The embedding $W^{1,\infty}(\Omega) \hookrightarrow L^{2}(\Omega)$ for a regular bounded open set $\Omega \subset \mathbb{R}^N$

Question

Is the embedding $W^{1,\infty}(\Omega) \hookrightarrow L^{2}(\Omega)$ compact? All I could find is the Rellich Kondrachov Theorem but it only gives that $W^{1,\infty}(\Omega) \hookrightarrow L^{\infty}(\Omega)$ is compact. My guess is we could use the fact that $L^{\infty}(\Omega) \hookrightarrow L^{2}(\Omega)$ is continuous and deduce the result?