Phylum Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subphylum Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (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 Cladopyxiineae Fensome et al. (1993)
             Family Cladopyxiaceae Stein (1883) see Family Cladopyxidaceae F. Stein (1883)
               ?Genus †Gillnia Okolodkov (2011), orth. inval. see Genus Gillinia Cookson & Eisenack (1960)