Finite Group Databasebeta

← #23781775

Subgroups — #23781775

Order 10432.

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

normal subgroups only

This group has 132 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
2C4×D652C211yesmaximal, characteristic, complemented
3#19104666C211yesmaximal, characteristic, complemented
4#19104656C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic, complemented
6#19104646C211yesmaximal, characteristic, complemented
7C4×D4×C163C211yesmaximal, characteristic, complemented
8C2×D652C2211yescharacteristic
9C2×C4×D163—21no—
10#14579684C414yescomplemented
11C2×C163⋊C8C2211yescharacteristic
12C2×C163⋊C8C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14(C2×D163)⋊C4—21no—
15C2×D4×C163C2211yescharacteristic
16C22×C4×C163—21no—
17C4⋊C4×C163C2211yescharacteristic
18C22⋊C4×C163—21no—
19C42×C163C2211yescharacteristic
20C22×D163—21no—
21D652—21no—
22D652C2×C412yescomplemented
23C2×Dic163—21no—
24C4×D163—42no—
25C163⋊C8—21no—
26C163⋊C8C2×C412yescomplemented
27C23×C163—21no—
28D4×C163—21no—
29D4×C163C2×C412yescomplemented
30C2×C4×C163—21no—
31C2×C4×C163—42no—
32C2×C4×C163D411yescharacteristic
33C2×C4×C163D411yescharacteristic
34C2×C4×C163C2311yescharacteristic
35C22×C163—22no—
36C22×C163—41no—
37C22×C163—41no—
38C22×C163C2×D411yescharacteristic
39C2×D163—22no—
40C2×D163—41no—
41C2×D163—41no—
42C4×C163—21no—
43C4×C163—21no—
44C4×C163—41no—
45C4×C163C22×C411yescharacteristic
46C4×C163#4111yescharacteristic
47Dic163—41no—
48C2×C163—42no—
49C2×C163C4×D411yescharacteristic
50C2×C163AGL(1,ℤ/8)11yescharacteristic
51C2×C163AGL(1,ℤ/8)11yescharacteristic
52D163—42no—
53C163#44211yescharacteristic, complemented, Sylow
54#442—1631nomaximal, Sylow
55C2×D8—1631no—
56C4×D4—1631no—
57C4×D4D16311yescharacteristic, complemented
58#106—1631no—
59#102—1631no—
60#102—1631no—
61#97—1631no—
62C2×D4—1631no—
63C2×D4C2×D16311yescharacteristic
64C22×C4—21no—
65C22×C4—3261no—
66D8—1634no—
67C2×C8—1631no—
68C2×C8—1631no—
69C4⋊C4—1631no—
70C4⋊C4C2×D16311yescharacteristic
71C22⋊C4—21no—
72C22⋊C4—3261no—
73C42C2×D16311yescharacteristic
74C23—21no—
75C23—3261no—
76D4—21no—
77D4—3261no—
78D4—1632no—
79D4C4×D16312yescomplemented
80C2×C4—21no—
81C2×C4—42no—
82C2×C4—3261no—
83C2×C4—6522no—
84C2×C4C22⋊D16311yescharacteristic
85C2×C4C22⋊D16311yescharacteristic
86C2×C4C22×D16311yescharacteristic
87C8—3261no—
88C8—1632no—
89C22—22no—
90C22—41no—
91C22—41no—
92C22—3262no—
93C22—6521no—
94C22—6521no—
95C22C2×C22⋊D16311yescharacteristic
96C4—21no—
97C4—21no—
98C4—41no—
99C4—6521no—
100C4C2×C4×D16311yescharacteristic
101C4#1457969911yescharacteristic
102C2—42no—
103C2—6522no—
104C2C4×C22⋊D16311yescharacteristic
105C2#1910476011yescharacteristic
106C2#1910476111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
FittingC4×D4×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579684C2
cosocleC2×C4×C163C23
hypercenterC4×D4D163
hypocenterC163#442
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D652C2semidirect
3. #19104666C2semidirect
4. #19104656C2semidirect
5. #19104655C2semidirect
6. #19104646C2semidirect
7. C4×D4×C163C2semidirect
10. #14579684C4semidirect
22. D652C2×C4semidirect
26. C163⋊C8C2×C4semidirect
29. D4×C163C2×C4semidirect
53. C163#442semidirect
57. C4×D4D163semidirect
79. D4C4×D163semidirect