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 $.