  Given a complete local Noetherian ring $(A,\m_A)$ with finite residue field
and a subfield $\pmb{k}$ of $A/\m_A$, we show that every closed subgroup $G$ of
$GL_n(A)$ such that $G\mod{\m_A}\supseteq SL_n(\pmb{k})$ contains a conjugate
of $SL_n(W(\pmb{k})_A)$ under some small restrictions on $\pmb{k}$. Here
$W(\pmb{k})_A$ is the closed subring of $A$ generated by the Teichm\"{u}ller
lifts of elements of the subfield $\pmb{k}$.
