"Hierarchical" vs. "hierarchic"

When do you use hierarchical and when hierarchic?

For example, hierarchical database sounds much more native to me, even as a non-native English speaker. But why isn't it hierarchic database?

Edit: I just realized there are more words this question applies to: acyclical/acyclic, aesthetical/aesthetic, cosmetical/cosmetic,...

Every single dictionary link I found redirects hierarchic to hierarchical. It seems as though there is absolutely no distinction between the meanings of two words and hierarchical is vastly preferred. NGram data fully supports this preference.

Therefore, always use hierarchical.

As for why it is hierarchical and not hierarchic, please see the previously linked question and answer: Why is it “geometric” but “theoretical”?