A sub broker carries out the same function a broker carries out, being the middleman between two parties. However, while a stock broker is the middle man between an investor and the stock exchange, a sub broker is the middle man for the stock broker and the investor.
A brokerage house (firm) is simply a place where investors and traders go for buying and selling stocks. The broker house acts as a middleman between buyers and sellers, and provides a trading platform for everyone. It charges commission on these transactions. Every time an investor buys a stock, a transaction fee is charged.