The classification of the Red Milkweed Beetle goes as follows

Domain: The T. Tetrophthalmus belongs to the domain Eukarya due to the fact that the organism contains a true nucleus along with eukaryotic cells. Eukaryotes also have organelles inside of their cells that are bound to the membrane, which is not found in the prokaryotic cells.
Kingdom: It belongs to the kingdom Animalia for many reasons. All members of the kingdom are multicellular and are heterotrophs. In order to belong to this kingdom, the organism must have some form of body support and the cells in their bodies must be specialized for specific functions. Those who belong to Animalia also reproduce sexually.
Phylum: The Red Milkweed Beetle belongs to the phylum Arthropoda due to its bilateral symmetry, jointed appendages, and an exoskeleton made from chitin. The jointed appendages are attached to the hard outer exoskeleton and allow the Arthropods to have flexibility and movement. All arthropods must shed their exoskeleton, through a process called "molting", in order to grow. All Arthropods also have an open circulatory system, in which they have a pump that acts like a heart that moves hemolymph throughout the body.
Class: The T. Tetrophthalmus is a member of the class Insecta because its body is divided into three parts: the abdomen, thorax, and head. All members of this class have a pair on antennae on their head and a set of wings that are used to fly.
Order: Coleoptera due to its food source being a plant. The insects in this order have chewing mouhparts and jaws that are powerful. The adult beetles have two pairs of wings; one set is small and hard protect the second pair. They have the ability to use the second set of wings to fly. (BioKids).
Family: Cerambycidae (subfamily Lamiinae) due to the characteristic of having long antennae on their head that are in close proximity to the organism's eyes. The antennae of the T. Tetrophthalmus is a perfect example of this because the antennae split each compound eye in two. 
Genus: The Red Milkweed Beetle belongs to the genus Tetraopes simply because it has the ability to live on the Milkweed plant, Asclepias syriaca  (BugGuide, 2003). Since most organisms are not able to live on this specific plant, this Arthropod with long antennae is given its own genus.      

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