Yes, large planets can have small moons. The size and composition of moons can vary greatly depending on the planet and its specific characteristics. While some large planets have large moons, like Earth's moon, others have smaller moons or even a system of moons of various sizes.
The size of a moon is typically determined by factors such as the planet's mass, gravitational influence, and the conditions during its formation. Moons can form through various processes, including capture of passing objects, accretion of material in the planet's vicinity, or as remnants of a larger body that broke apart.
For example, Jupiter, the largest planet in our solar system, has more than 70 moons, with four of them being relatively large and known as the Galilean moons (Io, Europa, Ganymede, and Callisto). These moons are comparable in size to some of the smaller planets in our solar system, such as Mercury and Pluto.
Saturn, another gas giant, also has a diverse system of moons. Its largest moon, Titan, is even larger than the planet Mercury. Additionally, there are smaller moons like Enceladus and Mimas, which have distinctive features and are much smaller in comparison.
Therefore, while large planets can indeed have small moons, they can also have moons of varying sizes, ranging from tiny irregularly shaped bodies to substantial spherical moons.