What impact did Socrates have on Greek society?

Very little at the time. He was killed off to stop him. He was made fun of by his contemporary Aristophanes who included him in his comedies. His influence came later - as he had written nothing, it was up to Plato and Xenophon to write seriously about what he had said, so this is second hand, and may have been manipulated by them for their own purposes. However this did have an influence on philosophical thought and reasoning methods. But Greek society as a whole went on its own way, as it always had, oblivious of the philosophical wranglings of a few.