Structure of non abelian finite p-groups

Question

I am familiar with the concepts of direct products, semi-direct products, wreath products and central products of groups. After seeing the classification of finite $p$-groups upto order $p^4$,(Theory of Groups of Finite Order; W.Burnside), I have observed that most of these groups are in the form involving the products mentioned above. My question is the if we can write any non abelian finite p-group in some form of the products mentioned above ? And if not ? Kindly provide me with a suitable counterexample .