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 Goniodomineae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
             Family Pyrocystaceae (F. Schütt) Lemmerm. (1899) [monotypic]
               Genus Pyrocystis J. Murray ex Haeckel (1890)