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Abstract
Frattini subgroup, , of a group G is the intersection of all the maximal subgroups of G, or else G itself if G has no maximal subgroups. If G is a group, then is the smallest normal subgroup such the quotient group is an elementary abelian group. It is against this background that the concept of subgroup and fitting subgroup play a significant role in determining Frattini subgroup (especially its order) of dihedral groups. A lot of scholars have written on Frattini subgroup, but no substantial relationship has so far been identified between the parent group G and its Frattini subgroup which this tries to establish using the approach of Jelten B. Napthali who determined some internal properties of non abelian groups where the centre Z(G) takes its maximum size.
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