Adding Security Groups to Teams

We are updating our Teams structure and changing how we handle memberships. I created several Security Groups containing different department heads. The thought with this is so we can add a group to a team, and if someone is hired/fired they are automatically removed/added to the teams necessary without worrying about personal membership. We have our new teams created however, when I go to add membership and type in a new security group, it comes up with zero results. When I try to add members though, it says you can add a security group. Any suggestions? I have tried in the Teams app, in the Admin Center, and in the Sharepoint site.