  The simulation of lattice gauge theories on quantum computers necessitates
digitizing gauge fields. One approach involves substituting the continuous
gauge group with a discrete subgroup, but the implications of this
approximation still need to be clarified. To gain insights, we investigate the
subduction of $ SU(2) $ and $ SU(3)$ to discrete crystal-like subgroups. Using
classical lattice calculations, we show that subduction offers valuable
information based on subduced direct sums, helping us identify additional terms
to incorporate into the lattice action that can mitigate the effects of
digitization. Furthermore, we compute the static potentials of all irreducible
representations of $ \Sigma(360 \times 3) $ at a fixed lattice spacing. Our
results reveal a percent-level agreement with the Casimir scaling of ( SU(3) )
for irreducible representations that subduce to a single $ \Sigma(360 \times 3)
$ irreducible representation. This provides a diagnostic measure of
approximation quality, as some irreducible representations closely match the
expected results while others exhibit significant deviations.
