By default, you can have up to 200 members in a group.
If you want your group to be larger than 200 members, simply submit a request. Be sure to include the group ID, the group name, the new group limit and the phone number you registered to GroupMe with.
It is possible to have remarkably large GroupMe groups, but keep in mind that groups larger than 200 people can get noisy. GroupMe is reply-all, so whenever a member replies to the group number, everyone in the group will get a text message or push notification. Additionally, everyone in the group has to respond to the group at least once in order to stay in.
Members are encouraged to text #stay to stay in the group, which doesn't send a message to the whole group.
#) GroupMe Support