  Let $A$ be a central division algebra of prime degree $p$ over $\mathbb{Q}$.
We obtain subconvex hybrid bounds, uniform in both the eigenvalue and the
discriminant, for the sup-norm of Hecke-Maass forms on the compact quotients of
$\operatorname{SL}_p(\mathbb{R})/\operatorname{SO}(p)$ by unit groups of orders
in $A$. The exponents in the bounds are explicit and polynomial in $p$. We also
prove subconvex hybrid bounds in the case of certain Eichler-type orders in
division algebras of arbitrary odd degree.
