2 classes of echinoderms and a member of each class?

There's actually 8 "types"(which i consider classes) of echinoderms we know today, 2 of them are extincted, the 2 extincted ones are homalozoa and helicoplacoidea. The 6 living today are crinoidea(includes sea lilies)asteroidea(which includes star fishes)ophiuroidea(which includes brittle stars) echinoidea (which includes sea urchin)holothuroidea(which includes sea cucumber, which i like to call sea pickles) and last and least, concentricycloidea(which includes sea dasies, the reason they're least is because there's only 2 species of them known so far). If you're talking about sub-phylums of echinoderms, i believe there are 2 of them, i have no idea what the 2 extincted ones go in to, but i think scienctists only classify species that's not dead, the 2 subphylum are pelmatozoa(which includes only crinoidea) and there's eleutherozoa(which includes all of the classes except homalazoa, heli and crinoidea)