FNS-groups With Nilpotent Class2and The Derived Subgroup Being Of Order4

A finite non-abelian p-group G is called FNS-group if K≤Z(G) or G’≤K for every normal subgroup K of G. The paper is the study about FNS-groups with nilpotent class2and the derived subgroup being of order4. Some properties about FNS-groups are given and FNS-groups with3-generator or4-generator are classified respectively.