Degree of sub sheaf of locally free sheaf is bounded

Question

Let $X$ be smooth projective curve over a field $k$.

Let $\mathcal F$ be a finite rank locally free sheaf on $X$. Now, consider the set $ D = \{\operatorname {deg}(\mathcal G) : \mathcal G$ is a subsheaf of $\mathcal F \}$. Why is set $D$ bounded, i.e. $\operatorname {sup} D$ is less than $n$, $n \in \mathbb{Z}$?