Can the subsidiary system be looser than the group system?

You can't. Because the subsidiary's system should be unified with the group's system, which is fair to every employee, and strict management of the company's employees is also beneficial to the company's management, so the subsidiary's system cannot be looser than the group's system. The company should be legal and reasonable when setting up the system, conform to the labor contract law, and protect the personal interests and rights of employees.