Modified August 13, 2014. to place the Poposauridae outside the Archosauria.
Lotosaurus adentus (Zhang 1975. Figure 1) Anisian, Early Triassic ~240 mya, 2.5 m in length, the only toothless sailback archosaur, has been a difficult taxon to nest because it is so unlike other archosaurs.
Nesbitt (2003) nested Lotosaurus with the other sailback archosaurs, Arizonasaurus and Ctenosauriscus, despite the obvious differences (like teeth vs. no teeth). He recovered these within the otherwise sail-less Poposauridae along with Chatterjeea (aka Shuvosaurus) and within the otherwise sail-less Rauisuchia (top Triassic predators, like Prestosuchus). The Lotosaurus skull (wider than tall and lacking teeth) was actually quite different than the rest of the rauisuchians. The hips were different too.
Later, Nesbitt (2011) nested Lotosaurus between Sillosuchus and Poposaurus, one node beyond Arizonasaurus and Xilosuchus, all within the Poposauroidea with Qianosuchus at its base. This branch nested as a sister to Rauisuchidae + Crocodylomorpha together called Loricata, a resurrected clade name from 1820 that was defined by Nesbitt as the most inclusive clade containing Crocodylus niloticus (the Nile crocodile), but not Poposaurus, Ornithosuchus, or Aetosaurus. Ticinosuchus nested as basal to all these taxa in an older clade, Paracrocodylomorpha (the last common ancestor of Poposauridae and Crocodylomorpha and all of its descendants).
So the questions are:
1) What is Lotosaurus, if not a rauisuchid?
2) What is Arizonasaurus, if not a poposauroid? And
3) How does Ctenosauriscus. known only by a giant sailback fit it?
Let’s Compare the Candidates
When you compare Lotosaurus to its most parsimonious sister taxa and other sailback archosaurs (Figure 1), the affinities and shared traits become more apparent. Here Vjushkovia was basal to the rauisuchians and these included Arizonasaurus and Xilosuchus. The surprisingly long neck of Xilosuchus demonstrates affinities to another sister, Qianosuchus.
Phylogenetic Analysis
The large reptile tree nested Lotosaurus with Silesaurus (Figure 1) and both of these within the Poposauridae outside the Archosauria. Overall similar, the ilia of both taxa were virtually identical and both had laterally oriented acetabula. The scapulae had the same shape. Both were plant-eaters, based on the leaf-like teeth of Silesaurus and the toothless jaws of Lotosaurus.
The large study nested Arizonasaurus with Yarasuchus and Qianosuchus with Ticinosuchus and aetosaurs. Arizonasaurus had a smaller pectoral girdle and longer ventral pelvis, suggesting it was a biped. The sail extended only between the pectoral girdle and tail.
By contrast, the sail extended anterior to the scapula in Lotosaurus and Ctenosauriscus. That may be the only clear clue as to the affinities of the first (to be discovered) and largest of the saibacks.

Figure 4. Lotosaurus family tree according to the large study, not the Nesbitt study. Pisanosaurus is no longer a poposaurid but a basal ornithiscian.
Let’s Compare Skulls
The skulls of candidate and sister taxa help differentiate the two sailbacks from one another. The pink band illustrates the lineage of rauisuchians from Vjushkovia to Aetosaurus, which Nesbitt (2011) found were sister to Lotosaurus. The yellow and green bands are the two clades within the Poposauridae. Unfortunately no skull is known for Poposaurus. Evidently, all poposaurids were plant eaters with shorter skulls and several were toothless.
References
Nesbitt SJ 2003. Arizonasaurus and its implications for archosaur divergence
Sterling J. Nesbitt Proceedings of the Royal Society, London B (Suppl.) 270, S234–S237. DOI 10.1098/rsbl.2003.0066
Weinbaum JC and Hungerbuhler A 2007. A Revision of Poposaurus gracilis (Archosauria: Suchia) based on two new specimens from the Late Triassic of the southwestern USA. Palaeontologische Zeitschrift 81(2):131-145.
Zhang F-K 1975. A new thecodont Lotosaurus, from Middle Triassic of Hunan. Vertebrata PalAsiatica 13:144-147.