For the most part, women were very much subjugated to men in the Roman republic.
The dominant idea in Rome at the time was that women needed to have male guardians. This was necessary because of the "fact" that women were the weaker sex not just physically but mentally and emotionally as well. Because of this, women were legally under the control of their fathers and then of their husbands during much of the time of the Roman republic.
Upper class women did sometimes get educated and could have some degree of power. They were often forced to manage estates for their husbands while the men were off serving in the military or the government. This gave them some informal power.
Overall, though, women in the Roman republic had little in the way of rights or power.