Consider the Galois extension $K/\mathbb{Q}$ where $K=\mathbb{Q}(e^{2\pi i/11})$. I am asked to calculate the lattice of the intermediate groups of $G$.
I know that the minimal polynomial of $e^{2\pi i/11}$ over $\mathbb{Q}$ is $m(x)=x^{10}+x^9+ ... + 1$ and therefore $G$ has $10$ elements, and every element moves one root of $m(x)$ to another. The roots of $m(x)$ are the roots of unity $\xi,\xi^2,...\xi^{10}$ where $\xi^{11}=1$
How do I follow?