Did you rmb to balance your equation? It should be:
2HCl + MgO --> MgCl2 + H2O
So n(MgO) = 1/2 * n(HCl) used
= 1/2 * 0.19606mol
= 0.09803mol (instead of 0.19606mol which is what you got)
From there,
since n(MgO) in the 100mL aliquot = 0.09803mol,
then n(MgO) in the original 1L solution...