NP-Complete refers to the hardest known problems within the complexity class NP
NP-hard problems (Non-deterministic Polynomial-time hard problems) are those problems which are not easier than any problem in NP; in other words, an algorithm for an NP-hard problem can be used to solve any problem in NP by transforming the input in polynomial time
"If there exists a np-hard problem that is not in np to the best of my knowledge no such problem has been proved to fall in this category at this moment of time such problem is harder than np-complete problems"
from question "NP-Complete VS NP-Hard"
|Problem not harder||
"As i understand it an np-hard problem is not harder than an np-complete problem"
from question "What are the differences between NP, NP-Complete and NP-Hard?"