How did the imperial power, gentry power and clan power coordinate in ancient rural governance in China?

Imperial power, clan power and gentry power are actually a logic in which A is greater than B and C is greater than C. In ancient China, imperial power was supreme, but the emperor could not bow to local governance, so the governance of grass-roots organizations was mainly through local bureaucracy. The most basic local organization is the village-level organization. Rural governance is mainly through clan rights. The patriarch has the power to kill and plunder the people, and the patriarch is in the hands of the local rural sages and some respected or influential gentry. So in ancient China, clan power was the embodiment of imperial power. For example, the purpose of "Lushi Township Covenant" is the same as imperial power. If you are interested, you can read more books about rural conventions. These books are basically about the mode and operation of rural governance. Since the Song Dynasty, the role of rural sages has been more prominent, but since the Ming Dynasty, the imperial power has strengthened the control and intervention of rural customs. Talking about rural conventions is bound within the scope of imperial power.