You are looking for Module Filter, it quickly find the module you are looking for and with filter option and category.
The modules list page can become quite big when dealing with a fairly
large site or even just a dev site meant for testing new and various
modules being considered. What this module aims to accomplish is the
ability to quickly find the module you are looking for without having
to rely on the browsers search feature which more times than not shows
you the module name in the 'Required by' or 'Depends on' sections of
the various modules or even some other location on the page like a
Take a look at Enabled Modules (enabled_modules) module provides lists of all enabled modules on a website.
These features are useful for moving sites to a whole new code base
and rebuilding fresh with only the modules actually in use, or doing
clean up on your modules folders.
and also Views System module extends the Views module and allows to create customized lists (pages, blocks) of modules, themes, and theme engines that are or have been installed in Drupal's file system.
Using Drush check this List of all active modules used in a site.