How did the church make up for the lack of a central government in the feudal period?

The church had a very strictly defined hierarchy that was understood and complied by every religious official (and common religious person as well). With this hierarchy, where the pope represented the ultimate authority of the church, everybody knew his place in the hierarchical pyramid. A command, order, or news given out by the pope was delegated to lower church officials down to the lowest branches where it could be heard by peasants attending church gatherings.