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 Gymnodiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Ptychodiscales Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
           Family Ptychodiscaceae Lemmerm. (1899)
             1 Subfamily †Dinogymnioideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
             2 Subfamily Ptychodiscoideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)