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Shareholding networks structured in a complex manner create complex control associations. The actual controllers, paths through which control is created between companies, and control scopes of specified companies are all hidden in shareholding networks. The discovery and analysis of these crucial control associations is essential for corporate governance. However, relative to ultimate shareholders’ control power, existing control studies based on the voting game ignore the critical role of intermediate companies in integrating outer shareholders’ votes and transferring control to the inner shareholders. Therefore, a foundation for discovering control associations within networks is lacking. We measure control by considering ultimate shareholders and intermediate companies based on the voting game approach and thus propose the Control Transfer Index (Cti) to measure the strength of the control relationship between any two companies and corresponding Control Transfer Index Calculation (CTIC) algorithm to calculate Cti precisely. Based on it, we propose the concept and algorithm of Crucial Control Path (CCP) to discover more essential control paths between companies. We also propose the concept and algorithm of the Company Control Community (CCC) to identify overlapping company communities that meet the control degree threshold. This study illustrates the effectiveness of these algorithms in identifying actual controllers, discovering control formation paths, and analyzing control scopes by analyzing the aforementioned crucial control associations in the context of control and risk cases.