Is however a cunjuctive?

I do like milk; however, I prefer chocolate milk.

Nevertheless, still, yet, though, nonetheless, in spite of, despite that, conversely, on the other hand, but, after all, be that as it may, anyhow, for all that, howbeit, notwithstanding, per contra,...

Most words do not have antonyms. 'However' does not.

That depends on what you feel is insufficient about the word 'however'. Synonyms are nevertheless, nonetheless, but, still, yet, though, although, notwithstanding

A however statement is a statement that says for example, Cafeteria rules are stupid; however, they have been improving the way the cafeteria runs