Carlyle Group, the largest investor in Wesco Aircraft Holdings Inc., is selling off a portion of its holding through a public offering of 15 million shares of common stock. Affiliates of the Washington, D.C. private equity firm also could sell an additional 2.25 million shares in the Valencia aerospace parts supplier should the offering sell out. If all 17.25 million shares are sold, Carlyle will retain a 38.6 percent stake in Wesco. Carlyle bought a majority stake in the company in 2006 when it was privately held, and took it public in July 2011, raising $315 million in the initial public offering. The proceeds of the sale went to Wesco CEO Randy J. Snyder and Carlyle. Wesco also would not receive any proceeds from the secondary sale. Shares gained 7 cents, or a fraction of a percent, to close at $16.64 on the New York Stock Exchange.