  We present the evaluation of the complete set of NLO corrections to three-jet
production at the LHC. To this end we consider all contributions of
$\mathcal{O}(\alpha_s^n\alpha^m)$ with $n+m=3$ and $n+m=4$. This includes in
particular also subleading Born contributions of electroweak origin, as well as
electroweak virtual and QED real-radiative corrections. As an application we
present results for the three- over two-jet ratio $R_{32}$. While the impact of
non-QCD corrections on the total cross section is rather small, they can exceed
$-10\%$ for high jet transverse momenta. The $R_{32}$ observable turns out to
be very stable against electroweak corrections, receiving absolute corrections
below $5\%$ even in the high-$p_T$ region.
