VC Dimension of a Countably Infinite Class

I know that there are many examples of classes where the VC Dimension is finite/infinite even though the size of the class is Uncountably Infinite.

However, I could not argue if the VC Dimension of a Countably Infinite class is always finite? (I feel that its size will be smaller than the size of a power set of an arbitrarily large set)

Any help on this is appreciated.