The original investors and founders own them.
Think about it this way - When you hear that an IPO priced at $10 opened at $50, is that 'good or 'bad'? Of course, it depends who you are. If you are the guy that got them at $10, you're happy. If you are the founder of the company, you are thinking the banker you paid to determine a market price for the IPO failed. Big. He blew it, basically as you just sold your company for 20% of the perceived value.
But, instead of selling all the shares, just sell, say, 5%. Now, the IPO opening price is just a way to understand the true value of your company while keeping 95% of the upside once the market settles down to a regular trading pattern. You can slowly sell these shares into the market or you can use them as cash to take over other companies by buying with these shares instead of actual cash.
Either way, the publicly traded shares should trade based on the total value of the company and the fraction they represent.