Proof of Points on an elliptic curve over a finite field being generators of subgroups.

Question

My understanding is that an important result used in ECC is that any point $P$ $\in E(F_p)$ (where $E(F_p)$ is the group of points on an elliptic curve over the finite field $F_p$) is the generator of a subgroup of $E(F_p)$. Is there a simple way of showing this? Am I over looking something?