Finite Group Databasebeta

← #20268222

Subgroups — #20268222

Order 6592.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15693044C211yesmaximal, characteristic, complemented
2#15693040C211yesmaximal, characteristic, complemented
3#15692967C211yesmaximal, characteristic, complemented
4#15692966C211yesmaximal, characteristic, complemented
5#15692962C211yesmaximal, characteristic, complemented
6C16×D103C211yesmaximal, characteristic, complemented
7SD32×C103C211yesmaximal, characteristic, complemented
8#13110106—21no—
9#13110104—21no—
10Dic412C2211yescharacteristic
11#13110093—21no—
12#13110092—21no—
13D824C2211yescharacteristic
14C8×D103C2211yescharacteristic
15C103⋊C16C2211yescharacteristic
16Q16×C103C2211yescharacteristic
17D8×C103C2211yescharacteristic
18C16×C103C2211yescharacteristic
19Q8×C103—21no—
20D4×C103—21no—
21C22⋊D103—41no—
22C2×Dic103—41no—
23D412—21no—
24D412—41no—
25C4×D103—41no—
26C4×D103D411yescharacteristic
27Dic206—21no—
28C8×C103C2311yescharacteristic
29C103⋊C8D411yescharacteristic
30C22×C103—41no—
31C2×D103—41no—
32C2×D103D811yescharacteristic
33C4×C103—41no—
34C4×C103C2×D411yescharacteristic
35Dic103—41no—
36Dic103D811yescharacteristic
37C2×C103—81no—
38C2×C103C2×D811yescharacteristic
39D103—21no—
40D103—81no—
41C103#50811yescharacteristic, complemented, Sylow
42#508—1031nomaximal, Sylow
43#135—1031no—
44#135—1031no—
45Q32—1031no—
46SD32—1031no—
47SD32D10311yescharacteristic, complemented
48D16—1031no—
49C2×C16—1031no—
50#41—2061no—
51#41—2061no—
52Q16—1031no—
53Q16C2×D10311yescharacteristic
54SD16—2061no—
55SD16—2061no—
56D8—1031no—
57D8C2×D10311yescharacteristic
58C2×C8—1031no—
59C16—1031no—
60C16C2×D10311yescharacteristic
61Q8—21no—
62Q8—2061no—
63D4—21no—
64D4—4121no—
65D4—4121no—
66D4—2061no—
67C2×C4—1031no—
68C2×C4—4121no—
69C2×C4—4121no—
70C8—1031no—
71C8C22×D10311yescharacteristic
72C22—41no—
73C22—1031no—
74C22—4121no—
75C4—41no—
76C4—1031no—
77C4—4121no—
78C4D4×D10311yescharacteristic
79C2—81no—
80C2—8241no—
81C2—2061no—
82C2D8×D10311yescharacteristic
subgroupG/H
centerC2D8×D103
commutatorC8×C103C23
FrattiniC8C22×D103
FittingSD32×C103C2
socleC2×C103C2×D8
hypercenterSD32D103
hypocenterC103#508
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #15693044C2semidirect
2. #15693040C2semidirect
3. #15692967C2semidirect
4. #15692966C2semidirect
5. #15692962C2semidirect
6. C16×D103C2semidirect
7. SD32×C103C2semidirect
41. C103#508semidirect
47. SD32D103semidirect