Nonrecombining genomic variants underlie spectacular social polymorphisms, from bird mating systems to ant social organization. Because these "social supergenes" affect multiple phenotypic traits linked to survival and reproduction, explaining their persistence remains a substantial challenge. Here, we investigate how large nonrecombining genomic variants relate to colony social organization, mating system and dispersal in the Alpine silver ant, Formica selysi. The species has colonies headed by a single queen (monogynous) and colonies headed by multiple queens (polygynous). We confirmed that a supergene with alternate haplotypes-Sm and Sp-underlies this polymorphism in social structure: Females from mature monogynous colonies had the Sm/Sm genotype, while those from polygynous colonies were Sm/Sp and Sp/Sp. Queens heading monogynous colonies were exclusively mated with Sm males. In contrast, queens heading polygynous colonies were mated with Sp males and Sm males. Sm males, which are only produced by monogynous colonies, accounted for 22.9% of the matings with queens from mature polygynous colonies. This asymmetry between social forms in the degree of assortative mating generates unidirectional male-mediated gene flow from the monogynous to the polygynous social form. Biased gene flow was confirmed by a significantly higher number of private alleles in the polygynous social form. Moreover, heterozygous queens were three times as likely as homozygous queens to be multiply mated. This study reveals that the supergene variants jointly affect social organization and multiple components of the mating system that alter the transmission of the variants and thus influence the dynamics of the system.