The Collaborative International Dictionary of English v.0.48:

Thallogen \Thal"lo*gen\, n. [Gr. ? young shoot or branch, frond
   + -gen.] (Bot.)
   One of a large class or division of the vegetable kingdom,
   which includes those flowerless plants, such as fungi, algae,
   and lichens, that consist of a thallus only, composed of
   cellular tissue, or of a congeries of cells, or even of
   separate cells, and never show a distinction into root, stem,
   and leaf.
   [1913 Webster]