How many satellites orbit their planet faster than the planet rotates?

Jupiter has a sidereal rotation period or day of 9.925 hours.

https://en.wikipedia.org/wiki/Jupiter

The two innermost moons of Jupiter, Metis and Adrastea, have orbital periods of 7 hours 10 minutes 16 seconds and 7 hours 15 minutes 21 seconds respectively.

https://en.wikipedia.org/wiki/Moons_of_Jupiter#List

Saturn has a sidereal rotation period or day of 10 hours 33 minutes 38 seconds, or 0.4400231 Earth days.

https://en.wikipedia.org/wiki/Saturn

The innermost confirmed moon, S/2009 S1, has an orbital period of 0.47 Earth days, which is longer than Saturn's day.

https://en.wikipedia.org/wiki/Moons_of_Saturn#List

So I have checked the moons of two of the giant planets, leaving two giant planets, Uranus and Neptune, to be checked.

I note that a number of objects in the solar system which are not classified as planets, but as dwarf planets, Trans Neptunian Objects, asteroids, etc., have been discovered to have moons. If you are interested whether any of them orbit in less than a day of their primary, you should know that:

Of the objects within our Solar System known to have natural satellites, there are 76 in the asteroid belt (five with two each), four Jupiter trojans, 39 near-Earth objects (two with two satellites each), and 14 Mars-crossers.2 There are also 84 known natural satellites of trans-Neptunian objects.2 Some 150 additional small bodies have been observed within the rings of Saturn, but only a few were tracked long enough to establish orbits.

https://en.wikipedia.org/wiki/Natural_satellite#Natural_satellites_of_the_Solar_System

So there would be a lot of checking to do to find which of them might orbit faster than one day of their primary.

Uranus rotates once every 0.718 days. 11 of its satellites have a shorter orbital period. These are inner satellites of Uranus which are roughly in the equatorial plane of Uranus. I don't quite understand what direction they orbit in compared to the direction in which Uranus spins.

Neptune rotates once every 0.671 days. 5 of its satellites have a shorter orbital period and orbit prograde.

Jupiter rotates once every 10 hours. 2 of its satellites have a shorter orbital period and orbit prograde.

Saturn rotates once every 0.4 days and none of its satellites orbit faster than that.

So Phobos is not alone in its case. Around Mars, Jupiter and Neptune (and maybe Uranus), there are moons that orbit so fast that they rise in the west and set in the east.