Count the special subsets

Let us consider a set $X = \{1,2,3,4\}$ . we know that number of subsets of $X$ is 16. So the question is how many of these subsets have a complement of size greater than or equal to original subset size?

For example, $\{1\}$ is a subset of size 1 whose complement is $\{2,3,4\}$ has size 3. So out of 16 subsets how many satisfy the condition mentioned above