  In this paper, the concept of a maximal L-subgroup of an L-group has been
defined in the spirit of classical group theory. Then, a level subset
characterization has been established for the same. Then, this notion of
maximal L-subgroups has been used to define Frattini L-subgroups. Further, the
concept of non-generators of an L-group has been developed and its relation
with the Frattini L-subgroup of an L-group has been established like their
classical counterparts. Moreover, several properties pertaining to the concepts
of maximal L-subgroups and Frattini L-subgroup have also been investigated.
These two notions have been illustrated through several examples.
