  Motivated by the maximal subgroup problem of the finite classical groups we
begin the classification of imprimitive irreducible modules of finite
quasisimple groups. We obtain our strongest results for modules over fields of
characteristic 0, although much of our analysis carries over into positive
characteristic.
  If G is a finite quasisimple group of Lie type, and K an algebraically closed
field of cross characteristic, we prove that an imprimitive irreducible
KG-module is Harish-Chandra induced.
  We then specialize to the case when K has characteristic 0 and apply
Harish-Chandra philosophy to classify irreducible Harish-Chandra induced
modules in terms of Harish-Chandra series, as well as in terms of Lusztig
series. One of the surprising outcome of our investigations is the fact that,
asymptotically, most of the irreducible KG-modules are imprimitive in this
situation.
  For exceptional groups of Lie type of rank at most 2, and for sporadic
groups, we list all ordinary irreducible imprimitive characters.
