If by big we mean physical dimension, the largest known galaxy is most likely IC1101. IC1101 is gargantuan even among galaxies; it’s a super elliptical galaxy with a diffuse stellar halo that to extends to at least 1.4 million light years. The Milky Way’s halo by comparison extends to about 100.000 lights years.

In the picture we see an artistic rendition of IC1101 compared to actual photos scaled to size of M31 (Andromeda) and M87, a local super giant elliptical galaxy.