Allee effects in group-living species are common, but little is known about the way in which Allee effects at the group-level scale up to influence population dynamics. Most notably, it remains unclear whether component Allee effects within groups (where some component of fitness in small groups decreases with decreasing group size) will translate into a population-level demographic Allee effect (where per capita fitness in small populations decreases with decreasing overall population size). The African wild dog (Lycaon pictus) is an obligate cooperative breeder that lives in packs and has a multitude of group-level component Allee effects. With the African wild dog as a case study, we use models to determine the effect that group structure has on the population dynamics of social animals and, specifically, whether Allee effects operating at the group level lead to a demographic Allee effect at the population level. We developed a suite of models to analyse the population dynamics of group-living species, as well as comparable "packless" models lacking group structure. By comparing these models, we can identify how Allee effects within groups influence population-level dynamics. Our results show that group structure buffers populations against a demographic Allee effect, because mechanisms affecting birth and mortality are more strongly influenced by group size than population size. We find that interactions between groups are vital in determining the relationship between density dependence within groups and density dependence at the population level. As sufficiently large groups provide protection against positive density dependence, even at low overall population sizes, our results have conservation implications for group-living species, as they suggest group size is a necessary population feature to consider in efforts to manage population size. Furthermore, we provide novel insight regarding the role that dispersal and pack size variation play in the buffering nature of social structure in groups subject to Allee effects.