Maximal Compact and Hyperspecial Subgroup

Let $k$ be a nonarchimedean local field with ring of integers $\mathcal O_k$.

A maximal compact subgroup of $G(k)$ is a compact open subgroup maximal under inclusion.

A subgroup $K$ is hyperspecial if $G$ extends to a reductive group scheme $\mathcal G/\mathcal O_k$ and $K=\mathcal G(\mathcal O_k)$.