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
     01 Class Dinophyceae Pascher (1914)
     02 Class Blastodiniphyceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic] see Class Haplozooidea Poche, 1911
     03 Class Noctiluciphyceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic]
     04 Family †Arpyloraceae Sarjeant (1978), incertae sedis [monotypic]
     05 Genus Agrosphaera Lo Bianco (1903), incertae sedis
     10 Genus Geodinium Chodat (1922), incertae sedis
     11 Genus Gleba Bruguière (1791), incertae sedis
     12 Genus Glenoaulax Diesing (1866), incertae sedis
     14 Genus Halophilodinium Loebl. & A.R. Loebl. (1966), incertae sedis
     15 Genus Parapodinium Chatton (1920), incertae sedis
     16 Genus Proaulax Diesing (1866), incertae sedis
     17 Genus Pterocystis Lohmann (1904), incertae sedis
     18 Genus Radiozoum Mingazzini (1904), incertae sedis