  We study the quantization of the M-theory G-flux on elliptically fibered
Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic
gauge groups. We seek and find its relation to the Freed-Witten quantization of
worldvolume fluxes on 7-branes in type IIB orientifold compactifications on
Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles
on which to calculate the periods of the second Chern class of the fourfolds,
we find that there is a half-integral shift in the quantization of G-flux
whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold.
This correspondence of quantizations holds for all unitary and symplectic gauge
groups, except for SU(3), which behaves mysteriously. We also perform our
analysis in the case where, in addition to the aforementioned gauge groups,
there is also a 'flavor' U(1)-gauge group.
