Finite Group Databasebeta

← #23781740

Subgroups — #23781740

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×#14579683C211yesmaximal, characteristic, complemented
2C2×#14579682C211yesmaximal, characteristic, complemented
3C4×C22⋊D163C211yesmaximal, characteristic
4Dic163⋊C8C211yesmaximal, characteristic, complemented
5(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
6C8×Dic163C211yesmaximal, characteristic, complemented
7C22⋊C8×C163C211yesmaximal, characteristic, complemented
8C2×C22⋊D163C411yescharacteristic
9C2×C4×D163C2211yescharacteristic
10#14579683—22no—
11#14579682—22no—
12C2×C163⋊C8C2211yescharacteristic
13C2×C163⋊C8C2211yescharacteristic
14Dic163⋊C4C411yescharacteristic
15C22⋊Dic163C411yescharacteristic
16(C2×D163)⋊C4C411yescharacteristic
17C4×Dic163C2211yescharacteristic
18C22×C4×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C2×C8×C163C2211yescharacteristic
21C22×D163C2×C411yescharacteristic
22C22⋊D163—22no—
23C2×Dic163C2×C411yescharacteristic
24C2×Dic163C2×C411yescharacteristic
25C2×Dic163C2×C411yescharacteristic
26C4×D163—21no—
27C4×D163—21no—
28C163⋊C8—21no—
29C163⋊C8D412yescomplemented
30C23×C163C2×C411yescharacteristic
31C2×C4×C163—21no—
32C2×C4×C163—21no—
33C2×C4×C163C2×C411yescharacteristic
34C2×C4×C163C2311yescharacteristic
35C8×C163—21no—
36C8×C163—21no—
37C22×C163—21no—
38C22×C163—21no—
39C22×C163—21no—
40C22×C163C22×C411yescharacteristic
41C2×D163—21no—
42C2×D163—21no—
43C2×D163—21no—
44C4×C163—21no—
45C4×C163C2×D411yescharacteristic
46C4×C163#4111yescharacteristic
47Dic163—21no—
48Dic163—21no—
49Dic163M1612yescomplemented
50C2×C163—41no—
51C2×C163C4×D411yescharacteristic
52C2×C163C2×M1611yescharacteristic
53C2×C163#13111yescharacteristic
54D163—41no—
55C163#43611yescharacteristic, complemented, Sylow
56#436—1631nomaximal, Sylow
57C2×M16—1631no—
58C2×M16—1631no—
59C4×D4—1631no—
60C4⋊C8—1631no—
61C22⋊C8—1631no—
62C22⋊C8D16311yescharacteristic, complemented
63C4×C8—1631no—
64C2×D4—1631no—
65C22×C4—1631no—
66C22×C4C2×D16311yescharacteristic
67M16—3262no—
68M16—3262no—
69C2×C8—1631no—
70C2×C8—1631no—
71C2×C8C2×D16311yescharacteristic
72C2×C8C2×D16311yescharacteristic
73C4⋊C4—1631no—
74C22⋊C4—1631no—
75C22⋊C4—1631no—
76C42—1631no—
77C23—1631no—
78C23C4×D16311yescharacteristic
79D4—3262no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3261no—
83C2×C4—3261no—
84C2×C4—1631no—
85C2×C4—1631no—
86C2×C4—1631no—
87C2×C4C4×D16311yescharacteristic
88C2×C4C22×D16311yescharacteristic
89C8—21no—
90C8—21no—
91C8—3261no—
92C8—1632no—
93C22—21no—
94C22—21no—
95C22—21no—
96C22—3261no—
97C22—3261no—
98C22—3261no—
99C22C2×C4×D16311yescharacteristic
100C4—21no—
101C4—3261no—
102C4—3261no—
103C4—1632no—
104C4D4×D16311yescharacteristic
105C4#1457969811yescharacteristic
106C2—41no—
107C2—6521no—
108C2(C22⋊D163)⋊C411yescharacteristic
109C2M16×D16311yescharacteristic
110C2#1910474111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D163
commutator, socleC22×C163C22×C4
FittingC22⋊C8×C163C2
prime radicalC2×C22⋊D163C4
cosocleC2×C4×C163C23
hypercenterC22⋊C8D163
hypocenterC163#436
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14579683C2semidirect
2. C2×#14579682C2semidirect
4. Dic163⋊C8C2semidirect
5. (C2×D163)⋊C8C2semidirect
6. C8×Dic163C2semidirect
7. C22⋊C8×C163C2semidirect
29. C163⋊C8D4semidirect
49. Dic163M16semidirect
55. C163#436semidirect
62. C22⋊C8D163semidirect