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Some galaxies, such as NGC821 are classified as "isolated galaxies", others form parts of distinct groups or clusters (relevant link) Although isolated galaxies may be accompanied by small satellites, they are distinct from the three large galaxies in the M66 group or the many galaxies in the Coma cluster. Those galaxies are part of an obvious grouping.

Among large galaxies (and ignoring the many dwarf galaxies) what proportion are isolated, like NGC821, and what proportion are found in groups or clusters?

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    $\begingroup$ Define 'partner' - there are very large structures in the galaxy encompassing many (many many) galaxies - are they all partners? $\endgroup$
    – Jon Custer
    Apr 12, 2023 at 12:47
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    $\begingroup$ What is a "partner" - I suppose it is clear that the magellanic clouds are partners to the milky way, What about the Andromeda Galaxy? Is it a partner, or is it just another galaxy that happens to be nearby. Then the local group of galaxies can be seen as being on a spur of the Virgo cluster: are all the Virgo cluster galaxies partners to the Milky Way? NGC 821 doesn't have any obvious partners, but if you look hard enough there are "stellar populations" that are small galaies that are in the the process of merging. academic.oup.com/mnras/article/362/3/857/976947 $\endgroup$
    – James K
    Apr 12, 2023 at 13:19
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    $\begingroup$ The notion of isolated galaxies seems to be a reasonable one, and should include galaxies like NGC821, which are not part of a group, even if they have small satellites and so the question could be focussed more on non-dwarf galaxies. There is an interesting question here. Relevant definition is given here astronomy.swin.edu.au/cosmos/i/Isolated+Galaxies $\endgroup$
    – James K
    Apr 12, 2023 at 13:20
  • $\begingroup$ I've tried adding details and examples to your question. $\endgroup$
    – James K
    Apr 12, 2023 at 14:23
  • $\begingroup$ The question could have been how many fossil galaxies are there since isolated galaxies are suspected to be unions of other galaxies. $\endgroup$
    – user50623
    Apr 12, 2023 at 16:18

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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).

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