  As searches for thermal and self-annihilating dark matter (DM) intensify, it
becomes crucial to include as many relevant physical processes and ingredients
as possible to refine signal predictions, in particular those which directly
relate to the intimate properties of DM. We investigate the combined impact of
DM subhalos and of the (velocity-dependent) Sommerfeld enhancement of the
annihilation cross section. Both features are expected to play an important
role in searches for thermal DM particle candidates with masses around or
beyond TeV, or in scenarios with a light dark sector. We provide a detailed
analytical description of the phenomena at play, and show how they scale with
the subhalo masses and the main Sommerfeld parameters. We derive approximate
analytical expressions that can be used to estimate the overall boost factors
resulting from these combined effects, from which the intricate phenomenology
can be better understood. DM subhalos lead to an increase of the Sommerfeld
effect by several orders of magnitude (for both $s$- and $p$-wave annihilation
processes), especially on resonances, which makes them critical to get sensible
gamma-ray signal predictions for typical targets of different masses (from
dwarf galaxies to galaxy clusters).
