# Fields such as all finite extensions are Galois

What can we say on a plot $$F$$ such as any extension over $$K / F$$ is Galois?

Clearly, $$F$$ is perfect. For example, is it $$F$$ need to be algebraically closed? If not, what properties does $$F$$ Do you have any examples?
The only thing I can say is that $$F$$ should contain all the roots of unity, since $$F ( sqrt[n]{a}) / F$$ is Galois for every $$a in F, n geq 1$$.