It will work with SDHC and SDXC.
The difference between HC and XC is that the size of HC is between >2 and 32 GB and the size of XC is 32 GB to 2TB. (And from 32 onwards you can not use FAT32 formatting).
There is no max size for your phone the 128 GB is "just" put in the spec because that is the current max size for microSD cards and SDXC because 128 is bigger than 32 But 200 microSD cards are being developed and there are already 512 GB SD cards.
Side note
- A class 4 card may not work because it is to slow.
-UHS (Ultra High Speed bus) standard is not supported so you will not get 30 or 48 MB/s because the max speed of the HIgh Speed bus in your phone is 25 MB/s.