Class †Placodermi McCoy, 1848
   Order †Arthrodira Woodward, 1891 see [unranked] Arthrodira Woodward, 1891
     †coccosteids Asmuss, 1856
       Genus †Fallocosteus "Long, 1990", orth. inval. see Genus Fallacosteus Long, 1990
         †Fallocosteus turneri "Long, 1990", comb. inval. see Fallacosteus turneri Long, 1990