The Military Society of the War of 1812 was formed by officers of the War of 1812 to press for pensions and bounty land legislation.
"On January 3, 1826, pursuant to notice published in the newspapers of the City of New York of December 31, 1825, a number of commissioned officers and ex-officers, who resided or were stationed in the vicinity, and who had served with reputation in the Army of the United States in the War of 1812, met at the Broadway House, corner of Broadway and Grand Streets. ...as a reward for their services, sufferings, and losses during the Second War of Independence." [Source]
From an earlier time: The Military Society of the War of 1812: annals, regulations, and roster (1895):
After 1840, only annual meeting's were held, and on January 8, 1848, the Military Society of the War of 1812 consolidated with "The Veteran Corps of Artillery," in which many of its members were already enrolled, and was afterward generally known by the latter title.