Is there any name for the set of 'sets which contains only numbers'? I know that groups, rings and fields are the sets which contains only numbers but they bears additional properties too or to say that these are just the subsets of the set I'm talking about.
The required set is the set of subsets of the set of real/complex numbers.
PS
The numbers can either be real or complex.

EDIT:
Suppose that I pick an arbitrary set from this set then do we have a special name for it to differentiate it from other type of sets which may contain other mathematical objects too?
 A: The set of subsets of a set $X$ is called the power set of $X$ and is denoted $\mathcal{P}(X)$. The set you are thinking of is $\mathcal{P}(\mathbb{C})$, i.e. the set of all subsets of the set of complex numbers.
EDIT: Note Friedrich's comment which points out that $\mathcal{P}(\mathbb{C})$ contains $\emptyset$, the empty set, which is the set containing no elements. This is trivially a subset of any set, so it is an element of any $\mathcal{P}(X).$
A: Here are some arbitrary sets:
$$
A = \left\{ 1,2,3,4 \right\},\ B = \left\{ a,b,c,d \right\},\ C = \left\{ -10, 3.1415, 10^{98}\right\},\ D = \left\{ 2, x, 4, y \right\} \;.
$$
Obviously, $A$ and $C$ contain only numbers, $B$ contains only letters, and $C$ contains numbers and letters. Therefore, there are only the following three sets of those sets that contain only numbers:
$$
\left\{ A \right\}, \quad \left\{ C \right\}, \quad \left\{ A, C \right\} \;.
$$
You can refer to them as sets of numeric sets; but is there a special name for them? No, unless you given them one.
