Finite Group Databasebeta

← #23782099

Subgroups — #23782099

Order 10432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19104754C211yesmaximal, characteristic, complemented
2D8×D163C211yesmaximal, characteristic, complemented
3#19104680C211yesmaximal, characteristic, complemented
4#19104679C211yesmaximal, characteristic, complemented
5#19104676C211yesmaximal, characteristic, complemented
6#19104674C211yesmaximal, characteristic, complemented
7D16×C163C211yesmaximal, characteristic, complemented
8#14579698—21no—
9D4×D163—21no—
10Dic652C2211yescharacteristic, complemented
11#14579687—21no—
12D1304C2211yescharacteristic
13#14579684—21no—
14C8×D163C2211yescharacteristic
15C163⋊C16C2211yescharacteristic, complemented
16D8×C163C2211yescharacteristic
17D8×C163C2211yescharacteristic, complemented
18C16×C163C2211yescharacteristic, complemented
19C22×D163—41no—
20Dic326—21no—
21D652—21no—
22C22⋊D163—41no—
23C22⋊D163—41no—
24C2×Dic163—41no—
25C4×D163D411yescharacteristic
26C163⋊C8D411yescharacteristic
27D4×C163—21no—
28D4×C163—21no—
29C8×C163C2311yescharacteristic
30C22×C163—41no—
31C22×C163—41no—
32C2×D163—41no—
33C2×D163—82no—
34C2×D163D811yescharacteristic
35C4×C163C2×D411yescharacteristic
36Dic163—41no—
37Dic163D811yescharacteristic
38C2×C163—81no—
39C2×C163—81no—
40C2×C163C2×D811yescharacteristic
41D163—21no—
42D163—81no—
43C163#50911yescharacteristic, complemented, Sylow
44#509—1631nomaximal, Sylow
45#135—1631no—
46C2×D8—1631no—
47SD32—1631no—
48SD32—1631no—
49D16—1631no—
50D16D16311yescharacteristic, complemented
51M32—1631no—
52#41—3261no—
53C2×D4—3261no—
54Q16—1631no—
55SD16—3261no—
56D8—3261no—
57D8—1631no—
58D8C2×D16311yescharacteristic
59D8C2×D16311yescharacteristic, complemented
60C2×C8—1631no—
61C16—1631no—
62C16C2×D16311yescharacteristic, complemented
63C23—6521no—
64Q8—3261no—
65D4—21no—
66D4—21no—
67D4—3261no—
68D4—6521no—
69D4—6521no—
70C2×C4—6521no—
71C2×C4—1631no—
72C8—1631no—
73C8C22×D16311yescharacteristic
74C22—41no—
75C22—41no—
76C22—13042no—
77C22—6521no—
78C22—1631no—
79C4—6521no—
80C4—1631no—
81C4D4×D16311yescharacteristic
82C2—81no—
83C2—81no—
84C2—13041no—
85C2—3261no—
86C2D8×D16311yescharacteristic
subgroupG/H
centerC2D8×D163
commutator, cosocleC8×C163C23
FrattiniC8C22×D163
FittingD16×C163C2
socleC2×C163C2×D8
hypercenterD16D163
hypocenterC163#509
LCSG ▷ C8×C163 ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #19104754C2semidirect
2. D8×D163C2semidirect
3. #19104680C2semidirect
4. #19104679C2semidirect
5. #19104676C2semidirect
6. #19104674C2semidirect
7. D16×C163C2semidirect
10. Dic652C22semidirect
15. C163⋊C16C22semidirect
17. D8×C163C22semidirect
18. C16×C163C22semidirect
43. C163#509semidirect
50. D16D163semidirect
59. D8C2×D163semidirect
62. C16C2×D163semidirect