Finite Group Databasebeta

← #23781859

Subgroups — #23781859

Order 10432.

140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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×D1304C211yesmaximal, characteristic, complemented
2C2×#14579684C211yesmaximal, characteristic, complemented
3#19104731C211yesmaximal, characteristic, complemented
4#19104697C211yesmaximal, characteristic, complemented
5Dic163⋊C8C211yesmaximal, characteristic, complemented
6#19104655C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×D652C2211yescharacteristic
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—21no—
11C2×C22⋊D163—21no—
12C2×C4×D163—21no—
13D1304—22no—
14#14579684—22no—
15C2×C163⋊C8C2211yescharacteristic
16(C2×D163)⋊C4—21no—
17C4×Dic163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163—21no—
22C22×D163—21no—
23D652—21no—
24D652—21no—
25D652—21no—
26D652D412yescomplemented
27C22⋊D163—42no—
28C22⋊D163—42no—
29C2×Dic163D411yescharacteristic
30C2×Dic163D411yescharacteristic
31C4×D163—42no—
32C163⋊C8—21no—
33C23×C163—21no—
34D4×C163—21no—
35D4×C163—21no—
36C2×C4×C163—21no—
37C2×C4×C163C2311yescharacteristic
38C8×C163—21no—
39C22×C163—41no—
40C22×C163—41no—
41C22×C163—41no—
42C22×C163C2×D411yescharacteristic
43C2×D163—22no—
44C2×D163—41no—
45C2×D163—41no—
46C2×D163—41no—
47C2×D163—41no—
48C2×D163—41no—
49C4×C163—41no—
50C4×C163C2×D411yescharacteristic
51C4×C163#4111yescharacteristic
52Dic163—21no—
53Dic163D812yescomplemented
54C2×C163—81no—
55C2×C163#12111yescharacteristic
56C2×C163C2×D811yescharacteristic
57C2×C163AGL(1,ℤ/8)11yescharacteristic
58D163—42no—
59D163—81no—
60C163#45911yescharacteristic, complemented, Sylow
61#459—1631nomaximal, Sylow
62C2×D8—1631no—
63C2×D8—1631no—
64#127—1631no—
65C4×D4—1631no—
66C4⋊C8—1631no—
67#102—1631no—
68#102D16311yescharacteristic, complemented
69C2×D4—3261no—
70C2×D4—3261no—
71C2×D4—1631no—
72C2×D4—1631no—
73C2×D4C2×D16311yescharacteristic
74C22×C4—3261no—
75D8—3262no—
76D8—3262no—
77C2×C8—1631no—
78C2×C8C2×D16311yescharacteristic
79C4⋊C4C2×D16311yescharacteristic
80C22⋊C4—3261no—
81C42—1631no—
82C23—21no—
83C23—3261no—
84C23—3261no—
85D4—21no—
86D4—21no—
87D4—3261no—
88D4—3261no—
89D4—3261no—
90D4—6522no—
91D4—6522no—
92D4—1632no—
93C2×C4—21no—
94C2×C4—6522no—
95C2×C4—1631no—
96C2×C4—1631no—
97C2×C4C22×D16311yescharacteristic
98C8—21no—
99C8—3261no—
100C22—41no—
101C22—41no—
102C22—41no—
103C22—3262no—
104C22—6521no—
105C22—6521no—
106C22—6521no—
107C22—6521no—
108C22—6521no—
109C22D4×D16311yescharacteristic
110C4—41no—
111C4—3261no—
112C4—1632no—
113C4D4×D16311yescharacteristic
114C4#1457969911yescharacteristic
115C2—81no—
116C2—13041no—
117C2—6522no—
118C2#1910470811yescharacteristic
119C2D8×D16311yescharacteristic
120C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
hypercenter#102D163
hypocenterC163#459
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×D1304C2semidirect
2. C2×#14579684C2semidirect
3. #19104731C2semidirect
4. #19104697C2semidirect
5. Dic163⋊C8C2semidirect
6. #19104655C2semidirect
7. #102×C163C2semidirect
26. D652D4semidirect
53. Dic163D8semidirect
60. C163#459semidirect
68. #102D163semidirect