M5-branes in AdS${}_4\times Q^{1,1,1}$ spacetime

In this paper, we study the M5-brane configurations in AdS$_4 \times Q^{1,1,1}$spacetime\mathrm{.}WeconsidertheconfigurationswithanAdS$_2$ factor embedding into AdS${}_4$, and manage to construct two solutions, which could be dual to line defects in the boundary gauge theory. Moreover we discuss their BPS nature and find that neither of them is supersymmetric. We show that the M5-brane with a R${}_t$ or an AdS${}_3$ factor found before is half-BPS.