How to disabled update notification from subsite administrator?

I'd like to disable (not just hide by CSS) the WP core, themes, plugins, and other related update notification from all subsite administrators but work as normal only with network super admin. I use this code below in mu-plugins and doesn't seem to work.

function hide_update_notice_to_all_but_admin_users()
{
    if (!current_user_can('update_core')) {
        remove_action( 'admin_notices', 'update_nag', 3 );
    }
}
add_action( 'admin_head', 'hide_update_notice_to_all_but_admin_users', 1 );

Please advice.