The "Club of the Sons" was designed as a special designation for the sons of the elite, rich industrialists that ran the city. The Club provided the sons with exclusive access to the Eternal Gardens, special access to the stadium, special privileges at Yoshiwara's House of Sin, and other benefits befitting of the offspring of the very rich and powerful.
There are a few rules surrounding admittance into the "Club of the Sons". the first is the most obvious, you have to be a son to one of the elite, this will be someone with a resources skill of 7 or better. Any less than that and you are not considered the proper caliber to mingle with ruling class.
Because of their father's wealth the sons are able to twist the laws and often times outright break them, however this does come at a price. If a son is doing something so obviously contrary to what is expected of them, or they make fools of themselves (or the masters) in front of the unwashed masses, they will be reprimanded and possibly have their membership privileges revoked (or worse).