Belongs within: Atrypida.
The Lissatrypidae are a family of smooth-shelled brachiopods known from the Middle Ordovician to the Middle Devonian (Boucot et al. 1965).
<==Lissatrypidae
| i. s.: Barkolia Zhang 1983M03
| Webbyspira principalis Percival 1991HB93
| Holynatrypa crucifera Havlíček 1973HB93
|--Septatrypinae [Atrypellinae, Atrypopsinae]MM02
| | i. s.: Atrypopsis Poulsen 1943BJ65
| | `--*A. varians Poulsen 1943BJ65, M03
| | Cromatrypa Havlíček 1987MM02
| | |--*C. orbis Havlíček 1987MM02
| | `--C. pubes Musteikis & Modzalevskaya 2002MM02
| |--+--Dubaria Termier 1936B75, BJ65 [incl. Rhynchatrypa Siehl 1962BJ65]
| | | |--*D. lantenoisi Termier 1936BJ65
| | | |--D. tenera Nikiforova & Modzalevskaya 1968M03
| | | `--D. thetis (Barrande 1847) [=Terebratula thetis, *Rhynchatrypa thetis]BJ65
| | `--Septatrypa Kozłowski 1929B75, M03
| | |--*S. secreta Kozłowski 1929MM02
| | |--S. saphoBJ65
| | `--S. subaequalis Bassett 1979MM02
| `--+--Cryptatrypa Siehl 1962B75, BJ65
| | `--*C. philomela (Barrande 1847) [=Terebratula philomela]BJ65
| `--Atrypoidea Mitchell & Dun 1920MM02 [=Atrypella Kozlowski 1929B75, BJ65]
| |--*A. prunum (Dalman 1828)MM02 [=Atrypa prunumMM02, *Atrypella prunumBJ65]
| |--A. angusta Mitchell & Dun 1920F71
| |--A. australis (Dun 1904) [=Meristina australis]F71
| |--‘Atrypella’ carinataBJ65
| |--A. phoca (Salter 1852)MM02 [=Atrypella phocaB75]
| `--‘Atrypella’ scheiiB75
`--Lissatrypinae [Glassiidae, Glassiinae]MM02
| i. s.: PeratosHB93
| |--P. beyrichi (Kayser 1872)HB93
| `--P. drevermanni Maillieux 1936HB93
|--Meifodia Williams 1951B75, BJ65 [incl. Tyrothyris Öpik 1953BJ65]
| |--*M. subundata (M’Coy 1851) [=Hemithyris subundata]BJ65
| |--M. ovalisBJ65
| | |--M. o. ovalisBJ65
| | `--M. o. supercedensBJ65
| `--‘*Tyrothyris’ tyro Öpik 1953BJ65
`--+--Lissatrypoidea Boucot & Amsden 1958B75, BJ65
| `--*L. concentrica (Hall 1859) [=Nucleospira concentrica; incl. Lissatrypa decaturensis Amsden 1949]BJ65
|--+--Australina Clarke 1913 non Gaud. 1826 (ICBN)B75, BJ65
| | `--*A. jachalensis Clarke 1913BJ65
| `--Nanospira Amsden 1949B75, BJ65
| `--*N. parvula Amsden 1949BJ65
`--Lissatrypa Twenhofel 1914B75, MM02 [incl. Glassia Davidson 1881BJ65]
|--*L. atheroidea Twenhofel 1914MM02
|--L. lenticulataH79
|--L. leprosaBJ65
|--L. lithuanica Paškevičius, Modzalevskaya & Musteikis in Musteikis & Modzalevskaya 2002MM02
|--‘Glassia’ minuta Rybnikova 1967HB93
|--L. obovata (Sowerby 1839)MM02 [=Atrypa obovataMM02, *Glassia obovataBJ65; incl. G. rotunda Rybnikova 1967MM02]
`--‘Glassia’ sulcataBJ65
*Type species of generic name indicated
References
[B75] Boucot, A. J. 1975. Evolution and Extinction Rate Controls. Elsevier Scientific Publishing Company.
[BJ65] Boucot, A. J., J. G. Johnson, C. W. Pitrat & R. D. Staton. 1965. Spiriferida. In: Moore, R. C. (ed.) Treatise on Invertebrate Paleontology pt H. Brachiopoda vol. 2 pp. H632–H728. The Geological Society of America, Inc.: Boulder (Colorado), and The University of Kansas Press: Lawrence (Kansas).
[F71] Fletcher, H. O. 1971. Catalogue of type specimens of fossils in the Australian Museum, Sydney. Australian Museum Memoir 13: 1–167.
[HB93] Harper, D. A. T., C. H. C. Brunton, L. R. M. Cocks, P. Copper, E. N. Doyle, A. L. Jeffrey, E. F. Owen, M. A. Parkes, L. E. Popov & C. D. Prosser. 1993. Brachiopoda. In: Benton, M. J. (ed.) The Fossil Record 2 pp. 427–462. Chapman & Hall: London.
[H79] House, M. R. 1979. Devonian in the Eastern Hemisphere. In: Robison, R. A., & C. Teichert (eds) Treatise on Invertebrate Paleontology pt A. Introduction. Fossilisation (Taphonomy), Biogeography and Biostratigraphy pp. A183–A217. The Geological Society of America, Inc.: Boulder (Colorado), and The University of Kansas: Lawrence (Kansas).
[M03] Modzalevskaya, T. L. 2003. Silurian and Devonian brachiopods from Severnaya Zemlya (Russian Arctic). Geodiversitas 25 (1): 73–107.
[MM02] Musteikis, P., & T. L. Modzalevskaya. 2002. Some Silurian brachiopods from Lithuania and their palaeobiogeographical significance. Palaeontology 45 (3): 595–626.