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)
             1 Family †Mancodiniaceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
             2 Family Cladopyxiaceae Stein (1883) see Family Cladopyxidaceae F. Stein (1883)
             3 Family †Scriniocassiaceae Sarjeant & Downie (1966)
             4 Family †Lotharingiaceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
             5 Family †Pareodiniaceae Gocht (1957)
             6 Genus †Rhiptocorys Lejeune-Carpentier & Sarjeant (1983), incertae sedis