8. Lunularia. Gemmæ in crescent-shaped receptacles. Fertile receptacle cruciform.

[+][+] Gemmæ wanting.

[++] Receptacle conic-hemispherical, 2–4-lobed; perianth lobed or fringed.

2. Preissia. Receptacle 2–4-lobed, with as many alternate rib-like rays. Perianth 4–5-lobed.

3. Fimbriaria. Receptacle 4-lobed. Perianth conspicuous, split into 8–16 fringe-like segments.

[++][++] Receptacle more or less conical; perianth none.

4. Conocephalus. Thallus very large, strongly areolate. Receptacle conical, membranous.

5. Grimaldia. Thallus small. Peduncle chaffy at base and apex. Receptacle conic-hemispheric, truncately 3–4-lobed.

6. Asterella. Thallus eporose. Receptacle conic-hemispheric, becoming flattened, acutely 4- (1–6-) lobed.

[*][*] Thallus thin, ecostate or barely costate.