Hi HomerJ,
The latest supported versions are listed on the HP live Network page for equipment specifications:
https://hpln.hp.com/page/alm-qc-enterprise-technical-specifications

and they are based upon the build numbers of the various supported environments. When the installation proceeds the installer checks the installed OS and DB version build numbers (and not the version numbers) against a set of coded ''officially supported'' versions. What this does is insures that the version you are installing on is checked and vetted as supported for the software installation.

With the use of validator switch overrides, these checks can be bypassed to allow the software to be installed on non-officially supported versions (see the installation guides for overriding these validators when needed as sometimes it is necessary to override the checks during installation, as a later patch may add support back in and immediately after installation that patch is installed to gain official support). Note: overriding the switches allows usage on an non-supported version but is not recommended (if issues arise, technical support can and may be denied based upon the usage of non- supported environments, until such time as a supported environment is installed).

Hope this helps,
Dan