Administration :

1. management of business: the management of the affairs of a business or organization

2. management staff: the staff of a business or institution whose task is to manage its affairs

3. management of government: the management of public affairs or the affairs of a government

4. staff of government: a government’s staff whose task is to manage its affairs

5. term of office: the duration of a particular office, usually a political one

6. government: a government, especially its executive branch

7. U.S. government agency: a United States government agency or board

8. legal disposal of estate: the disposal or management of a deceased person’s estate or an estate held in trust

9. administering something to somebody: the act of administering something such as an oath, medicine, or sacrament

Management:

1. administration of business: the organizing and controlling of the affairs of a business or a particular sector of a business

2. managers as a group: managers and employers considered collectively, especially the directors and executives of a business or organization

3. handling of something successfully: the act of handling or controlling something successfully

4. skill in handling or using something: the skillful handling or use of something such as resources

'Management' is what the 'Administration' does

Administration is in a way inferior to management in general business environment. Management is to administer management objective. The term manage is "the process of dealing with or controlling things or people -- Oxford-Amereican Dictionary".
Administration is a part of management process, not other way round.
To adminster means to apply.
I said administration is inferior to management in general, but there is an exception. Administration is used in very high ranking social setting, and it is in Capital letter -- such as Bush Administraion.