The Muslim Brotherhood wanted complete Islamic rule of Egypt.
The Muslim Brotherhood was founded in 1928 (a decade after the end of World War I). Hassan al-Banna, an Egyptian schoolteacher, founded the movement with the goal of implementing traditional Islamic Sharia law for all aspects of life in Egypt.
Still today that remains a goal of the Muslim Brotherhood in Egypt. As one of their leaders, Khairat al-Shater, stated in a speech in 2011, the Muslim Brotherhood is "a means to Islamize life in its entirety and institute religion."