Egg is a mixture of proteins and fats.
I suggest you try a laundry detergent containing enzymes. Avoid detergents with added bleach. Mix the detergent with very warm water and scrub the surface. If this doesn't work, make a poultice by mixing the detergent solution with a filler such as talc, powdered silica or bentonite until you have a thick paste that can be applied with a trowel onto the stained area. Cover with plastic and let it stand for at least an hour.