elementary set theory - How "many" sub-sequences in a given sequence (cardinality of the set of countably infinite subsets of a countably infinite set)

I don't know how "many" (cardinality) sub-sequences are there in a sequence.

Or equivalently,

What is the cardinality of the set of countably infinite subsets of a countably infinite set?

I guess it should not be $\aleph_0$, maybe $2^{\aleph_0}$ ($\aleph_0$ is the cardinality of natural numbers).

Thank you.