I presume you want to graft hickory onto pecan or something similar. The general answer is that some hickory species are 64 chromosome and some are 32 chromosome. A rule of thumb is that 32 can be grafted onto 32 and 64 onto 64. However, I have pictures in a book of pecan grafted successfully onto Mockernut. The major problem with grafting hickory is that it is difficult to match the vigor of the rootstock with the scion. For example, if pecan is grafted onto most other slower growing hickory species, the resulting tree has a large diameter above the graft and much smaller stem below. It looks very unbalanced. The reverse graft of shagbark hickory onto pecan rootstock is very successful.

There are some good sources of info on the web.
Northern Nut Growers
Nolin Nursery

Here are a few of the species chromosome counts that I recall off the top of my head.

The genus Carya has 17 to 19 recognized species.
Carya Ovata - Shagbark Hickory - 32 chromosome
Carya Laciniosa - Shellbark Hickory - 32 chromosome
Carya Illinoinsis - Pecan - 32 chromosome
Carya Aquatica - Water Hickory - 32 chromosome
Carya Cordiformis - Bitternut Hickory - 32 chromosome

Carya Tomentosa - Mockernut Hickory - 64 chromosome (Mockernut is the most common hickory in southern upland soils)

DarJones

E,
DarJones' post, above, is a pretty good guideline.

Most stuff I've seen from the past, by folks like Carl Weschke, suggest that pignut is worthless as an understock, mockernut variable, bitternut OK for most pecans.

For the most part, I just use pecan as an understock for shagbark and shellbark.
Friend in NJ likes seedlings of Fayette shellbark as an understock for hickories - and he seems to think an interstem of 'Fayette' conveys some vigor; heck I have a hard enough time getting one 'take', I'm not fixin' to start doing interstem grafts on nut trees!

I've seen some claims made that may or may not be substantiable - like "J.Yoder #1" is incompatible with bitternut understock, 'Fox' or 'Davis' shagbarks are compatible with mockernut, etc. Had one fellow tell me that 'Cody Cox' will not work on pecan - only on hickory - but others have told me that's BS. Some of those claims may be anecdotal at best and may be a result of failure on the part of the grafter or bad/damaged scionwood, more than a true incompatibility.
Additionally, I'm not convinced but that there may be differences in geographic 'races' of a species that may contribute to compatibility/incompatibility - but that's sheerly conjecture on my part.

I can't contribute anything to this thread yet but I'm interested in what others experiences are. I also have some wild Carya species that I'm going to graft to this year. I'm new to this, but have gotten lots of help from people on this forum. Hopefully I'll have something to contribute to this thread in the future.