# if $G$ is a divisible group then any subgroup of $G$ is also divisible

Is it true that if $$G$$ is a divisible group then any subgroup of G is also divisible?

I know that if $$H \leq G$$ then for any $$h \in H$$ and for any $$k \in \mathbb{N}$$ then there exists $$x \in G$$ such that $$x^{k}=h$$, therefore I can show that $$x^{k} \in H$$. But, is it always true that $$x \in H$$ or there exists a counterexample?

The group $$\mathbb{Q}$$ of rational numbers under addition is divisible. The group $$\mathbb{Z}$$ of integers is a subgroup, but is not divisible.