Finite Group Databasebeta

← #23781900

Subgroups — #23781900

Order 10432.

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

normal subgroups only

This group has 134 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×#14579684C211yesmaximal, characteristic, complemented
2C2×C8×D163C211yesmaximal, characteristic, complemented
3#19104710C211yesmaximal, characteristic, complemented
4#19104706C211yesmaximal, characteristic, complemented
5#19104668C211yesmaximal, characteristic, complemented
6#19104657C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×D652—21no—
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—21no—
11C2×C4×D163C2211yescharacteristic
12#14579684—22no—
13C2×C163⋊C8C2211yescharacteristic
14C8×D163—22no—
15C4⋊Dic163C2211yescharacteristic
16C22⋊Dic163—21no—
17(C2×D163)⋊C4—21no—
18C2×D4×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163—21no—
22C22×D163D411yescharacteristic
23D652—21no—
24D652—21no—
25D652—42no—
26C22⋊D163—42no—
27C2×Dic163—21no—
28C2×Dic163D411yescharacteristic
29C4×D163—21no—
30C4×D163—21no—
31C163⋊C8D412yescomplemented
32C23×C163—21no—
33D4×C163—21no—
34D4×C163—21no—
35C2×C4×C163—21no—
36C2×C4×C163C2311yescharacteristic
37C8×C163—21no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163—41no—
41C22×C163C2×D411yescharacteristic
42C2×D163—21no—
43C2×D163—21no—
44C2×D163—41no—
45C2×D163—41no—
46C2×D163—41no—
47C2×D163D812yescomplemented
48C4×C163—41no—
49C4×C163C2×D411yescharacteristic
50C4×C163#4111yescharacteristic
51Dic163—21no—
52Dic163—41no—
53C2×C163—81no—
54C2×C163#12111yescharacteristic
55C2×C163C2×D811yescharacteristic
56C2×C163#13511yescharacteristic
57D163—22no—
58D163—81no—
59C163#46611yescharacteristic, complemented, Sylow
60#466—1631nomaximal, Sylow
61C2×D8—1631no—
62C22×C8—1631no—
63#121—1631no—
64#121—1631no—
65#107—1631no—
66#102—1631no—
67#102D16311yescharacteristic, complemented
68C2×D4—3261no—
69C2×D4—3261no—
70C2×D4—1631no—
71C2×D4C2×D16311yescharacteristic
72C22×C4—1631no—
73D8—3262no—
74C2×C8—3262no—
75C2×C8—1631no—
76C2×C8C2×D16311yescharacteristic
77C4⋊C4—1631no—
78C4⋊C4C2×D16311yescharacteristic
79C22⋊C4—3261no—
80C22⋊C4—3261no—
81C23—21no—
82C23—3261no—
83C23—1631no—
84D4—21no—
85D4—21no—
86D4—3261no—
87D4—3261no—
88D4—6522no—
89D4—6522no—
90C2×C4—21no—
91C2×C4—3261no—
92C2×C4—3261no—
93C2×C4—3261no—
94C2×C4—1631no—
95C2×C4C22×D16311yescharacteristic
96C8—21no—
97C8—1632no—
98C22—41no—
99C22—41no—
100C22—41no—
101C22—3261no—
102C22—3261no—
103C22—6521no—
104C22—6521no—
105C22—6521no—
106C22—1632no—
107C22D4×D16311yescharacteristic
108C4—41no—
109C4—3261no—
110C4—6521no—
111C4D4×D16311yescharacteristic
112C4#1457969911yescharacteristic
113C2—81no—
114C2—13041no—
115C2—3262no—
116C2#1910470811yescharacteristic
117C2D8×D16311yescharacteristic
118C2#1910475611yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
hypercenter#102D163
hypocenterC163#466
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×#14579684C2semidirect
2. C2×C8×D163C2semidirect
3. #19104710C2semidirect
4. #19104706C2semidirect
5. #19104668C2semidirect
6. #19104657C2semidirect
7. #102×C163C2semidirect
31. C163⋊C8D4semidirect
47. C2×D163D8semidirect
59. C163#466semidirect
67. #102D163semidirect