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 Peridiniales Haeckel (1894)
           Suborder Heterocapsineae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic] see Order Peridiniales Haeckel (1894)
             Family Heterocapsaceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
               01 Genus †Andreedinium Below (1987)
               02 Genus †Angustidinium Goodman & Evitt (1981)
               05 Genus Heterocapsa F. Stein (1883)
               06 Genus †Liasidium Drugg (1978)
               07 Genus †Moesiodinium Antonescu (1975)
               08 Genus †Ovalicysta Bjaerke (1980)
               09 Genus †Parvocysta Bjaerke (1980)
               10 Genus †Reutlingia Drugg (1978)
               11 Genus †Susadinium Dörhöfer & Davies (1980)