Finite Group Databasebeta

← #20268221

Subgroups — #20268221

Order 6592.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15693043C211yesmaximal, characteristic, complemented
2#15692967C211yesmaximal, characteristic, complemented
3#15692965C211yesmaximal, characteristic, complemented
4#15692964C211yesmaximal, characteristic, complemented
5#15692962C211yesmaximal, characteristic, complemented
6C2×C103⋊C16C211yesmaximal, characteristic, complemented
7#135×C103C211yesmaximal, characteristic, complemented
8#13110105—21no—
9Dic412C2211yescharacteristic
10#13110094—21no—
11D824C2211yescharacteristic
12C103⋊C16C2211yescharacteristic
13C103⋊C16C2211yescharacteristic
14#41×C103—21no—
15Q16×C103C2211yescharacteristic
16SD16×C103—21no—
17D8×C103C2211yescharacteristic
18C2×C8×C103C2211yescharacteristic
19Q8×C103—21no—
20D4×C103—21no—
21D4×C103—41no—
22C2×C4×C103—41no—
23C2×C4×C103D411yescharacteristic
24C22⋊D103—41no—
25D412—21no—
26C4×D103—41no—
27Dic206—21no—
28C8×C103D411yescharacteristic
29C8×C103C2311yescharacteristic
30C22×C103—41no—
31C22×C103D811yescharacteristic
32C2×D103—41no—
33C4×C103—41no—
34C4×C103D811yescharacteristic
35C4×C103C2×D411yescharacteristic
36Dic103—41no—
37C2×C103—21no—
38C2×C103—81no—
39C2×C103C2×D811yescharacteristic
40D103—81no—
41C103#50811yescharacteristic, complemented, Sylow
42#508—1031nomaximal, Sylow
43#135—1031no—
44#135D10311yescharacteristic, complemented
45Q32—1031no—
46SD32—1031no—
47SD32—1031no—
48D16—1031no—
49C2×C16—1031no—
50#41—21no—
51#41—2061no—
52Q16—1031no—
53Q16C2×D10311yescharacteristic
54SD16—21no—
55SD16—2061no—
56D8—1031no—
57D8C2×D10311yescharacteristic
58C2×C8C2×D10311yescharacteristic
59C16—1031no—
60C16—1031no—
61Q8—21no—
62Q8—2061no—
63D4—21no—
64D4—41no—
65D4—4121no—
66D4—2061no—
67C2×C4—41no—
68C2×C4—4121no—
69C2×C4C22⋊D10311yescharacteristic
70C8C22⋊D10311yescharacteristic
71C8C22×D10311yescharacteristic
72C22—41no—
73C22—4121no—
74C22#1311009011yescharacteristic
75C4—41no—
76C4—4121no—
77C4#1311009011yescharacteristic
78C4C2×C22⋊D10311yescharacteristic
79C2—21no—
80C2—81no—
81C2—8241no—
82C2C2×#1311009011yescharacteristic
subgroupG/H
centerC4#13110090
commutatorC8×C103C23
FrattiniC8C22×D103
Fitting#135×C103C2
socleC2×C103C2×D8
hypercenter#135D103
hypocenterC103#508
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15693043C2semidirect
2. #15692967C2semidirect
3. #15692965C2semidirect
4. #15692964C2semidirect
5. #15692962C2semidirect
6. C2×C103⋊C16C2semidirect
7. #135×C103C2semidirect
41. C103#508semidirect
44. #135D103semidirect