  The production of top-quark pairs that subsequently decay hadronically and
leptonically (lepton+jets channel) is one of the key processes for the study of
top-quark properties at the LHC. In this article, NLO QCD corrections of order
$\mathcal{O}{\left(\alpha_{\rm s}^3\alpha^{4}\right)}$ to the hadronic process
${\rm p}{\rm p}\to \mu^-\bar{\nu}_\mu{\rm b}\bar{{\rm b}} {\rm j} {\rm j}$ are
presented. The computation includes off-shell as well as non-resonant
contributions, and experimental event selections are used in order to provide
realistic predictions. The results are provided in the form of cross sections
and differential distributions. The QCD corrections are sizeable and different
from the ones of the fully leptonic channel. This is due to the different final
state where here four jets are present at leading order.
