  The detailed study of the Higgs boson is one of the main tasks of
contemporary particle physics. Gluon fusion, the main production channel of
Higgs bosons at the LHC, has been successfully modelled in QCD up to
$\text{N}^3\text{LO}$. To fully exploit this unprecedented theoretical effort,
sub-leading contributions, such as electroweak corrections, must be
investigated. I will present the analytic calculations of the gluon- and
quark-induced Higgs plus jet amplitudes in mixed QCD-electroweak corrections
mediated by light quarks up to order $v \alpha^2 \alpha_S^{3/2}$.
