Perhaps it is better to phrase the question in terms of Lie algebras. For instance, if you want to know which are the possible codimension one Lie subalgebras of a given finite dimensional Lie algebra then there is a result of Tits which address exactly this.

Let $\mathfrak g$ be a finite
dimensional Lie algebra over a field of characteristic zero. If
$\mathfrak h$ is a codimension one
subalgebra then there exists a
morphism $\phi : \mathfrak g \to
> \mathfrak{sl}(2)$ with kernel
contained in $\mathfrak h$.

This result has been explored by Hoffman to provide a classification of codimension one
subalgebras of Lie algebras in this paper.