Spotted hyaenas live in unusually large social groups for a carnivore. Since, all else equal, the ‘infertility trap’ (a negative relationship between fertility and the number of females in a group) limits social group sizes to ~5 reproductive females in mammals, hyaena must, like other very social species, have found a way to mitigate the stresses involved in order to do so. From a comparative analysis of data from 19 well‐studied Crocuta crocuta populations, I show (1) that the distribution of hyaena clan sizes is multimodal, with a fractal scaling ratio close to 3 and a base unit of 12–15 individuals (3–5 reproductive females), (2) that fertility is a negative function of number of females in the group and (3) that there is a trade‐off between the benefits of having more males in the group and the costs incurred by having more females. Although females do buffer themselves against the infertility trap by forming matrilineal alliances (thereby creating a primate‐like multilevel structure), males seem to play an important role, such that, in areas with a low density of males, clan sizes are much smaller.