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
           1 Subsuperfamily Dactyliosphaerilae Squinabol, 1904 see Superfamily Dactyliosphaeroidea Squinabol, 1904
           2 Subsuperfamily †Patulibracchiilae Pessagno, 1971 see Order Lobatiradiata Afanasieva & Amon, 2005
           3 Subsuperfamily Pyloniilae Haeckel, 1881 see Superfamily Pylonioidea Haeckel, 1881
           4 Subsuperfamily Larnacillilae Haeckel, 1887 see Superfamily Larnacillioidea Haeckel, 1887