Customizing category/tag results

Under the uajax_result function:

function uajax_result($arg, $id,$pagenumber,$getdata){
		$query = new WP_Query( $arg );
		$html = '';
			//print_r($query);	// The Loop
		if ( $query->have_posts() ) {
		  	$html .= '<h1>'.__('Search Results :', 'UWPQSF' ).'</h1>';
			$html .= '<article role="article">';
			$html .= '<section class="entry-content cf">';
			$html .= '<div class="post">';
			$html .= '<div class="entry">';
			$html .= '<ol class="test">';
		  	while ( $query->have_posts() ) {
				$query->the_post(); global $post;
				$result = apply_filters('uwpqsf_result_template', $output = '', $post);

				if( empty($result) ){
					$html .= '<li>';
					$html .= '<a href="'. get_permalink() .'"><img src="'. get_field('image').'"/><span>' .get_the_title().'</span></a>';
					$html .= '</li>';
				} else {
					$html .= $result;
				}
			}
			$html .= $this->ajax_pagination($pagenumber,$query->max_num_pages, 4, $id,$getdata);
			$html .= '</ol>';
			$html .= '</div>';
			$html .= '</div>';
			$html .= '</section>';
			$html .= '</article>';
		} else {
			$html .= __( 'Nothing Found', 'UWPQSF' );
		}
/* Restore original Post Data */
		wp_reset_postdata();
		return $html;
	}//end result

I have every post showing up, but I’d like to sort those posts into their separate categories. Like Below

Search Results:
-Category 1
–result 1
–result 2
-Category 2
— result 1

https://wordpress.org/plugins/ultimate-wp-query-search-filter/