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 Nassellaria Ehrenberg, 1875 see Class Nassellaria Ehrenberg, 1847
         Superfamily Acanthodesmiacea Haeckel, 1862 see Order Spyridinata Ehrenberg, 1847
           Family Acanthodesmiidae Haeckel, 1862
             01 Genus Acanthodesmiaᵀ Müller, 1856
             02 Genus Circospyris Haeckel, 1881
             03 Genus Dictyospris De Wever, Dumitrica, Caulet, Nigrini & Caridroit, 2001, nom. null. see Genus Dictyospyris Ehrenberg, 1847
             04 Genus Dipocoronis Haeckel, 1881
             05 Genus Eucoronis Haeckel, 1881
             06 Genus Lithocircus Müller, 1856
             07 Genus Nephrodictyum Haeckel, 1881
             08 Genus Paradictyum Haeckel, 1881
             09 Genus Microcubus Haeckel, 1881
             10 Genus Perispyris Haeckel, 1881
             11 Genus Psychospyris Riedel & Sanfilippo, 1971
             12 Genus Semantis Haeckel, 1887
             13 Genus Tricolospyris Haeckel, 1881
             14 Genus Tricyclidium Haeckel, 1881
             15 Genus Trissocyclus Haeckel, 1881
             16 Genus Tympanidium Haeckel, 1881
             17 Genus Tympaniscus Haeckel, 1887
             18 Genus Tympanomma Haeckel, 1887
             19 Genus Zygocircus Bütschli, 1881
             20 Genus Zygostephanus Haeckel, 1862
             21 Genus Lithotympanum Haeckel, 1881