Finite Group Databasebeta

← #23781766

Subgroups — #23781766

Order 10432.

120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 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
1Q8×Dic163C211yesmaximal, characteristic, complemented
2D4×Dic163C211yesmaximal, characteristic
3#19104669C211yesmaximal, characteristic, complemented
4#19104659C211yesmaximal, characteristic, complemented
5#19104656C211yesmaximal, characteristic
6#19104645C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic
8C22×Dic163—21no—
9C2×C163⋊C8C2211yescharacteristic
10C4⋊Dic163—21no—
11C4⋊Dic163C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13C22⋊Dic163—21no—
14C4×Dic163—21no—
15C4×Dic163C2211yescharacteristic
16C2×Q8×C163C2211yescharacteristic
17C2×D4×C163C2211yescharacteristic
18SD16×C163C414yescomplemented
19C2×C8×C163C2211yescharacteristic
20C2×Dic163—21no—
21C2×Dic163—21no—
22C2×Dic163—42no—
23C2×Dic163D411yescharacteristic
24C2×Dic163D411yescharacteristic
25C163⋊C8—21no—
26C23×C163—21no—
27Q8×C163—21no—
28Q8×C163C2×C412yescomplemented
29D4×C163—21no—
30D4×C163C2×C412yes—
31C2×C4×C163—21no—
32C2×C4×C163C2311yescharacteristic
33C8×C163C2×C412yescomplemented
34C22×C163—22no—
35C22×C163—41no—
36C22×C163—41no—
37C22×C163C2×D411yescharacteristic
38C4×C163—22no—
39C4×C163C22×C411yescharacteristic
40C4×C163#4111yescharacteristic
41Dic163—21no—
42Dic163—21no—
43Dic163—41no—
44Dic163—41no—
45C2×C163—42no—
46C2×C163C4×D411yescharacteristic
47C2×C163AGL(1,ℤ/8)11yescharacteristic
48C2×C163#13711yescharacteristic
49C163#44011yescharacteristic, complemented, Sylow
50#440—1631nomaximal, Sylow
51C2×SD16D16311yescharacteristic
52C4×Q8—1631no—
53C4×D4—1631no—
54#107—1631no—
55#103—1631no—
56#102—1631no—
57#97—1631no—
58C2×Q8C2×D16311yescharacteristic
59C2×D4C2×D16311yescharacteristic
60C22×C4—3261no—
61SD16Dic16314yescomplemented
62C2×C8—1631no—
63C2×C8C2×D16311yescharacteristic
64C4⋊C4—3261no—
65C4⋊C4—1631no—
66C4⋊C4—1631no—
67C22⋊C4—3261no—
68C42—3261no—
69C42—1631no—
70C23—21no—
71Q8—21no—
72Q8C2×Dic16312yescomplemented
73D4—21no—
74D4C2×Dic16312yes—
75C2×C4—21no—
76C2×C4—3261no—
77C2×C4—3261no—
78C2×C4—6522no—
79C2×C4—1631no—
80C2×C4—1631no—
81C2×C4C22×D16311yescharacteristic
82C8—3261no—
83C8C2×Dic16312yescomplemented
84C22—22no—
85C22—41no—
86C22—41no—
87C22D4×D16311yescharacteristic
88C4—22no—
89C4—3261no—
90C4—3261no—
91C4—6521no—
92C4—6521no—
93C4C22×Dic16311yescharacteristic
94C4#1457969811yescharacteristic
95C2—42no—
96C2D4×Dic16311yescharacteristic
97C2#1910476211yescharacteristic
98C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radicalC2×D4×C163C22
cosocleC2×C4×C163C23
hypercenterC2×SD16D163
hypocenterC163#440
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic163C2semidirect
3. #19104669C2semidirect
4. #19104659C2semidirect
6. #19104645C2semidirect
18. SD16×C163C4semidirect
28. Q8×C163C2×C4semidirect
33. C8×C163C2×C4semidirect
49. C163#440semidirect
61. SD16Dic163semidirect
72. Q8C2×Dic163semidirect
83. C8C2×Dic163semidirect