Another sufficient condition is that if $G$ is solvable, then for every prime $l$, every absolutely irreducible characteristic $l$ representation can be lifted to the complex numbers. In fact, solvability is not really necessary; $l$-solvability suffices.This is the Fong-Swan theorem.

Another sufficient condition is that if $G$ is solvable, then for every prime $l$, every absolutely irreducible characteristic $l$ representation can be lifted to the complex numbers. In fact, solvability is not really necessary; $l$-solvability suffices.  This is the Fong-Swan theorem.

Added later: Since groups with order not divisible by $l$ are trivially $l$-solvable, this sufficient condition includes, and is more general than the the condition stated by Pete L. Clark.