Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Nassellaria Ehrenberg, 1847
       Order Cyrtidinata Haeckel, 1862
         Superfamily Acropyramidoidea Haeckel, 1881
           Family Sethophormididae Haeckel, 1881
             Subfamily Theopiliinae Haeckel, 1881
               01 Genus †Anthocyrtella Haeckel, 1887
               02 Genus Cecryphalium Haeckel, 1881
               03 Genus Clathrocyclas Haeckel, 1881
               04 Genus Clathrocycloma Haeckel, 1887
               05 Genus Diplocyclas Haeckel, 1881
               06 Genus Eucecryphalus Haeckel, 1860
               07 Genus †Haeckelicyrtium Kozur & Mostler, 1979
               08 Genus Phrenocodon Haeckel, 1887
               09 Genus Pterocorythium Haeckel, 1881
               10 Genus †Salpingocapsa Rüst, 1885
               11 Genus †Squinabolella Pessagno, 1969
               12 Genus Stichopilium Haeckel, 1881
               13 Genus Theocalyptra Haeckel, 1881
               14 Genus Theopilium Haeckel, 1881