Classification of compact connected Lie subgroup of $U(2)$

Question

I am trying to find a way to classify all compact connected Lie group of unitary group $U(n)$. For simplicity, I would like to deal with $U(2)$. We have learned about using Dynkin diagram to classify compact simple Lie group. So, maybe I can do the same on $U(2)$. However, I don't know how to determine the simple root system of $U(2)$ explicitly, which is the cornerstone of Dynkin diagram. How someone could help. Thanks!