James Murdoch has been re-elected BSkyB chairman, but a fifth of shareholders voted against his reappointment.
A number of key shareholders voted against him at the company's annual general meeting on Tuesday, as they would like a fully independent chairman rather than an executive of News Corp.
News Corp owns 39% of BSkyB as well as being the parent of News International, which is also chaired by Mr Murdoch.
News International owns the News of the World, which closed over phone hacking.
As well as that, he holds the post of deputy chief operating officer at News Corp.
Provisional figures announced at the meeting gave Mr Murdoch 81.24% of the vote, with 18.76% against.
When votes withheld were taken into account, he received the support of 75.4% of shareholders, versus 17.4% opposed and 7.2% withheld.
Excluding votes cast by News Corporation, he received the support of 55% of independent shareholders.
In July, News Corp had to withdraw a $US12 billion offer for the 61% of BSkyB it does not own as a result of the hacking scandal surrounding the News of the World .
Mr Murdoch was not running the newspaper division when the hacking took place.
The BBC reports there is disagreement about how much he knew about what had happened. He has twice been questioned by a panel of MPs.
One of the shareholders who voted against Mr Murdoch's re-election was Standard Life Investments, which manages six million shares in BSkyB, which wants a new and independent chairman appointed.
Mr Murdoch, 38, is the son of Rupert Murdoch.