Queen Beatrix of the Netherlands showed Washington yesterday what it takes to be a thoroughly modern monarch. By nightfall, without having to wave her royal scepter once, she probably could have counted several thousand new subjects she never knew she had.

More than 425 of them, elegantly attired in designer gowns and expensive jewels, willingly answered her command last night at the National Gallery of Art. She and her husband, Prince Claus, entertained at a dinner after opening the exhibition "Mauritshuis: Dutch Painting of the Golden Age," from the Royal Picture Gallery in The Hague.

Minus her diamond and pearl tiara and dressed in navy blue taffeta, Beatrix made up for her otherwise subdued attire--for a queen, that is--by pinning a spectacular diamond and sapphire heirloom brooch to her bosom and wearing its matching earrings and bracelet, a gift from her mother, Queen Juliana, that had been handed down through the House of Orange.

She and her husband were joined in the receiving line by Paul Mellon, chairman of the NGA board, his wife, Bunny, an NGA trustee, and Max van der Stoel, the Dutch minister of foreign affairs. The turnout was like a Who's Who in government, the arts, diplomacy and business.

The queen bubbled nonstop with excitement. "She enjoys this sort of thing, really likes it," said one of her aides. "And she never wears out. She's like her mother and her grandmother that way. We in the Netherlands always say of the women of the House of Orange, they're as strong as an ox."

First through the line was Soviet Ambassador Anatoliy F. Dobrynin; last through were Secretary of State Alexander M. Haig Jr. and Vice President George Bush. In between: International Communication Agency director Charles Z. Wick; Smithsonian Institution Secretary S. Dillon Ripley; Riggs National Bank Chairman Joe L. Allbritton; Librarian of Congress Daniel Boorstin, Sens. Charles McC. Mathias (R-Md.), James McClure (R-Idaho), John Heinz (R-Pa.), Carl Levin (D-Mich.) and Charles Percy (R-Ill.); Reps. Guy Vander Jagt (R-Mich.), Edward Derwinski (R-Ill.), Dante Fascell (D-Fla.); Virginia Gov. Charles Robb; Zbigniew Brzezinski; Chief Justice Warren Burger and Justices John Paul Stevens and Sandra Day O'Connor.

Some, like Senate Foreign Relations Committee chairman Percy, were immersed in global politics and talking about Haig's travels between Great Britain and Argentina over the Falkland Islands dispute, a journey that had ended in the wee hours of Tuesday morning when he returned to Washington.

"Shuttle diplomacy has run its course now," said Percy, strolling along to the dinner tables set among lighted ficus trees. "General Motors would never have settled with the UAW with shuttle diplomacy. Haig has done a fabulous job so far in trying to see what the dimensions of the job are, but they really will get no resolution now unless they put someone in a room who can make a decision."

Brzezinski's solution was more dramatic: "Sixty-foot waves to overrun the islands, then there would be no problems. Internationalization is the only solution."

After dinner, the queen, speaking in accentless English about the exhibition, said: "It could not have taken place in a more dignified and appropriate setting . . . Your forefathers acquired a great number of beautiful Dutch paintings at a time when they were affordable."

She also cited painters Willem de Kooning, Piet Mondrian and American sculptor Alexander Calder, the shadow of whose mobile swept across her as she spoke.

Vice President Bush, responding to her toast, began with a personal observation. "You showed me," he said to the queen, "Rembrandt's very early self-portrait. And then we saw the later self-portrait of Rembrandt, somewhat tired, somewhat older. I thought of Al Haig when I saw that."

Earlier in the day, the biggest pushovers were at the National Press Club where the articulate, self-assured and congenial 44-year-old queen held her own in discussing some of the critical issues before her countrymen today.

Take these as evidence:

Q. What are the major misconceptions the Dutch have of the United States and vice versa?

A. Maybe there have been some misunderstandings, some misinterpretations of certain ideas and movements which have taken place. I happen to be here in the press club and I hope you don't mind, but sometimes one does not always get an objective picture of what is happening. You have a great responsibility in undoing these misconceptions.

Q. Will the peace movement in Europe get stronger or weaker?

A. One cannot talk about one peace movement. There are various movements. I think one can say they are mainly antinuclear and people in Europe are becoming more and more aware of the dangers of nuclear war . . . People want to bring up their children without fear. Fortunately we all live in countries where we can express these fears.

Q. As a mother, are you personally concerned about the possibility of nuclear weapons being moved into Europe?

A. Who with children--even people who don't have children--wouldn't be worried?

Constitutionally limited by what she is allowed to say about political matters, the queen turned other questions on the Falkland Islands dispute, El Salvador, Ronald Reagan's position on nuclear weapons and the peace movement over van der Stoel, the minister of foreign affairs.

So it wasn't all weighty and serious matters to which the queen addressed herself as she stood before the crowded press club while Prince Claus watched intently from the sidelines. The auburn-haired monarch, who wore one of the six hats in the room, also won her audience with with her light touches.

When press club president Vivian Valhberg asked how Queen Beatrix, the mother of three sons, felt about being the "last queen," the queen looked startled at first but then smiled.

"I just started," she said. It has been two years since Queen Juliana abdicated so that Queen Beatrix could ascend the throne.

Another question had to do with a remark made by her father, Prince Bernhard, that "in the home" he was boss. What about Queen Beatrix's home, Vahlberg asked.

"Better ask my husband. It's never been a problem," replied the queen, eyes twinkling.

Later, when Valhberg asked her about published reports that she is "willful and independent," the queen's dimples were evident again. "Ask others, not me," she said.

To the surprise of the audience, the tall, good-looking, German-born Prince Claus, 55, one object of her willful determination, slipped from his place at the head table and walked to the podium.

"The only thing I can do is answer in the affirmative," said the prince, whose engagement to the then-princess created a furor because he had been in the Hitler Youth and then the German army during World War II. "But besides these traits she has many others--smoothness, gentleness and kindness."

That about sewed up the audience, which responded with enthusiastic applause and laughter. Valhberg's thank-you gifts for the queen's appearance included a National Press Club windbreaker and an honorary membership, making her the only reigning monarch to have club privileges.

As firetrucks roared up to the old Willard Hotel across the street from the National Press Building, the queen's motorcade whisked the royal couple to upper Northwest Washington where St. Columba's Episcopal Church celebrated 200 years of American-Dutch diplomatic relations by dedicating its $140,000 Dutch-built Flentrop pipe organ.

There, the gifts to the queen included a copy of "Flentrop in America" by John Fesperman, the Smithsonian Institution's curator of musical instruments, and a tin of homemade shortbread by Mrs. C. Randolph Mengers. Barbara Bush, a St. Columba parishioner with her husband, the vice president, watched the presentations from a front-row pew.

Next stop was Meridian House International, where Queen Beatrix and U.S. Postmaster General William F. Bolger exchanged albums containing first-day issues of commemorative Dutch-American stamps.

"I knew both these albums would be here because you sent yours through the Netherlands Post," Bolger told the queen, "and I sent ours through the U.S. mail."

Festivities marking the queen's visit wind up tonight when the public can hear the Dutch Marine Band and the U.S. Marine Band in a combined concert at Sylvan Theater on The Mall starting at 7:30. At 9, there will be fireworks, concluding with set pieces showing the Dutch and American flags and a tulip that starts out as bud and bursts into full bloom.