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.
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