Supersymmetry $\mathcal{N}$ constrained by spacetime dimensions $D$

Question

Given some spacetime dimensions $D$, are there only certain allowed supersymmetry charge nunbers $\mathcal{N}$?

What are the relations of $\mathcal{N}$ and $D$ for the following cases:

1. When the theory is conformal. 

2. When the theory does not have to be conformal.

3. When the theory is Lorentz invariant.

4. When the theory does not have to be Lorentz invariant.

Possible other situations are worthwhile to comment on relating $\mathcal{N}$ and $D$?