America’s largest and most powerful private companies might be the most exclusive boys’ club of all, according to Fortune.

Just 6.2 percent of board seats are held by women within U.S.-based “unicorn” companies, that rare breed of private firm whose value is more than $1 billion, based on fundraising. America’s 55 unicorn companies collectively represent 354 board director seats, the Fortune analysis shows, and only 22 are held by women.

A full 60 percent – or 33 – of the U.S. unicorn companies have all-male boards, as compared with nearly 5 percent of Fortune 500 companies.

The startups with all-male boards include some of the most celebrated brands, such as Uber, Snapchat, Tinder and Airbnb. These are the wildly influential innovators that the rest of the startup world strives to emulate.

None of the 55 companies have more than one woman on their board. Some research suggests that boards need at least three women in order to achieve the effective critical mass that leads to improved performance and governance.

Fortune reached out to all 33 U.S.-based unicorns that have all-male boards. Only seven – JustFab, Lookout, Pluralsight, Razer, Slack, Snapchat, and Legendary Entertainment – offered comments. Most stressed their commitment to diversity, but noted that early-stage startup boards tend to be composed of founders and investors, who were men.