Finite Group Databasebeta

← #23781750

Subgroups — #23781750

Order 10432.

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

normal subgroups only

This group has 122 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×#14579686C211yesmaximal, characteristic
2Q8×Dic163C211yesmaximal, characteristic, complemented
3#19104697C211yesmaximal, characteristic
4#19104666C211yesmaximal, characteristic, complemented
5#19104657C211yesmaximal, characteristic
6C8×Dic163C211yesmaximal, characteristic, complemented
7#103×C163C211yesmaximal, characteristic, complemented
8C2×D652C2211yescharacteristic
9C2×C4×D163—21no—
10#14579686C414yescomplemented
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163—21no—
13C4⋊Dic163C2211yescharacteristic
14(C2×D163)⋊C4—21no—
15C4×Dic163—21no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×C8×C163C2211yescharacteristic
19C4⋊C4×C163C2211yescharacteristic
20C22×D163—21no—
21D652—21no—
22D652C2×C412yes—
23C2×Dic163—21no—
24C2×Dic163D411yescharacteristic
25C2×Dic163D411yescharacteristic
26C4×D163—42no—
27C163⋊C8C2×C412yescomplemented
28Q8×C163—21no—
29Q8×C163C2×C412yescomplemented
30C2×C4×C163—21no—
31C2×C4×C163—21no—
32C2×C4×C163C2311yescharacteristic
33C8×C163—21no—
34C22×C163C2×D411yescharacteristic
35C2×D163—22no—
36C2×D163—41no—
37C2×D163—41no—
38C4×C163—22no—
39C4×C163—41no—
40C4×C163C22×C411yescharacteristic
41C4×C163#4111yescharacteristic
42Dic163—21no—
43Dic163—41no—
44Dic163SD1612yescomplemented
45C2×C163C4×D411yescharacteristic
46C2×C163C2×SD1611yescharacteristic
47C2×C163#13511yescharacteristic
48D163—42no—
49C163C4×SD1611yescharacteristic, complemented, Sylow
50C4×SD16—1631nomaximal, Sylow
51C2×SD16—1631no—
52C4×Q8—1631no—
53C4×D4—1631no—
54#106—1631no—
55#103D16311yescharacteristic, complemented
56#102—1631no—
57C4×C8—1631no—
58C2×Q8C2×D16311yescharacteristic
59C2×D4—1631no—
60C22×C4—3261no—
61SD16—1634no—
62C2×C8—1631no—
63C2×C8C2×D16311yescharacteristic
64C4⋊C4—3261no—
65C4⋊C4—1631no—
66C4⋊C4C2×D16311yescharacteristic
67C22⋊C4—3261no—
68C42—3261no—
69C42—1631no—
70C23—3261no—
71Q8—21no—
72Q8C4×D16312yescomplemented
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—21no—
83C8—1632no—
84C22—3262no—
85C22—6521no—
86C22—6521no—
87C22D4×D16311yescharacteristic
88C4—22no—
89C4—41no—
90C4—3261no—
91C4—6521no—
92C4—1632no—
93C4C2×C4×D16311yescharacteristic
94C4#1457969811yescharacteristic
95C2—6522no—
96C2(C22⋊D163)⋊C411yescharacteristic
97C2SD16×D16311yescharacteristic
98C2#1910475811yescharacteristic
subgroupG/H
centerC22D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#103×C163C2
socleC22×C163C2×D4
prime radicalC2×D652C22
cosocleC2×C4×C163C23
hypercenter#103D163
hypocenterC163C4×SD16
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. Q8×Dic163C2semidirect
4. #19104666C2semidirect
6. C8×Dic163C2semidirect
7. #103×C163C2semidirect
10. #14579686C4semidirect
27. C163⋊C8C2×C4semidirect
29. Q8×C163C2×C4semidirect
44. Dic163SD16semidirect
49. C163C4×SD16semidirect
55. #103D163semidirect
72. Q8C4×D163semidirect