non-split extension of the simple group $L_3(4)$

Question

I would like to know the structure of the groups $L_3(4).C_2$ and $L_3(4).C_{11}$.

(By $C_n$ I mean the cyclic group of order $n$ and by $G=K.L$ I mean the non-spli extension of $K$ by $L$, were $K$ is a normal subgroup of $G$.)

Answer 1

It appears there are no nonsplit extensions of $L_3(4)$ by $C_{11}$ or $C_2$.

(This CW answer posted to remove this question from the unanswered queue. All credit to Jack Schmidt in the comments.)