Imaginary Multiquadratic Fields of Class Number Dividing $2^m$

This paper gives a method to find all imaginary multiquadratic fields of class number dividing $2^m,$ provided the list of all imaginary quadratic fields of class number dividing $2^{m+1}$ is known. We give a bound on the degree of such fields. As an application of this algorithm, we compute a complete list of imaginary multiquadratic fields with class number dividing $32.$