Let $X$ be a finite connected pointed CW-complex and $H_{\ast}(\Omega X)$ the integral homology of the loop space on $X$. Are the homology groups $H_{n}(\Omega X)$ finitely generated abelian groups for any $n$ ?

If the answer is negative, what are the sufficient conditions to impose on $\pi_{1}(X)$ such that the homology groups $H_{n}(\Omega X)$ turns out to be finitely generated ?

My goal is to collect different sufficient conditions on the fundamental group for which a positive answer holds.