Kingdom Chromalveolata Adl et al., 2005 see Kingdom Chromista Caval.-Sm. (1981)
   Infrakingdom Alveolata Cavalier-Smith, 1991 see [unranked] Alveolata Cavalier-Smith, 1991
     Phylum Myzozoa Cavalier-Smith & Chao, 2004 see Subphylum Myzozoa Cavalier-Smith & Chao, 2004
       Superclass Dinokaryota Fensome et al., 1993
         Class Dinoflagellata Bütschli, 1885 see Superclass Dinoflagellata Bütschli, 1885
           01 Order Haplozooidea Poche, 1913 see Order Haplozoonales Poche (1913)
           01.0 [Order Haplozoonales Poche (1913)]
           02 Order Dinotrichales Pascher (1914)
           03 Order Dinococcales Pascher (1914)
           04.59 Genus Akashiwo Gert Hansen & Moestrup (2000) [within unnamed taxon]
           05 Order Brachidiniales A.R. Loebl. ex Sournia (1984) [monotypic]
           06 Order Gymnodiniales Apstein (1909)
           07 Order Ptychodiscales Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic]
           08 Order Thoracosphaerales Tangen (1982) see Order Peridiniales Haeckel (1894)
           09 Order Peridiniales Haeckel (1894)
           10.1 Family Tovelliaceae Moestrup, K.C.R. Lindb. & Daugbjerg (2005), incertae sedis
           10.2 Family Woloszynskiaceae Bourr. ex Starmach (1974), incertae sedis [monotypic]
           11 Family Apodiniaceae Chatton (1920), incertae sedis
           12 Order Actiniscales Sournia (1984) [monotypic]
           13 Order Amphilothales Er. Lindem. (1928) [monotypic]
           14 Order Prorocentrales Lemmerm. (1910)
           15 Order Dinophysales Er. Lindem. (1928)
           16 Order Blastodiniales Chatton (1906) [monotypic]
           17 Order Gonyaulacales F.J.R. Taylor (1980)
           17.0 [Order Pyrocystales Apstein (1909)] see Order Gonyaulacales F.J.R. Taylor (1980)
           18.255 Genus Berghiella Kof. & J.R. Michener (1911), incertae sedis
           19.256 Genus Ceratoperidinium Margalef ex A.R. Loebl. (1980), incertae sedis [monotypic]
           20.257 Genus Pyramidodinium T. Horig. & C. Sukigara (2005), incertae sedis
           21.258 Genus Pseudoactiniscus Bursa (1969), incertae sedis
           22.259 Genus Thaumatodinium Böhm (1933), incertae sedis