Which term is applied to people that have power in modern societies according to max weber?

It is "bureaucracy".

Bureaucracy alludes to both a non-elective government authorities and an authoritative strategy making gathering. The German social scientist Max Weber contended that bureaucracy comprises the most productive and judicious manner by which one can organize the human action and that precise procedures and sorted out hierarchies are important to look after order, boost effectiveness, and kill partiality.