Hillary Clinton did not shatter that “highest and hardest glass ceiling,” as she said again Wednesday during her concession speech. But in the wake of this week's election, it's worth remembering the other high-ranking government jobs that women haven't attained: several Cabinet positions, and the senator or governor positions in more than 20 states.

Besides the vice presidency — which has had two major-party female candidates — there are four Cabinet or designated Cabinet-level positions that have yet to be occupied by a woman. They are defense secretary, treasury secretary, secretary of veterans affairs and White House chief of staff. (There are other top government positions, such as FBI Director, director of the National Security Agency and other top intelligence jobs that have always been male. The chief justice of the United States has never been a woman.)

Until Trump's stunning win this week, it appeared that some of that track record in the Cabinet might change. There was wide speculation that Michèle Flournoy, who took herself out of the running in 2014 to replace Chuck Hagel, was considered a likely candidate for secretary of defense in a Clinton administration. Federal Reserve Governor Lael Brainard was seen as a front-runner at the Treasury Department. Facebook Chief Operating Officer Sheryl Sandberg also received some speculation for the job. Clinton had talked about naming a Cabinet that “looks like America, and 50 percent of America is women,” all but promising to nominate a gender-balanced Cabinet.

We don't know yet what Trump's Cabinet will look like, but reports about his shortlist show an overwhelmingly male selection of contenders, and no women for those above four Cabinet jobs. Reports from Politico and BuzzFeed News show women being considered for attorney general, labor secretary and the Environmental Protection Agency. Four are reportedly under consideration for interior secretary.

But their numbers are dwarfed in the reports by contenders who are male — and mostly white. Naming a Cabinet with diversity, said Debbie Walsh, director of the Center for American Women and Politics at Rutgers University, “is an opportunity for [Trump] to show that he's willing to go outside of those same white men that he has been surrounding himself with.” She notes that's particularly important because “these are the first decisions we will get to see him make about how he is going to shape his administration.”

Meanwhile, 21 states have never sent a woman to the U.S. Senate. Female candidates in three of those states — Arizona, Utah and Pennsylvania — lost this year, and only one loss, of Democrat Katie McGinty's to Republican Patrick J. Toomey in Pennsylvania, was close.

Three new women will join the Senate in 2017, and notably, one is biracial, one is Thailand-born, and one is Latina: Kamala Harris, Tammy Duckworth and Catherine Cortez Masto, respectively. Yet with two female senators retiring, the total comes to 21, just one more than currently serves. Walsh said progress is slow. “Part of the challenge is the pace of change is reflected in the pace of change in the number of women running. We aren't seeing big breakthroughs” in how many women run.

Women fare slightly better in the House of Representatives. Only two states — Vermont and Mississippi — have never sent a woman there; Delaware will drop off that list with its election of Lisa Blunt Rochester, its first female and African American representative, this week.

Meanwhile, 23 states have not yet elected a woman to be governor, and those numbers did not change this year. Walsh says the same gender stereotypes that women face about leadership in top roles such as chief executive — or the presidency — have held back the number of women in state chief executive jobs, too.

Still, she thinks those sentiments could be changing. Since the 1930s, Gallup has asked people whether they would vote for a woman for president, a percentage that has gone from just 33 percent in 1937 to 92 percent last year. “One of the things that gives me hope out of this election, and I think this is meaningful . . . is that for the first time Americans had a real opportunity to vote on that issue. While [Clinton] did not win the electoral votes to win the presidency, she did win the popular vote,” Walsh said.

“A majority of women did pull the lever for a woman to be the chief executive of the country. For me that is a breakthrough, and hopefully it will also be meaningful for women chief executives in the states, too.”

Read also:

Like On Leadership? Follow us on Facebook and Twitter, and subscribe to our podcast on iTunes.