It's a bit hard to pick an obvious "large galaxy" threshold. This is partly because most galaxy group catalogs are based on galaxy catalogs that are limited by apparent magnitude, meaning that it includes lower-luminosity galaxies at small distances but only high-luminosity galaxies at large distances. Thus, how many galaxies are in each "group" (this includes massive clusters and groups with only one galaxy, which are "isolated galaxies") will unfortunately depend on how distant the group is.
So, keeping that in mind...
The Yang et al. (2007) group catalog, based on Data Release 4 of the Sloan Digtal Sky Survey, used around 400,000 galaxies with redshifts between 0.01 and 0.2. In their Sample II (more accurate, but possibly missing some groups), there are 369,000 galaxies, of which 271,000 (73%) are isolated. In their Sample III (more complete, but probably erroneously includes some isolated galaxies into groups), there are 408,000 galaxies, of which 250,000 (61%) are isolated.
A much more local group catalog is that of Kourkchi & Tully (2017), which looks at galaxies within 3500 km/s ($z < 0.011$). This includes NGC 821 (classed as a "group" with 1 member, so indeed isolated) and the Leo Triplet ("M66 Group" classed as a group with 15 members). 7290 of the 15,004 galaxies are isolated, for a isolation fraction of 49%. The fact that this is lower than the Yang et al. results is undoubtedly due to Kourkchi & Tully including more dwarf galaxies.
(If I arbitrarily define "cluster" as "group with $> 100$ galaxies -- which correctly gets the Virgo and Fornax Clusters), then in the Kourkchi & Tully catalog there are 1339 galaxies in clusters, for a cluster fraction of $\sim 9$%.)
But, generally, I think you could say that $\sim 50-65$% of "large" galaxies are isolated, with about 9% (maybe less) in proper clusters, and the remainder in groups (mostly small groups).