The M\"obius Function of the Affine Linear Group $\text{AGL}(1,{\mathbb{F}}_q)$

Let $\text{AGL}(1,{\mathbb{F}}_q)$ denote the affine linear group of dimension one over the finite field ${\mathbb{F}}_q$. We determine the M"obius function of the lattice of subgroups of $\text{AGL}(1,{\mathbb{F}}_q)$.