ORDER BY is always last...
However, you need to pick the fields you ACTUALLY WANT then select only those and group by them. SELECT * and GROUP BY Email will give you RANDOM VALUES for all the fields but Email. Most RDBMS will not even allow you to do this because of the issues it creates, but MySQL is the exception.
SELECT Email, COUNT(*)
FROM user_log
GROUP BY Email
HAVING COUNT(*) > 1
ORDER BY UpdateDate DESC