LOS ANGELES — They have shaken up 21st Century Fox’s profile in Washington, replacing their father’s Republican lobbying chief with a Democratic one. They have jettisoned film executives, overhauled foreign TV operations and dug into the evolution of cable channels like National Geographic.

Their father, Rupert Murdoch, handed them the reins of 21st Century Fox only a year ago. But since then, James and Lachlan Murdoch have been remaking the company at breakneck speed.

Yet there remains one corner of the company — a critically important one — where the generational shift has not been visible: Fox News.

The brothers have left it alone for two reasons. First, Fox News, which continues to dominate in the ratings, contributes roughly 20 percent of the conglomerate’s annual earnings, and any changes, even seemingly minor ones, could endanger that profit. Second, Roger Ailes, who has run Fox News for 20 years, has little interest in corporate oversight. He has sparred with Lachlan Murdoch in the past — and won.