Class Actinopoda Calkins, 1902 see Parvkingdom Actinopoda Calkins, 1902
   Subclass Radiolaria Müller, 1858 see Phylum Actinopoda Calkins, 1902
     Superorder Polycystina Ehrenberg, 1838 see Class Polycystinea Ehrenberg, 1838
       Order Spumellaria Ehrenberg, 1875 see Class Spumellaria Ehrenberg, 1875
         Superfamily Pyloniacea Haeckel, 1881 see Superfamily Pylonioidea Haeckel, 1881
           Subsuperfamily †Patulibracchiilae Pessagno, 1971 see Order Lobatiradiata Afanasieva & Amon, 2005
             Family †Angulobracchiidae Baumgartner, 1980
               01 Genus †Angulobracchiaᵀ Baumgartner, 1980
               02 Genus †Bistarkum Yeh, 1987
               03 Genus †Cyclastrum Rüst, 1898
               04 ?Genus †Danubea Whalen & Carter, 1998
               05 Genus †Deviatus Li, 1986
               06 ?Genus †Loupanus Carter, 1993
               07 Genus †Paronaella Pessagno, 1971
               08 ?Genus †Protopsium Pessagno & Poisson, 1981
               09 Genus †Risella Carter, 1993, nom. illeg.
               10 Genus †Sontonaella Yeh, 1987
               11 ?Genus †Thurstonia Whalen & Carter, 1998, nom. illeg.