I couldn't help but notice she looked a lot like one of my favorite John Singer-Sargent paintings, Madame X.
The painting was quite scandalous in its day—her strap was originally falling off of her shoulder (it was later repainted).
Though the title was supposed to give the subject anonymity, it was very obvious to viewers that this was a painting of Virginie Amélie Gautreau. To add more to the scandal, the painting was hung right near a painting of Dr. Samuel Pozzi, a gentleman with whom Madame Gautreau was an extramarital affair. I think the allusion made in Mad Men was an excellent one.