  Veech groups are an important tool to examine translation surfaces and
related mathematical objects. Origamis, also known as square-tiled surfaces,
form an interesting class of translation surfaces with finite index subgroups
of SL(2,Z) as Veech groups. We study when Veech groups of origamis with maximal
symmetry group are totally non-congruence groups, i.e., when they surject onto
SL(2, Z/nZ) for each natural number n. For this, we use a result of
Schlage-Puchta and Weitze-Schmith\"usen to deduce sufficient conditions on the
deck transformation group of the origami. More precisely, we show that origamis
with certain quotients of triangle groups as deck transformation groups satisfy
this condition. All Hurwitz groups are such quotients.
