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 Goniodomaceae Er. Lindem. (1928) see Family Goniodomataceae Er. Lindem. (1928)
               Subfamily Pyrodinioideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Subfamily Subfamily of Ostreopsis F. Gómez (2012)
                 02 Genus †Alisocysta Stover & Evitt (1978) see Genus Eisenackia Deflandre & Cookson (1955)
                 03 Genus †Biconidinium Islam (1983)
                 04 Genus †Dinopterygium Deflandre (1935)
                 05 Genus †Eisenackia Deflandre & Cookson (1955)
                 06 Genus †Eocladopyxis Morgenroth (1966)
                 08 Genus †Homotryblium Davey & Williams (1966)
                 12 Genus Pyrodinium L. Plate (1906)
                 13 Genus †Taleisphaera Duxbury (1979)
                 15 Genus †Tubidermodinium Morgenroth (1966)