Finite Group Databasebeta

← #23781765

Subgroups — #23781765

Order 10432.

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

normal subgroups only

This group has 120 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×#14579687C211yesmaximal, characteristic
2C4×Dic326C211yesmaximal, characteristic, complemented
3#19104668C211yesmaximal, characteristic, complemented
4#19104658C211yesmaximal, characteristic, complemented
5#19104656C211yesmaximal, characteristic
6#19104646C211yesmaximal, characteristic, complemented
7C4×D4×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9#14579687C414yescomplemented
10C2×C163⋊C8C2211yescharacteristic
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13Dic163⋊C4—21no—
14C4×Dic163—21no—
15C2×D4×C163C2211yescharacteristic
16C22×C4×C163—21no—
17C4⋊C4×C163C2211yescharacteristic
18C22⋊C4×C163—21no—
19C42×C163C2211yescharacteristic
20Dic326—21no—
21Dic326C2×C412yescomplemented
22C2×Dic163—21no—
23C2×Dic163—21no—
24C163⋊C8—21no—
25C163⋊C8C2×C412yescomplemented
26C23×C163—21no—
27D4×C163—21no—
28D4×C163C2×C412yes—
29C2×C4×C163—21no—
30C2×C4×C163—42no—
31C2×C4×C163D411yescharacteristic
32C2×C4×C163D411yescharacteristic
33C2×C4×C163C2311yescharacteristic
34C22×C163—22no—
35C22×C163—41no—
36C22×C163—41no—
37C22×C163C2×D411yescharacteristic
38C4×C163—21no—
39C4×C163—21no—
40C4×C163—41no—
41C4×C163C22×C411yescharacteristic
42C4×C163#4111yescharacteristic
43Dic163—22no—
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×SD16—1631no—
52C4×Q8—1631no—
53C4×D4D16311yescharacteristic
54#107—1631no—
55#103—1631no—
56#102—1631no—
57#97—1631no—
58C2×Q8—1631no—
59C2×D4C2×D16311yescharacteristic
60C22×C4—21no—
61SD16—1634no—
62C2×C8—1631no—
63C2×C8—1631no—
64C4⋊C4—3261no—
65C4⋊C4—1631no—
66C4⋊C4C2×D16311yescharacteristic
67C22⋊C4—21no—
68C42—3261no—
69C42C2×D16311yescharacteristic
70C23—21no—
71Q8—3261no—
72Q8—1632no—
73D4—21no—
74D4C4×D16312yes—
75C2×C4—21no—
76C2×C4—42no—
77C2×C4—3261no—
78C2×C4—3261no—
79C2×C4C22⋊D16311yescharacteristic
80C2×C4C22⋊D16311yescharacteristic
81C2×C4C22×D16311yescharacteristic
82C8—3261no—
83C8—1632no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22C2×C22⋊D16311yescharacteristic
88C4—21no—
89C4—21no—
90C4—41no—
91C4—3262no—
92C4—6521no—
93C4C2×C4×D16311yescharacteristic
94C4#1457969911yescharacteristic
95C2—42no—
96C2C4×C22⋊D16311yescharacteristic
97C2#1910476111yescharacteristic
98C2#1910476511yescharacteristic
subgroupG/H
centerC22C2×C22⋊D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
FittingC4×D4×C163C2
socleC22×C163C2×D4
prime radicalC2×D4×C163C22
cosocleC2×C4×C163C23
hypercenterC4×D4D163
hypocenterC163#440
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×Dic326C2semidirect
3. #19104668C2semidirect
4. #19104658C2semidirect
6. #19104646C2semidirect
9. #14579687C4semidirect
21. Dic326C2×C4semidirect
25. C163⋊C8C2×C4semidirect
49. C163#440semidirect