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.