  We provide a framework to classify hyperbolic monopoles with continuous
symmetries and find a Structure Theorem, greatly simplifying the construction
of all those with spherically symmetry. In doing so, we reduce the problem of
finding spherically symmetric hyperbolic monopoles to a problem in
representation theory. Additionally, we determine constraints on the structure
groups of such monopoles. Using these results, we construct novel spherically
symmetric $\mathrm{Sp}(n)$ hyperbolic monopoles.
