  We present the fully integrated form of the two-loop four-gluon amplitude in
$\mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group
SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in
the fundamental representation. Our result maintains full dependence on $N_c$
and $N_f$, and relies on the existence of a compact integrand representation
that exhibits the duality between color and kinematics. Specializing to the
$\mathcal{N} = 2$ superconformal theory, where $N_f = 2N_c$ , we obtain
remarkably simple amplitudes that have an analytic structure close to that of
$\mathcal{N} = 4$ super-Yang-Mills theory, except that now certain lower-weight
terms appear. We comment on the corresponding results for other gauge groups.
