Finite Group Databasebeta

← #23781764

Subgroups — #23781764

Order 10432.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14579688C211yesmaximal, characteristic
2#19104700C211yesmaximal, characteristic, complemented
3#19104697C211yesmaximal, characteristic
4#19104658C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic
6#19104645C211yesmaximal, characteristic, complemented
7#107×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10C2×C4×D163—21no—
11#14579688C414yescomplemented
12C2×C163⋊C8C2211yescharacteristic
13Dic163⋊C4—21no—
14(C2×D163)⋊C4—21no—
15C4×Dic163—21no—
16C4×Dic163C2211yescharacteristic
17C2×C8×C163C2211yescharacteristic
18C4⋊C4×C163C2211yescharacteristic
19C4⋊C4×C163C2211yescharacteristic
20C22×D163—21no—
21Dic326—21no—
22Dic326C2×C412yescomplemented
23D652—21no—
24D652C2×C412yes—
25C2×Dic163—21no—
26C2×Dic163D411yescharacteristic
27C2×Dic163D411yescharacteristic
28C4×D163—42no—
29C163⋊C8—21no—
30C2×C4×C163—21no—
31C2×C4×C163—21no—
32C2×C4×C163C2311yescharacteristic
33C8×C163C2×C412yescomplemented
34C22×C163C2×D411yescharacteristic
35C2×D163—22no—
36C2×D163—41no—
37C2×D163—41no—
38C4×C163—41no—
39C4×C163—41no—
40C4×C163C22×C411yescharacteristic
41C4×C163#4111yescharacteristic
42Dic163—22no—
43Dic163—21no—
44Dic163—21no—
45C2×C163C4×D411yescharacteristic
46C2×C163AGL(1,ℤ/8)11yescharacteristic
47C2×C163#13711yescharacteristic
48D163—42no—
49C163#44011yescharacteristic, complemented, Sylow
50#440—1631nomaximal, Sylow
51C2×SD16—1631no—
52C4×Q8—1631no—
53C4×D4—1631no—
54#107D16311yescharacteristic, complemented
55#103—1631no—
56#102—1631no—
57#97—1631no—
58C2×Q8—1631no—
59C2×D4—1631no—
60C22×C4—3261no—
61SD16—1634no—
62C2×C8—1631no—
63C2×C8C2×D16311yescharacteristic
64C4⋊C4—3261no—
65C4⋊C4C2×D16311yescharacteristic
66C4⋊C4C2×D16311yescharacteristic
67C22⋊C4—3261no—
68C42—3261no—
69C42—1631no—
70C23—3261no—
71Q8—3261no—
72Q8—1632no—
73D4—3261no—
74D4—1632no—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—3261no—
78C2×C4—6522no—
79C2×C4—1631no—
80C2×C4—1631no—
81C2×C4C22×D16311yescharacteristic
82C8—3261no—
83C8C4×D16312yescomplemented
84C22—3262no—
85C22—6521no—
86C22—6521no—
87C22D4×D16311yescharacteristic
88C4—41no—
89C4—41no—
90C4—3262no—
91C4—3261no—
92C4—3261no—
93C4C2×C4×D16311yescharacteristic
94C4#1457970011yescharacteristic
95C2—6522no—
96C2#1910469711yescharacteristic
97C2#1910475911yescharacteristic
98C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#107×C163C2
socleC22×C163C2×D4
prime radicalC2×D652C22
cosocleC2×C4×C163C23
hypercenter#107D163
hypocenterC163#440
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #19104700C2semidirect
4. #19104658C2semidirect
6. #19104645C2semidirect
7. #107×C163C2semidirect
11. #14579688C4semidirect
22. Dic326C2×C4semidirect
33. C8×C163C2×C4semidirect
49. C163#440semidirect
54. #107D163semidirect
83. C8C4×D163semidirect