Suppose we have a finite field $\mathbb{F}_{p^n} = \frac{\mathbb{F}_{p}[x]}{<f(x)>}$. I want a deterministic polynomial algorithm to compute all subfields of this field. I think we can do something using linear algebra.Can someone suggest a reference of this problem? I am unable to find it in standard texts.
Constructing subfields of a finite field
reference request;finite fields