I suppose that you're talking about a dropdown with the list of colors like some other pet games have. The problem is that other games don't have genetics behing their colors. Probably we can group it by color name but then " white" will list a dozen of different colors for different species. I'm not sure if this is what you want, but otherwise it wouldn't be possible at all.
There's a lot of holes which can't be covered by "one color genetics - one color in dropdown". I. e. what about different colors with the same name? A lot of species have a few whites and blacks, and some other colors duplicated as well. Such colors have different genetics, different database entries and different everything except name and appearance. How would someone know which "white" exactly they just chosen among the same 3 "whites" for Rocs for example? Also we can't uncover the real genetics behind the same "whites" in case if they aren't researched yet. If the search isn't filtered by species, then there will be a dozen of such "whites". Also all three deviant variants of the same color have the same name, like " Yellow *", so this may cause a lot of confusion as well. At the same time we can't write the genetics (for example, listing a color as "white A1 B1" or "white A1 B1 P01") to show the difference because this will uncover the color genetics for the pets that aren't researched yet.
So would sorting just by name work?