MySQL - How to GROUP BY more columns and SUM() each group?

MySQL - How to GROUP BY more columns and SUM() each group?

currently my query looks like this:
SELECT alias.name killer,
SUM(kill_stats.amount) amount
FROM kill_stats
JOIN pickup ON pickup.logfile = 'CTFCL-20130813-1456-shutdown2'
JOIN account ON account.steam_id = '0:1:705272'
JOIN player victim ON victim.pickup_id = pickup.id AND
victim.account_id = account.id
JOIN player killer ON killer.pickup_id = pickup.id AND
kill_stats.killer_id = killer.id
JOIN alias ON killer.alias_id = alias.id
WHERE kill_stats.victim_id = victim.id AND NOT killer.team_id =
victim.team_id
GROUP BY kill_stats.killer_id
ORDER BY amount DESC
kill_stats table layout:
CREATE TABLE `kill_stats` (
`killer_id` int(11) UNSIGNED NOT NULL,
`victim_id` int(11) UNSIGNED NOT NULL,
`weapon_id` int(11) UNSIGNED NOT NULL,
`conced` bit(1) NOT NULL,
`fc` bit(1) NOT NULL,
`amount` int(11) UNSIGNED NOT NULL,
PRIMARY KEY(`killer_id`, `victim_id`, `weapon_id`, `conced`, `fc`),
CONSTRAINT `Ref_Killer` FOREIGN KEY (`killer_id`)
REFERENCES `player`(`id`)
ON DELETE CASCADE
ON UPDATE CASCADE,
CONSTRAINT `Ref_Victim` FOREIGN KEY (`victim_id`)
REFERENCES `player`(`id`)
ON DELETE CASCADE
ON UPDATE CASCADE,
CONSTRAINT `Ref_Weapon` FOREIGN KEY (`weapon_id`)
REFERENCES `weapon`(`id`)
ON DELETE CASCADE
ON UPDATE CASCADE
)
ENGINE=INNODB
CHARACTER SET utf8
COLLATE utf8_unicode_ci ;
Here a more readable view replacing the foreign keys with dummy data:
+-----------+-----------+-----------+--------+----+--------+
| killer_id | victim_id | weapon_id | conced | fc | amount |
+-----------+-----------+-----------+--------+----+--------+
| Josephine | Frank | RPG | NO | NO | 14 |
+-----------+-----------+-----------+--------+----+--------+
| Josephine | Frank | Shotgun | YES | NO | 5 |
+-----------+-----------+-----------+--------+----+--------+
| Josephine | Frank | Shotgun | NO | NO | 3 |
+-----------+-----------+-----------+--------+----+--------+
| Miguel | Frank | Knife | NO | NO | 1 |
+-----------+-----------+-----------+--------+----+--------+
Using this example table the query above would return a table like this:
+-----------+--------+
| killer | amount |
+-----------+--------+
| Josephine | 22 |
+-----------+--------+
| Miguel | 1 |
+-----------+--------+
What I would like the output to be is:
+-----------+-------------+--------------+-----------------+
| killer | total_kills | conced_kills | victim_had_flag |
+-----------+-------------+--------------+-----------------+
| Josephine | 22 | 5 | 0 |
+-----------+-------------+--------------+-----------------+
| Miguel | 1 | 0 | 0 |
+-----------+-------------+--------------+-----------------+
Showing how often a certain player was killed by other players, the total
amount of times that they killed him, the amount of conced kills and how
often the player carried the flag when he got killed by them.
I'm not really sure how to achieve that, I have tried GROUP BY
kill_stats.killer_id, kill_stats.conced but the result is:
+-----------+--------+
| killer | amount |
+-----------+--------+
| Josephine | 14 | -> the ones with kill_stats.conced = NO
+-----------+--------+
| Josephine | 5 | -> the ones with kill_stats.conced = YES
+-----------+--------+
| Miguel | 1 | -> the ones with kill_stats.conced = NO (only row
for that `killer_id`)
+-----------+--------+
I get multiple rows for killer_id and I want one row per killer_id holding
all the data.