This research found that while both women and men have more favorable views of women, women's in-group biases were 4.5 times stronger than those of men. And only women (not men) showed cognitive balance among in-group bias, identity, and self-esteem, revealing that men lack a mechanism that bolsters automatic preference for their own gender.
To be fair, everyone has some degree of in-group bias.
But statistically, women have 4.5 times more in-group bias than men. In fact, men have almost no in-group bias:
https://en.wikipedia.org/wiki/Women-are-wonderful_effect