How can I programmatically create “child” pages on theme activation?

I know how to create pages automatically when a theme is activated, but I need help to figure out how to also programmatically create child pages at the same time.

For example:

- Page 1
  - Page 1.1
  - Page 1.2
- Page 2
  - Page 2.1
  - Page 2.2
  - Page 2.3
- Page 3
  - Page 3.1
- Page 4
  - Page 4.1
  - Page 4.2

And here is my function for automatic page creation (top level only).

if (isset($_GET['activated']) && is_admin()){
    add_action('init', 'create_initial_pages');
}

function create_initial_pages() {
    $pages = array(
        'page1' => 'Page 1',
        'page2' => 'Page 2',
        'page3' => 'Page 3',
        'page4' => 'Page 4'
    );
    foreach($pages as $key => $value) {
        $id = get_page_by_title($value);
        $page = array(
            'post_type'   => 'page',
            'post_title'  => $value,
            'post_name'   => $key,
            'post_status' => 'publish',
            'post_author' => 1,
            'post_parent' => ''
        );
        if (!isset($id)) wp_insert_post($page);
    };
}

Does anyone know how to extend this function to also create child pages (if they don’t already exist) when the theme is activated?

As @Soulseekah said, you can do this with post_parent. I didn’t test with the following code, but it should work

$pages = array( 
    array(
        'name' => 'page1',
        'title' => 'Page 1',
        'child' => array(
            array(
                'name' => 'page11',
                'title' => 'Page 1.1'
            ),
            array(
                'name' => 'page12',
                'title' => 'Page 1.2'
            )
        )
    ),
    array(
        'name' => 'page2',
        'title' => 'Page 2',
        'child' => array(
            array(
                'name' => 'page21',
                'title' => 'Page 2.1'
            ),
            array(
                'name' => 'page22',
                'title' => 'Page 2.2'
            )
        )
    ),
    array(
        'name' => 'page3',
        'title' => 'Page 3',
        'child' => array(
            array(
                'name' => 'page21',
                'title' => 'Page 2.1'
            ),
            array(
                'name' => 'page22',
                'title' => 'Page 2.2'
            )
        )
    ),
);

$template = array(
    'post_type' => 'page',
    'post_status' => 'publish',
    'post_author' => 1
);

foreach( $pages as $page ) {
    $exists = get_page_by_title( $page['name'] );

    if( !$exists ) {
        $my_page = array(
            'post_name' => $page['name'],
            'post_title' => $page['title']
        );
        $my_page = array_merge( $my_page, $template );

        $id = wp_insert_post( $my_page );

        //if there is any child page, create them by {$id} as 'post_parent'
        if( isset( $page['child'] ) ) {
            foreach( $page['child'] as $child ) {
                $child_page = array(
                    'post_name' => $child['name'],
                    'post_title' => $child['title'],
                    'post_parent' => $id
                );
                $child_page = array_merge( $child_page, $template );
                $id = wp_insert_post( $child_page );
            }
        }
    }
}