Finite Group Databasebeta

← #23781922

Subgroups — #23781922

Order 10432.

110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 39 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×#14579689C211yesmaximal, characteristic, complemented
2C2×#14579682C211yesmaximal, characteristic
3#19104715C211yesmaximal, characteristic
4#19104711C211yesmaximal, characteristic
5#19104666C211yesmaximal, characteristic, complemented
6#19104660C211yesmaximal, characteristic, complemented
7#103×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×C4×D163C2211yescharacteristic
10#14579689—22no—
11#14579682—22no—
12C2×C163⋊C8C2211yescharacteristic
13C4⋊Dic163—21no—
14C4⋊Dic163C2211yescharacteristic
15Dic163⋊C4—21no—
16(C2×D163)⋊C4—21no—
17(C2×D163)⋊C4—21no—
18C2×Q8×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163D411yescharacteristic
22Dic326—21no—
23Dic326—21no—
24C2×Dic163—21no—
25C2×Dic163—21no—
26C2×Dic163D411yescharacteristic
27C4×D163—21no—
28C4×D163—21no—
29C163⋊C8D412yes—
30Q8×C163—21no—
31Q8×C163—21no—
32C2×C4×C163—21no—
33C2×C4×C163—21no—
34C2×C4×C163C2311yescharacteristic
35C8×C163—21no—
36C22×C163C2×D411yescharacteristic
37C2×D163—21no—
38C2×D163—21no—
39C2×D163—21no—
40C4×C163—41no—
41C4×C163—41no—
42C4×C163C2×D411yescharacteristic
43C4×C163#4111yescharacteristic
44Dic163—21no—
45Dic163—41no—
46Dic163—41no—
47C2×C163#12111yescharacteristic
48C2×C163#13711yescharacteristic
49C2×C163#13711yescharacteristic
50D163—41no—
51C163#47011yescharacteristic, complemented, Sylow
52#470—1631nomaximal, Sylow
53C2×Q16—1631no—
54C2×M16—1631no—
55C22⋊Q8—1631no—
56C22⋊Q8—1631no—
57#106—1631no—
58#103—1631no—
59#103D16311yescharacteristic, complemented
60C2×Q8—1631no—
61C2×Q8C2×D16311yescharacteristic
62C22×C4—1631no—
63Q16—3262no—
64M16—3262no—
65C2×C8—1631no—
66C2×C8C2×D16311yescharacteristic
67C4⋊C4—3261no—
68C4⋊C4—3261no—
69C4⋊C4—1631no—
70C4⋊C4C2×D16311yescharacteristic
71C22⋊C4—3261no—
72C22⋊C4—3261no—
73C23—1631no—
74Q8—21no—
75Q8—21no—
76Q8—3261no—
77Q8—3261no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—3261no—
81C2×C4—3261no—
82C2×C4—3261no—
83C2×C4—3261no—
84C2×C4—1631no—
85C2×C4C22×D16311yescharacteristic
86C8—21no—
87C8—1632no—
88C22—3261no—
89C22—3261no—
90C22—3261no—
91C22D4×D16311yescharacteristic
92C4—41no—
93C4—41no—
94C4—3261no—
95C4—6521no—
96C4—6521no—
97C4D4×D16311yescharacteristic
98C4#1457969911yescharacteristic
99C2—6521no—
100C2#1910470811yescharacteristic
101C2#1910476411yescharacteristic
102C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#103×C163C2
socleC22×C163C2×D4
prime radicalC22×D163D4
hypercenter#103D163
hypocenterC163#470
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#14579689C2semidirect
5. #19104666C2semidirect
6. #19104660C2semidirect
7. #103×C163C2semidirect
51. C163#470semidirect
59. #103D163semidirect