A <div> element is just a block level container, with no semantic meaning of its own. You can have a button inside one, you can have a button outside one. It really depends on why you think you are using the <div> in the first place. At the moment, without understanding why you think you are using it, it’s difficult to suggest how it might be used better.
In general <div> tags are used as containing blocks for specific parts of a web page. They could be used as a main content section, a header, a sidebar, parts of a menu, a footer, a modal container, and probably a million other uses. With HTML5 though, there are usually more semantic tags (section, article, aside, header, footer, nav, figure, figcaption, time, mark & main) you could use, that have more meaning for accessibility and WAI-ARIA purposes. <div> though means whatever you decide it means, and that is largely based on what you decide to put inside it.
I’ve not tested it specifically, but that sounds about right. You’d be putting an inline element inside a block element. Again though, it depends on what you are trying to achieve.