Efficient algorithm for finding all maximal subsets

I have a collection of unique sets (represented as bit masks) and would like to eliminate all elements that are proper subsets of another element. For example:

input = [{1, 2, 3}, {1, 2}, {2, 3}, {2, 4}, {}]
output = [{1, 2, 3}, {2, 4}]

I have not been able to find a standard algorithm for this, or even a name for this problem, so I am calling it "maximal subsets" for lack of anything else. Here is an O(n^2) algorithm (in Python for concreteness), assuming is_subset_func is O(1):¹

def eliminate_subsets(a, cardinality_func, is_subset_func):
    out = []
    for element in sorted(a, reverse=True, key=cardinality_func):
        for existing in out:
            if is_subset_func(element, existing):
                break
        else:
            out.append(element)
    return out

Is there a more efficient algorithm, hopefully O(n log n) or better?

¹ For bit masks of constant size, as is true in my case, is_subset_func is just element & existing == element, which runs in constant time.