Finite Group Databasebeta

← #23781690

Subgroups — #23781690

Order 10432.

114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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×#14579682C211yesmaximal, characteristic
2C2×C8×D163C211yesmaximal, characteristic
3#19104692C211yesmaximal, characteristic
4C4⋊(C163⋊C8)C211yesmaximal, characteristic, complemented
5Dic163⋊C8C211yesmaximal, characteristic, complemented
6Dic163⋊C8C211yesmaximal, characteristic, complemented
7C4⋊C8×C163C211yesmaximal, characteristic, complemented
8C2×C4×D163C2211yescharacteristic
9#14579682—22no—
10C2×C163⋊C8C2211yescharacteristic
11C2×C163⋊C8C2211yescharacteristic
12C8×D163—22no—
13Dic163⋊C4C411yescharacteristic
14Dic163⋊C4C411yescharacteristic
15(C2×D163)⋊C4C411yescharacteristic
16(C2×D163)⋊C4C411yescharacteristic
17C4×Dic163C2211yescharacteristic
18C2×C8×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C42×C163C2211yescharacteristic
21C22×D163C2×C411yescharacteristic
22C2×Dic163C2×C411yescharacteristic
23C2×Dic163C2×C411yescharacteristic
24C2×Dic163C2×C411yescharacteristic
25C4×D163D412yes—
26C4×D163Q812yes—
27C163⋊C8—21no—
28C163⋊C8—21no—
29C2×C4×C163C2×C411yescharacteristic
30C2×C4×C163C2×C411yescharacteristic
31C2×C4×C163C2311yescharacteristic
32C8×C163—21no—
33C8×C163—21no—
34C22×C163C22×C411yescharacteristic
35C2×D163—21no—
36C2×D163—21no—
37C2×D163C4⋊C412yes—
38C4×C163—21no—
39C4×C163—21no—
40C4×C163C2×D411yescharacteristic
41C4×C163C2×Q811yescharacteristic
42Dic163—21no—
43Dic163—21no—
44Dic163C4⋊C412yes—
45C2×C163C2×C4⋊C411yescharacteristic
46C2×C163#13111yescharacteristic
47C2×C163#13111yescharacteristic
48D163—22no—
49C163#42411yescharacteristic, complemented, Sylow
50#424—1631nomaximal, Sylow
51C2×M16—1631no—
52C22×C8—1631no—
53#117—1631no—
54C4⋊C8—1631no—
55C4⋊C8—1631no—
56C4⋊C8—1631no—
57C4⋊C8D16311yescharacteristic, complemented
58C22×C4—1631no—
59M16—3262no—
60C2×C8—3262no—
61C2×C8—1631no—
62C2×C8—1631no—
63C2×C8C2×D16311yescharacteristic
64C2×C8C2×D16311yescharacteristic
65C4⋊C4—1631no—
66C4⋊C4—1631no—
67C22⋊C4—1631no—
68C22⋊C4—1631no—
69C42—1631no—
70C42C2×D16311yescharacteristic
71C23—1631no—
72C2×C4—1631no—
73C2×C4—1631no—
74C2×C4—1631no—
75C2×C4—1632no—
76C2×C4—1632no—
77C2×C4C4×D16311yescharacteristic
78C2×C4C4×D16311yescharacteristic
79C2×C4C22×D16311yescharacteristic
80C8—21no—
81C8—21no—
82C8—3261no—
83C8—3261no—
84C22—3261no—
85C22—3261no—
86C22—1632no—
87C22C2×C4×D16311yescharacteristic
88C4—21no—
89C4—21no—
90C4—3261no—
91C4—3261no—
92C4—1632no—
93C4D4×D16311yescharacteristic
94C4Q8×D16311yescharacteristic
95C2—3262no—
96C2C4⋊C4×D16311yescharacteristic
97C2#1910474111yescharacteristic
98C2#1910474311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D163
commutator, socleC22×C163C22×C4
FittingC4⋊C8×C163C2
prime radicalC22×D163C2×C4
cosocleC2×C4×C163C23
hypercenterC4⋊C8D163
hypocenterC163#424
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C4⋊(C163⋊C8)C2semidirect
5. Dic163⋊C8C2semidirect
6. Dic163⋊C8C2semidirect
7. C4⋊C8×C163C2semidirect
49. C163#424semidirect
57. C4⋊C8D163semidirect