The Mughal administration, a sophisticated and enduring system, was a remarkable synthesis of indigenous Indian practices and foreign, primarily Persian and Central Asian, elements. This amalgamation allowed the Mughals to govern a vast and diverse empire effectively.

Extra-Indian (Persian/Central Asian/Islamic) Elements:

1. Centralized Monarchy and Divine Kingship: The concept of a powerful, absolute monarch, often seen as divinely ordained (e.g., Akbar's 'Zill-i-Ilahi' or Shadow of God), was largely derived from Persian traditions. This contrasted with the more decentralized, regional power structures often seen in pre-Mughal India.
2. Mansabdari System: This unique military and civil administrative system, where every officer (Mansabdar) held a rank (mansab) denoting his status, salary, and military obligation, had Central Asian origins. It integrated military and civil functions, ensuring loyalty and efficiency.
3. Judicial System: The Qazi system, based on Islamic law (Sharia), formed the backbone of the judicial administration, particularly in criminal justice. The Emperor was the supreme judicial authority.
4. Language and Culture: Persian was the official language of administration and court, reflecting its influence on Mughal culture, literature, and architecture.
5. Architectural Styles: Mughal architecture, while incorporating Indian motifs, heavily drew from Persian and Central Asian styles, evident in features like domes, arches, and intricate tile work.

Indian Elements:

1. Land Revenue Administration: While the Mughals refined and standardized land revenue collection, many underlying principles and practices were adapted from existing Indian systems. For instance, Todar Mal's 'Zabti' system, based on measurement and classification of land, built upon earlier Indian methods. Concepts like 'Batai' (crop sharing) and 'Kankut' (estimation) were also prevalent.
2. Local Administration: The Mughals largely retained the existing village and local administrative structures, including the role of village headmen (Muqaddam) and accountants (Patwari). Zamindars, who were often hereditary local chieftains or landlords, were integrated into the administrative framework, acting as intermediaries for revenue collection and maintaining law and order at the local level.
3. Caste System and Social Norms: Although the Mughals were Islamic rulers, they largely respected the prevailing Hindu caste system and local social customs, avoiding direct interference in personal laws of non-Muslims.
4. Rajput Policy: Akbar's policy of forming alliances with Rajput rulers, incorporating them into the Mansabdari system, and allowing them autonomy in their territories, was a pragmatic adaptation to the Indian political landscape.

Synthesis:

The genius of Mughal administration lay in its ability to synthesize these diverse elements. The Mansabdari system, for example, incorporated both foreign military organization and Indian chieftains. The land revenue system combined Persian principles of assessment with local Indian practices of collection. This blend created a robust and flexible administrative machinery that could govern a vast and diverse subcontinent, leaving a lasting legacy on subsequent Indian administrative systems.