Can you clarify what you mean "hardware limit on the maximum number of HSRP group"?
The limit of 256 is an HSRP version 1 protocol limit with respect to the range that the HSRP group can be set to. If you look at RFC 2281 Cisco HSRP, you'll see this specified in section 5.1:
Group: 1 octet
This field identifies the standby group. For Token Ring, values
between 0 and 2 inclusive are valid. For other media values
between 0 and 255 inclusive are valid.
If you use HSRP version 2 the HSRP group number range is 0-4095 and once you've specified standby version 2 within the interface vlan context then the extended range can be seen.
So if you want to use more than 256 HSRP groups on a router then HSRP version 2 is the way to go. The only thing to be mindful of then is how that number of groups may affect the CPU utilisation of the router.
I'd rather have found some official documentation from Cisco that stated the limit they support, but in the absence of that I've tested it and it would seem there's no obvious limit as you found with the Catalyst 3750.
In the output of the show version you can see there are now 256 Virtual Ethernet Interfaces created, the show standby internal summary shows 247 configured interfaces and there's also a snip of the show standby brief.
There are only 247 interfaces seen in show standby internal summary as I already had some interfaces with GLBP running so couldn't configure those interfaces with HSRP. Note also that they show as INIT as I only configured one device.
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