Nearly 150 House Republicans supported President Donald J. Trump’s baseless claims that the election had been stolen from him. But Mr. Gosar and a handful of other Republican members of the House had deeper ties to extremist groups who pushed violent ideas and conspiracy theories and whose members were prominent among those who stormed the halls of Congress in an effort to stop certification of President-elect Joseph R. Biden Jr.’s victory.

Their ranks include Representative Andy Biggs of Arizona, who like Mr. Gosar was linked to the “Stop the Steal” campaign backing Mr. Trump’s effort to overturn the election’s outcome.

Representative Lauren Boebert of Colorado has close connections to militia groups including the so-called Three Percenters, an extremist offshoot of the gun rights movement that had at least one member who entered the Capitol on Jan. 6.