Finite Group Databasebeta

← #23781745

Subgroups — #23781745

Order 10432.

134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579684C211yesmaximal, characteristic
2D4×Dic163C211yesmaximal, characteristic, complemented
3#19104697C211yesmaximal, characteristic, complemented
4#19104668C211yesmaximal, characteristic, complemented
5#19104657C211yesmaximal, characteristic, complemented
6C8×Dic163C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×D652C2211yescharacteristic
9C22×Dic163—21no—
10C2×C4×D163—21no—
11#14579684C414yescomplemented
12C2×C163⋊C8C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14C22⋊Dic163—21no—
15(C2×D163)⋊C4—21no—
16C4×Dic163C2211yescharacteristic
17C2×D4×C163C2211yescharacteristic
18C2×C8×C163C2211yescharacteristic
19C4⋊C4×C163C2211yescharacteristic
20C22×D163—21no—
21D652—21no—
22D652C2×C412yescomplemented
23C2×Dic163—21no—
24C2×Dic163—42no—
25C2×Dic163D411yescharacteristic
26C2×Dic163D411yescharacteristic
27C4×D163—42no—
28C163⋊C8C2×C412yescomplemented
29C23×C163—21no—
30D4×C163—21no—
31D4×C163C2×C412yescomplemented
32C2×C4×C163—21no—
33C2×C4×C163C2311yescharacteristic
34C8×C163—21no—
35C22×C163—22no—
36C22×C163—41no—
37C22×C163—41no—
38C22×C163C2×D411yescharacteristic
39C2×D163—22no—
40C2×D163—41no—
41C2×D163—41no—
42C4×C163—41no—
43C4×C163C22×C411yescharacteristic
44C4×C163#4111yescharacteristic
45Dic163—21no—
46Dic163—41no—
47Dic163D812yescomplemented
48C2×C163—42no—
49C2×C163C4×D411yescharacteristic
50C2×C163C2×D811yescharacteristic
51C2×C163#13511yescharacteristic
52D163—42no—
53C163C4×D811yescharacteristic, complemented, Sylow
54C4×D8—1631nomaximal, Sylow
55C2×D8—1631no—
56C4×D4—1631no—
57C4×D4—1631no—
58#107—1631no—
59#102—1631no—
60#102D16311yescharacteristic, complemented
61C4×C8—1631no—
62C2×D4—1631no—
63C2×D4C2×D16311yescharacteristic
64C22×C4—3261no—
65C22×C4—3261no—
66D8—1634no—
67C2×C8—1631no—
68C2×C8C2×D16311yescharacteristic
69C4⋊C4—1631no—
70C4⋊C4C2×D16311yescharacteristic
71C22⋊C4—3261no—
72C22⋊C4—3261no—
73C42—1631no—
74C23—21no—
75C23—3261no—
76D4—21no—
77D4—3261no—
78D4—1632no—
79D4C4×D16312yescomplemented
80C2×C4—21no—
81C2×C4—3261no—
82C2×C4—6522no—
83C2×C4—6522no—
84C2×C4—1631no—
85C2×C4—1631no—
86C2×C4C22×D16311yescharacteristic
87C8—21no—
88C8—1632no—
89C22—22no—
90C22—41no—
91C22—41no—
92C22—3262no—
93C22—6521no—
94C22—6521no—
95C22D4×D16311yescharacteristic
96C4—41no—
97C4—3261no—
98C4—6521no—
99C4—1632no—
100C4C2×C4×D16311yescharacteristic
101C4#1457969811yescharacteristic
102C2—42no—
103C2—6522no—
104C2(C22⋊D163)⋊C411yescharacteristic
105C2D8×D16311yescharacteristic
106C2#1910475611yescharacteristic
subgroupG/H
centerC22D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579684C2
cosocleC2×C4×C163C23
hypercenter#102D163
hypocenterC163C4×D8
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D4×Dic163C2semidirect
3. #19104697C2semidirect
4. #19104668C2semidirect
5. #19104657C2semidirect
6. C8×Dic163C2semidirect
7. #102×C163C2semidirect
11. #14579684C4semidirect
22. D652C2×C4semidirect
28. C163⋊C8C2×C4semidirect
31. D4×C163C2×C4semidirect
47. Dic163D8semidirect
53. C163C4×D8semidirect
60. #102D163semidirect
79. D4C4×D163semidirect