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If $\mathbb F_I$ denotes the free group on $I$ generators with $\lvert I \rvert > 1$, then $L^\infty(0, 1) \overline \otimes L \mathbb F_I$ is not isomorphic to a von Neumann subalgebra of $L \mathbb F_I$. For $\lvert I \rvert > \aleph_0$ this is Corollary 6.4 in [S. Popa: Orthogonal pairs of subalgebras in finite von Neumann algebras, J. Op. Th. 9(1983), 253-268]. The general case $\lvert I \rvert > 1$ is Theorem 1 in [N. Ozawa: Solid von Neumann algebras, Acta Math. 192 (2004), 111-117].