I cant put a Group in a Group ??

Through some advice on this group Im trying to stop all but
administrators and specific users and groups from being able to log on
to a couple of computers.
This means that I go to

Start / Programs / Administrative Tools / Local Security Policy

Then /Security Settings / Local Policies / User Rights Assignments
and remove Users from the Logon Locally Profile and then add the
groups and/or users I specifically want to access this computer.

I have tested this by removing users and then specifically adding user
joe1 and it works great.

In our small school, for our purposes we have two groups staff and
students.

We want staff to be able to access this computer and just a few
students.

I thought, it would make sense to create a group in AD called Library
and then add to that group all the Groups and users that I want to
have access to that computer.

However I cant seem to add the group Staff to the Library group. When
I search for groups it only finds the built in groups not any of the
groups that we created.

I dont understand this.

Cant I add a security group that I created to another group. This
would mean that when ever I put Library group into permissions
properties it would include staff and other individuals that I
explicityly put in it ??

Thanks

.