Study: CEOs aren’t using social media to full potential and analytics firm Domo found that more than two-thirds of Fortune 500 chief executives have no social media presence at all.

Among Fortune 500 chief executives, only one, Mark Zuckerberg, is on all five major social networks. It probably helps that he invented one of them.

About 68 percent of the other CEOs have no social media presence at all, according to new research from and business analytics firm Domo. Of the 162 chief execs who do have social media presences, 110 are only on one social network.

This is the third year that Domo and have conducted their Social CEO Report, and the encouraging news for the social media-savvy is that CEO presence on most major social platforms—Twitter, Facebook, Google+, and Instagram—is increasing, if slowly. The only network from which CEOs seem to be retreating is also the one that’s also most popular among Fortune 500 chief execs, LinkedIn.

LinkedIn also appears to be where CEOs are most active. Only about 24 percent of the CEOs who are active there have 100 connections or fewer. Around 30 percent have more than 500 connections.

By contrast, the study found that although the CEOs who use Twitter have large followings—nearly 3.7 million combined—half of them have fewer than 100 tweets each.

In the study report’s conclusion, the researchers say CEOs who aren’t using social media are doing their organizations “a massive disservice.”

“Evidence suggests that CEOs who are on social media…are viewed as more innovative,” the report states. A recent Weber Shandwick survey of executives bears that out. In that survey, 78 percent of respondents said having a CEO on social media would improve an organization’s reputation.

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