How to identify groups where the group manager is NOT a group member

[SarahC1]

Hi all,
I am attempting pull a list of all groups where the group manager is NOT a group member, but I'm beginning to wonder if this is possible? Its straightforward enough to identify groups where the manager is a member of a specific group but I cannot seem to find a way to find the reverse.
Currently trying to achieve this with a database view but its not something I've used previously. 
The tables I'm concerned with are sys_user_group and sys_user_grmember.
Grateful for any tips or pointers, even if to confirm this is not something that is possible!

[Robert Campbell · Accepted solution]

Create a Script Include (System Definition -> Script Include).

function missingManager(){
    var groups = [];
    var grp = new GlideRecord('sys_user_group');
    grp.addNotNullQuery('manager');
    grp.query();
    while(grp.next()){
        var grMember = new GlideRecord('sys_user_grmember');
        grMember.addQuery('user',grp.manager.toString());
        grMember.addQuery('group',grp.getUniqueValue());
        grMember.query();
        if(!grMember.hasNext()){
                groups.push(grp.getUniqueValue());
        }
    }
    return groups.toString();
}

[SarahC1]

Thanks so much Robert for your comprehensive reply - missing completely accomplished!