The goal of this work is find a description for fields of two power conductor. By the Kronecker-Weber theorem, these amounts to find the subfields of cyclotomic field $\mathbb{Q}(\xi_{2^r})$, where $\xi_{2^r}$ is a $2^r$-th primitive root of unit and $r$ a positive integer. In this case, the cyclotomic extension isn't cyclic, however its Galois group is generated by two elements and the subfield can be expressed by $\mathbb{Q}(\theta)$ for a $\theta\in\mathbb{Q}(\xi_{2^r})$ convenient.Universidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, BrasilUniversidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, Brasil