  We compute the two-loop mixed QCD-Electroweak corrections to $q \overline{q}
\to H g$ and its crossed channels $q g \to H q$, $\overline{q} g \to H
\overline{q}$, limiting ourselves to the contribution of light virtual quarks.
We compute the independent helicity amplitudes as well as the form factors for
this process, expressing them in terms of hyperlogarithms with algebraic
arguments. The Feynman integrals are computed by direct integration over
Feynman parameters and the results are expressed in terms of a basis of
rational prefactors.
