permitting someone to use your car without insurance and without a license, what is the maximum penalty?

Cars are insured, not drivers so when you say she didn't have insurance, you are wrong. It is YOU who must have the insurance (on your car). If she doesn't have a license, that is her problem HOWEVER, you mentioned a citation but you failed to tell us what the citation was for? If it was the result of an accident that "she" had in your car, you could (Note: could and not will) be held responsible for damages.

Bottom line. We need more information to give you a better answer

I take it you're in the UK and if so, ignore the first two answers, the American system is different.

If it was your ex who was driving, deny giving her permission. That way she will be charge with taking a conveyance without consent (TWOC or TADA depending where you live).

If it was somebody else you can still go down that route or stand the cost, which is the same as if you were driving. 6-8 points and up to £800 fine.

Question is, do you have insurance on your vehicle?

Your ex does not need insurance to drive your vehicle, YOU do.

But, to legally drive, then that person needs to have a license.

So, she gets charged for no license, and you will have to prove you had insurance on the vehicle, and if not, you will be charges with no insurance, and could get your license suspended.

She is the one that will get charged if she was driving with no licence or insurance as long as you have it insured for you and you have a licence, Good Luck