Adding child elements to checkbox/radio form elements
I don't believe you can make a radio button a "parent".

Here's an example of using radios, checkboxes, and fieldsets.

http://api.drupal.org/api/examples/form_example!form_example_states.inc/function/form_example_states_form/7

You might take a look at http://api.drupal.org/api/drupal/developer!topics!forms_api_reference.html/7#container

Try removing search_attributes from search_product

$form['search_attributes'] = array(
    '#type' =&gt; 'checkboxes',
    '#options' =&gt; array(
        'name' =&gt; t('by Name'),
        'model' =&gt; t('by Model'),
        'catalog_no' =&gt; t('by Catalogue No.'),
        'manufacturer' =&gt; t('by Manufacturer'),
        'description' =&gt; t('by Description'),
    ),
);