Cxaxukluth is an Outer God and the offspring or "son" of Azathoth by spontaneous fission. He is the grandfather of Tsathoggua, and his progeny are Hziulquoigmnzhah and Ghisguth. Cxaxukluth is said to be superior to Nyarlathotep, the Ultimate Gods, and the Nameless Mist which is the creator of Yog-Sothoth. It sometimes has an Insectoid form, but is usually in a unnameable, amorphous form.
Cxaxukluth dwells on Yuggoth. His immediate family lived with him for a while, but soon left because of his cannibalistic appetites.
Connection to Nug and Yeb
The Second Epistle of Eibon unto his Disciples, or The Apocalypse of Eibon claims that Cxaxukluth is divided into a masculine and feminine aspect, which are Nug and Yeb, The Twin Blasphemies (Nug is also the parent of Cthulhu).
Behind the Mythos
The creature was invented, outside of fiction, in the letters by Clark Ashton Smith to Robert H. Barlow, and published in the article "The Family Tree of the Gods" in The Acolyte fanzine (issue 7, Summer 1944).