Calibre Companion supports grouping on calibre text-type custom columns (text, text like tags, fixed set of values, and built from other columns). To group on such a column, add that columnís calibre lookup key (the word beginning with #, as in #genre) to Calibre Companionís list of custom columns to show on the Group menu. You do this by clicking the menu button on your device (usually three dots), choosing "Settings", then choosing "Make groups for custom columns". Enter the names in the text box shown in the resulting dialog. Be sure to include the leading # character.
Note: it is not an error if a lookup name you enter does not actually exist in any books on your device. This can happen if you connect to multiple libraries that have differing custom column setups. That said, if you expect to see information when you click on a lookup name in the group menu but don't, check the spelling of the lookup key.
Note also that you can add calibre's date and pubdate lookup names to the group menu as pseudo custom columns. The date column will be grouped by yyyy-mm, and the pubdate column will be grouped by yyyy.
When you add or change the custom column keys, Calibre Companion must rebuild some information in the database. This rebuild process will happen next time Calibre Companion is "restarted", something that because of how android works could be at almost any time. If you have a large number of books in Calibre Companion this process can take a few moments. You can see a progress indicator by checking the status bar.