  In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1,
1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane
solutions are found. The first class of solutions includes $M2$-branes dual to
Wilson loops in the fundamental representation as special cases. The second
class includes the candidates of the holographic description of vortex loops in
the dual field theories.
