[Need Help] How can I create clusters of common features in a set of objects?

I have a dataset of about 15 features related to object. Here's a purely illustrative example of what the data looks like.

Blue Eyes   | Black Hair | Tall  |......  | Number of objects with feature set
Yes         |  Yes        | No   |......  | 150
Yes         |  Yes        | Yes  |......  | 70
Yes         |  No         | No    |......  | 200

I'd like to analyze these to get, maybe clusters of features that tend to occur together.

I tried some clustering algorithms on the dataset and got cluster tags for each object, but the method doesn't really tell me what the common set of features in each group are.

Any suggestions will be much appreciated! Thanks.