system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why don't moons have moons?
gpt
So many incorrect answers here. 

A sub moon has never been observed in our solar system or anywhere else. While there's nothing preventing one from existing for a short time, the system is not likely to be stable other than for some theoretical models. Saturn's moon Iapetus may be able to support a moon of its own but that's mathematical theory and Iapetus doesn't actually have a moon. 

Orbital mechanics are more complicated than x orbits y orbits z. Every object affects every other object all the time. With a moon of a moon, the interactions between the sun, the planet, the moon, and the second order moon become too unstable and the system will collapse, resulting in the second order moon colliding into the planet, escaping, or getting into its own orbit. 

You would be right to say that people have things orbiting the moon, those count don't they? Turns out the same problem applies here but the time scales make it irrelevant. Man made satellites orbiting our own moon have unstable orbits and have to keep themselves stable with their thrusters. Without corrections, the orbits of those satellites will decay over hundreds to thousands of years. Sounds like a long time but it's nothing compared to the billions of years that the solar system has existed. Any second order moon system that existed in our solar system has certainly decayed by now. 

TL;DR: Moons of moons don't exist. Orbital mechanics is complicated and causes and sub moons to not last very long.