Abstract: Primates use social grooming to service coalitions and it has been suggested that these directly affect the fitness of their members by allowing them to reduce the intrinsic costs associated with living in large groups. We tested two hypotheses about the size of grooming cliques that derive from this suggestion: (1) that grooming clique size should correlate with relative neocortex size and (2) that the size of grooming cliques should be proportional to the size of the groups they have to support. Both predictions were confirmed, although we show that, in respect of neocortex size, there are as many as four statistically distinct grades within the primates (including humans). Analysis of the patterns of grooming among males and females suggested that large primate social groups often consist of a set of smaller female subgroups (in some cases, matrilinearly based coalitions) that are linked by individual males. This may be because males insert themselves into the interstices between weakly bonded female subgroups rather than because they actually hold these subunits together.