The major way in which gender and social institutions interact is when the social institutions affect the ways in which we define gender in our society. Sociologists typically say that there are five social institutions. These are the family, religion, education, the economy, and politics. All of these institutions help to create our views of gender.
For example, the family can help to create a view of gender in which we see women as basically nurturing and, to some degree, subordinated. This can be caused by the fact that women have generally been the ones who stay home and raise children and who do not participate as much in the economic world.
As another example, religion can, at times, affect how we conceive of gender. Some churches teach that women should subordinate themselves to men. They have systems in which women cannot participate at the highest levels of church life. When they do this, they help to shape our views of what women should be like.
Thus, our social institutions help to create the views of gender that we hold in our society.