Division Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subdivision Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Superclass Dinokaryota Fensome et al., 1993
     Class Dinophyceae Pascher (1914)
       Subclass Peridiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Gonyaulacales F.J.R. Taylor (1980)
           Suborder Cladopyxiineae Fensome et al. (1993)
             Family Cladopyxiaceae Stein (1883) see Family Cladopyxidaceae F. Stein (1883)
               01 Genus Acanthodinium Kof. (1907) see Genus Cladopyxis F. Stein (1883)
               02 Genus Amphidoma F. Stein (1883)
               03 Genus †Beyrichodinium Below (1990)
               04 Genus †Cladopyxidium McLean (1972)
               05 Genus Cladopyxis F. Stein (1883)
               06 Genus †Druggidium Habib (1973)
               08 Genus †Fibradinium Morgenroth (1968)
               09 Genus †Freboldinium Below (1990)
               10 Genus †Gillinia Cookson & Eisenack (1960)
               11 Genus †Glyphanodinium Drugg (1964)
               12 Genus †Histiocysta Davey (1969)
               13 Genus †Hyalosphaera Prauss (1989) see Genus Praussia Williams, Lentin & Fensome (1998)
               14 Genus †Microdinium Cookson & Eisenack (1960)
               15 Genus †Mikrocysta Bjaerke (1980)
               16 Genus Palaeophalacroma J. Schiller (1928)
               17 Genus †Sinodinium D.S. Nie (1945) see Genus Palaeophalacroma J. Schiller (1928)
               18 Genus †Subtilidinium Morgenroth (1968)
               19 Genus †Wervekodinium Below (1990)
               20 Genus †Walvisia Miles (1990)