A set M satisfying {a} proper subsets in M and {a, B, C, D} proper subsets in M has

A set M satisfying {a} proper subsets in M and {a, B, C, D} proper subsets in M has

"Proper subset" means "is a subset of * *". As stated in the title: {a} is a proper subset of a set, and this set is a proper subset of {a, B, C, D}. How many are there? The set elements must be 2 or 3, including AB, AC, ad, ABC, abd, ACD six