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 Amphipyndacioidea Riedel, 1967
           1 Family †Canoptidae Pessagno, 1979
           2 Family †Parvicingulidae Pessagno, 1977
           3 Family †Syringocapsidae Foreman, 1973
           4 Family †Spongocapsulidae Pessagno, 1977
           5 Family Amphipyndacidae Riedel, 1967