Since you're on SDE, you can achieve what you're asking with:
UPDATE_DATE_DATE IN (SELECT MAX(UPDATE_DATE_DATE) FROM SO_SC_1 GROUP BY NUMBERCYLA)
As reference for others who may come across this in searching for a file geodatabase solution:
Note that file geodatabases are extremely limited with subqueries. See: http://resources.arcgis.com/EN/HELP/MAIN/10.2/index.html#/SQL_reference_for_query_expressions_used_in_ArcGIS/00s500000033000000/
If you were just trying to retrieve the overall maximum and it's in a file geodatabase or SDE:
UPDATE_DATE_DATE = (SELECT MAX(UPDATE_DATE_DATE) FROM SO_SC_1)
If it's in a personal geodatabase, then you need to move into the 21st century. J/K. see: https://gis.stackexchange.com/a/26750/10919
If you're interested in getting the maxima grouped by some other field and your feature class is in an FGDB, then you're out of luck. You will need to implement a work-around in which you identify, select, and export the features to a new feature class.