Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Superclass Dinokaryota Fensome et al., 1993
     Dinophyceae Pascher (1914)
       Peridiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Peridiniales Haeckel (1894)
           Peridiniineae Poche (1913) see Order Peridiniales Haeckel (1894)
             Peridiniaceae Ehrenb. (1831)
               Calciodinelloideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Family Calciodinellaceae Deflandre (1947)
                 †Pirumella H.M. Bolli (1980)