By the year 1821, the territorial organization of the First Mexican Empire was the largest extension of Mexico as an independent country. It held the territories of California, Texas, and New Mexico.
Through the years the empire was diminished from the south but it was not until 1836 when the Texas region declared its independence that the northern regions began to fall apart. In 1845 the United States annexed the Texas territory.
Finally, in 1848 the Treaty of Guadalupe Hidalgo ended the Mexican-American war, forcing large territorial concessions by Mexico.
I hope this answer helps you. I attached an image to show the extension of the First Mexican Empire.
