Phylum Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subphylum Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (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 Cladopyxis F. Stein (1883)
               02 Genus Amphidoma F. Stein (1883)
               03 ?Genus †Beyrichodinium Below (1990)
               04 Genus †Cladopyxidium McLean (1972)
               05 Genus †Druggidium Habib (1973)
               06 Genus †Fibradinium Morgenroth (1968)
               07 Genus †Freboldinium Below (1990)
               08 ?Genus †Gillnia Okolodkov (2011), orth. inval. see Genus Gillinia Cookson & Eisenack (1960)
               09 Genus †Glyphanodinium Drugg (1964)
               10 Genus †Histiocysta Davey (1969)
               11 Genus Micracanthodinium Deflandre (1937)
               12 Genus †Microdinium Cookson & Eisenack (1960)
               13 Genus †Mikrocysta Bjaerke (1980)
               14 Genus Palaeophalacroma J. Schiller (1928)
               15 Genus Peridiniella Kof. & J.R. Michener (1911)
               16 Genus †Praussia Williams, Lentin & Fensome (1998)
               17 Genus †Subtilidinium Morgenroth (1968)
               18 ?Genus †Walvisia Miles (1990)
               19 Genus †Wervekodinium Below (1990)