What classes are insects and arthropods in?

Under arthropoda are Subphyla Chelicerata, Myriapoda, Crustacea, and Hexapoda. (There is also an extinct class Marrellomorpha and an the extinct Trilobite subphylum). The chelicerata, like Spiders, scorpions, mites, etc., get their name from having appendages appear before the mouth; myriapods like centipedes and millipedes characterized by a high count of body segments and legs; crustaceans like crabs, shrimp, woodlice characterized by their biramous (two-part) limbs and a specialized larval form; hexapoda named for their consolidated thorax with only three pairs of legs.

There are many classes below these subphyla.. here is a list:

Trilobita - trilobites (extinct)

Arachnida - spiders, scorpions, etc.

Merostomata - horseshoe crabs, eurypterids (extinct), etc.

Pycnogonida - sea spiders

Chilopoda - centipedes

Diplopoda - millipedes

Pauropoda - sister group to millipedes

Symphyla - resemble centipedes

Branchiopoda - brine shrimp etc.

Remipedia - blind crustaceans

Cephalocarida - horseshoe shrimp

Maxillopoda - barnacles, copepods, fish lice, etc.

Ostracoda - seed shrimp

Malacostraca - lobsters, crabs, shrimp, etc.

Insecta - insects

Entognatha - wingless

Camptophyllia (extinct class)

Marrellomorpha (one extinct species)

Some classes are still uncertain and debate is ongoing as to placement in the taxonomic tree.