It seems that the L581/S398 SNP has been under-represented and under-analyzed in academic research (but may be indirectly reported in the literature as the J2a* paragroup).  It also seems to be associated with a DYS447 STR deletion.  Unfortunately, the L581/S398 SNP is not tested by Geno 2.0. 

The L581 SNP has been found in populations from Italy to India, including Lybia, Egypt, Germany, Lebanon, Turkey, Armenia, Iraq and Iran, among other places.  

According to thegeneticatlas.com:
"J2 (M172)  Marker of Paleolithic expansion in Mesopotamia
J2a (M410) Marker of Paleolithic expansion out of Mesopotamia
J2a2 (L581) Remained in Mesopotamia through the Paleolithic experienced later expansion in the Neolithic agricultural revolution
J2a2*  A minority lineage in Mesopotamia, Anatolia, experienced another expansion in the ancient Greek World"

If you have tested with Geno 2.0, and have a terminal SNP downstream of L212, but are negative for L26/L27, please join this project and order a single SNP L581 test through Family Tree DNA. 

Individuals who have tested positive for the following SNPs, but have not yet tested for L581, are encouraged to join this project and test for L581 through FTDNA:  PF5007, PF5008, PF5019, PF5030, PF5035, PF5039, PF5041, PF5044, PF5050, PF5053, PF5058, PF5073, PF7381, PF4993, PF4997, PF5000, PF5002, PF5004, PF5011, PF5013, PF5015, PF5016, PF5017, PF5021, PF5023, PF5027, PF5031, PF5032, PF5033, PF5036, PF5037, PF5038, PF5040, PF5043, PF5045, PF5047, PF5052, PF5054, PF5056, PF5059, PF5060, PF5062, PF5064, PF7380, PF7384

Individuals who have tested positive for L581, P279 and/or M340 are encouraged to join the L581 project.