In this paper, we study the attractor mechanism for extremal, spherically symmetric black holes in pure N = 4 Poincaré supergravity, which we demonstrate numerically. We further study the supersymmetries preserved by these solutions by focussing specifically on the constant moduli solutions and show that, for a generic dyonic charge configuration satisfying p²q²>(p.q)², they always preserve 1/4th of the total supersymmetries.