Let Sn,Tn,Pnand Pn\Tn be symmetric group,full transformation semigroup,partial transformation semigroup and the strictly par-tial trans formation semigroup on Xn={1,2,...,n} respectively.For 0 ≤ r≤n,put SP(n,r)={α∈Pnn \Tn:im(α)≤r},SP(n,r)are the two-sided ideals of Pn.For 0 ≤ r ≤ n-1,the maximal(regular)subsemigroups of the semigroup PS(n,r)=P(n,r)U Sn has been considered in this paper.In addition,this paper proved that the maximal subsemigroups and the maximal regular subsemigroups of are consistent.
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