Stensiö, 1959
       2.1 Genus †Harrytoombsia Miles & Dennis, 1979
       2.2.1 Genus †Torosteus Gardiner & Miles, 1990
       2.2.2.1.1 Genus †Mcnamaraspis Long, 1995, sedis mutabilis
       2.2.2.1.2 Genus †Compagopiscis Gardiner & Miles, 1994, sedis mutabilis
       2.2.2.1.3 Genus †Incisoscutum Dennis & Miles, 1981, sedis mutabilis
       2.2.2.2.1 Genus †Rolfosteus Dennis & Miles, 1979
       2.2.2.2.2.1 Genus †Tubonasus Dennis & Miles, 1979
       2.2.2.2.2.2.1 Genus †Fallocosteus "Long, 1990", orth. inval. see Genus Fallacosteus Long, 1990
       2.2.2.2.2.2.2.1 Genus †Camuropiscis Dennis & Miles, 1979
       2.2.2.2.2.2.2.2 Genus †Latocamurus Long, 1988