The direct control of management is on: 

In the context of the education system, management refers to the administrative and organizational framework responsible for planning, implementing, and supervising educational policies and institutions. 

Key Points

•  Educational management in India operates under both state and central bodies depending on the type and level of the institution.
• Schools and colleges may be managed directly by state education departments or central organizations like Kendriya Vidyalaya Sangathan or Navodaya Vidyalaya Samiti.
• States have control over institutions within their jurisdiction, handling teacher recruitment, budgets, and curriculum implementation.
• At the same time, central bodies set broad policies, provide funding, and manage centrally-run institutions.
• Thus, both state and central bodies exert direct administrative control over different types of educational institutions.

Hence, the correct answer is both State and Central Bodies.