Finite Group Databasebeta

← #20268225

Subgroups — #20268225

Order 6592.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15693040C211yesmaximal, characteristic, complemented
2D8×D103C211yesmaximal, characteristic, complemented
3#15692966C211yesmaximal, characteristic, complemented
4#15692965C211yesmaximal, characteristic, complemented
5#15692962C211yesmaximal, characteristic, complemented
6#15692960C211yesmaximal, characteristic, complemented
7D16×C103C211yesmaximal, characteristic, complemented
8#13110104—21no—
9D4×D103—21no—
10Dic412C2211yescharacteristic, complemented
11#13110093—21no—
12D824C2211yescharacteristic
13#13110090—21no—
14C8×D103C2211yescharacteristic
15C103⋊C16C2211yescharacteristic, complemented
16D8×C103C2211yescharacteristic
17D8×C103C2211yescharacteristic, complemented
18C16×C103C2211yescharacteristic, complemented
19C22×D103—41no—
20D4×C103—21no—
21D4×C103—21no—
22C22⋊D103—41no—
23C22⋊D103—41no—
24C2×Dic103—41no—
25D412—21no—
26C4×D103D411yescharacteristic
27Dic206—21no—
28C8×C103C2311yescharacteristic
29C103⋊C8D411yescharacteristic
30C22×C103—41no—
31C22×C103—41no—
32C2×D103—41no—
33C2×D103—82no—
34C2×D103D811yescharacteristic
35C4×C103C2×D411yescharacteristic
36Dic103—41no—
37Dic103D811yescharacteristic
38C2×C103—81no—
39C2×C103—81no—
40C2×C103C2×D811yescharacteristic
41D103—21no—
42D103—81no—
43C103#50911yescharacteristic, complemented, Sylow
44#509—1031nomaximal, Sylow
45#135—1031no—
46C2×D8—1031no—
47SD32—1031no—
48SD32—1031no—
49D16—1031no—
50D16D10311yescharacteristic, complemented
51M32—1031no—
52#41—2061no—
53C2×D4—2061no—
54Q16—1031no—
55SD16—2061no—
56D8—1031no—
57D8—2061no—
58D8C2×D10311yescharacteristic
59D8C2×D10311yescharacteristic, complemented
60C2×C8—1031no—
61C16—1031no—
62C16C2×D10311yescharacteristic, complemented
63C23—4121no—
64Q8—2061no—
65D4—21no—
66D4—21no—
67D4—4121no—
68D4—4121no—
69D4—2061no—
70C2×C4—1031no—
71C2×C4—4121no—
72C8—1031no—
73C8C22×D10311yescharacteristic
74C22—41no—
75C22—41no—
76C22—8242no—
77C22—1031no—
78C22—4121no—
79C4—1031no—
80C4—4121no—
81C4D4×D10311yescharacteristic
82C2—81no—
83C2—81no—
84C2—8241no—
85C2—2061no—
86C2D8×D10311yescharacteristic
subgroupG/H
centerC2D8×D103
commutatorC8×C103C23
FrattiniC8C22×D103
FittingD16×C103C2
socleC2×C103C2×D8
hypercenterD16D103
hypocenterC103#509
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #15693040C2semidirect
2. D8×D103C2semidirect
3. #15692966C2semidirect
4. #15692965C2semidirect
5. #15692962C2semidirect
6. #15692960C2semidirect
7. D16×C103C2semidirect
10. Dic412C22semidirect
15. C103⋊C16C22semidirect
17. D8×C103C22semidirect
18. C16×C103C22semidirect
43. C103#509semidirect
50. D16D103semidirect
59. D8C2×D103semidirect
62. C16C2×D103semidirect