Order formulas for linear groups of degree two

This article gives a list of formulas for the orders of the general linear group of degree two and some other related groups, both for a finite field of size $$q$$ and for related rings.

For the related formulas for degrees other than two, as well as for more detailed explanations of the order formulas, see order formulas for linear groups.

Formulas
In the formulas below, the field size is $$q$$. The characteristic of the field is a prime number $$p$$. $$q$$ is a prime power with underlying prime $$p$$. We let $$r = \log_pq$$, so $$q = p^r$$ and $$r$$ is a nonnegative integer.

Particular cases
The links are to the actual groups, which are not explicitly specified in order to save space.