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)
       Order Phytodiniales T. Christ. ex A.R. Loebl. (1970), incertae sedis see Order Dinococcales Pascher (1914)
         Family Phytodiniaceae G.A. Klebs (1912)
           Genus Stylodinium G.A. Klebs (1912)