Superpositions of social networks, such as communication, friendship, or trade networks, are called multiplex networks, forming the structural backbone of human societies. Novel datasets now allow quantification and exploration of multiplex networks. Here we study gender-specific differences of a multiplex network from a complete behavioral dataset of an online-game society of about 300,000 players. On the individual level females perform better economically and are less risk-taking than males. Males reciprocate friendship requests from females faster than vice versa and hesitate to reciprocate hostile actions of females. On the network level females have more communication partners, who are less connected than partners of males. We find a strong homophily effect for females and higher clustering coefficients of females in trade and attack networks. Cooperative links between males are under-represented, reflecting competition for resources among males. These results confirm quantitatively that females and males manage their social networks in substantially different ways.