Let H < G be countable discrete groups. In this talk, we discuss the following question: If H is a maximal subgroup among all subgroups with Haagerup property, is LH still a maximal von Neumann subalgebra among all von Neumann subalgebras with Haagerup property in LG? We present several concrete examples. As a by-product, we answer Ge’s questions on maximal von Neumann subalgebras. This is based on joint work with Adam Skalski.