In a recent paper, Horel–Krannich–Kupers proved that all endomorphisms of the little disk operad are automorphisms. This prompts the question whether this is true for other operads, in particular, the little disk operad with an action of a group. In this talk we are going to show some conditions of the group acting on the little disk operad in order for every endomorphism to be an automorphism and will apply this to the example of the framed little disk operad.