Soldiers after a battle

A general counts the number of surviving soldiers of a battle by aligning them successively in rows of certain sizes. Each time, he counts the number of remaining soldiers who failed to fill a row. The general initially had 1200 soldiers before the battle; after the battle

• aligning them in rows of 5 soldiers leaves 3 remaining soldiers;
• aligning them in rows of 6 soldiers leaves 3 remaining soldiers;
• aligning them in rows of 7 soldiers leaves 1 remaining soldier;
• aligning them in rows of 11 soldiers leaves 0 remaining soldiers.

How many soldiers survived the battle?