Domain:
Karenia brevis falls under the domain Eukarya as it has eukaryotic cells with membrane bound organelles, like mitochondria. This domain is comprised of cells that contain a true nucleus and no cell wall. Prokaryotes are set apart from these organelles as they do not have a true nucleus. Check out these organisms to better understand how broad this domain is. Some examples of eukaryotic organisms are Curcuma Longa L., Passiflora edulis, Papaver somniferum, Chlamydosaurus kingii, Giraffa camelopardalis, Bos taurus,  Carychium exiguum, Vertigo gouldii, Actinidia deliciosa, Anethum graveolens, and Pagophilus groenlandicus.

Kingdom:
Karenia brevis is categorized under the kingdom protozoa because it is a single celled eukaryote. Protozoa commonly have characteristics associated with animals like mobility and heterotrophy. This group is often grouped together with plant-like algae and slime molds. Protozoa are too small to be seen with the naked eye, but can be easily seen under a microscope.

I also found mixed information on Karenia brevis and what kingdom it could be classified under. I found it classified under kingdom chromista which entails colored, photosynthetic organisms that have chlorophyll c, but are not related to the plants and algae. Because kingdom chromista does not include algae, this is not the correct classification and as more research has been done, we now know this organism belongs to kingdom protozoa.

This is a plastid phylogeny using genes implicated in tertiary EGT in Karenia brevis. Photo drawn by author. Adapted from the hyperlinked page.

Phylum:
Dinophyta posses cellulose plates; they are unicellular, and most utilize two flagella. This phylum can also be autotrophic or heterotrophic and they are primary producers in marine systems. Since Karenia brevis is a primary producer in its marine system and can produce harmful toxins, this leads to more problems.

Class:
Karenia brevis belongs to the class dinophyceae as these organisms are unicellular and are free living, symbiotic, or parasitic organisms with a nucleus that have a large number of banded chromosomes. This group also utilizes its motile stage having two dissimilar flagella. An example of an organism from this class is Gonyaulax catenella.

Order:
This order classification has unarmored kinokont like cells that have lingulum and culcus. They have thecal vessels without thecal plates. Organisms in this class may be osmophlilic material with or without chloroplast. These organisms have nematocysts, ocelli or siliceous as internal structures.

This is a maximum likelihood phylogenetic tree based off of plastid and mitochondria-targeted translation. Photo drawn by author. Adapted from the hyperlinked page

Family:
The family Karenia brevis belongs to can produce toxins like brevetoxins (the one K. brevis produces) and gymnodimines, among others. This family is associated with harmful algal blooms and can cause marine animal illness and mortality. Family Kareniaceae is considered to be harmful.

Genus:
Genus Karenia is an unarmored dinoflagellate. This genus is found throughout the world, but usually in sparse abundance unless they are blooming. This genus is toxic and can be found in costal and oceanic water.

Species:
Karenia brevis final classification is given for its short blooms. "Brevis" in English means short, hence the short blooms as its name and this species can also be toxic.