  We study "how far away" a finite index subgroup G of SL(2,Z) is from being a
congruence group. For this we define its deficiency of being a congruence
group. We show that the index of the image of G in SL(2,Z/nZ) is biggest, if n
is the general Wohlfahrt level. We furthermore show that the Veech groups of
origamis (or square-tiled surfaces) in the stratum H(2) are far away from being
congruence groups and that in each genus one finds an infinite family of
origamis such that they are "as far as possible" from being a congruence group.
