Finite Group Databasebeta

← #23781808

Subgroups — #23781808

Order 10432.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14579699C211yesmaximal, characteristic, complemented
2C2×#14579687C211yesmaximal, characteristic, complemented
3C2×#14579684C211yesmaximal, characteristic, complemented
4#19104658C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic, complemented
6C22⋊(C163⋊C8)C211yesmaximal, characteristic, complemented
7#121×C163C211yesmaximal, characteristic, complemented
8#14579699—22no—
9#14579699—22no—
10C2×Dic326C2211yescharacteristic
11C2×D652C2211yescharacteristic
12C2×C22⋊D163—21no—
13C2×C4×D163—21no—
14#14579687—22no—
15#14579684—22no—
16C2×C163⋊C8C2211yescharacteristic
17C2×C163⋊C8C2211yescharacteristic
18C2×D4×C163—21no—
19C2×D4×C163C2211yescharacteristic
20C22×C4×C163C2211yescharacteristic
21C4⋊C4×C163C2211yescharacteristic
22C22⋊C4×C163—21no—
23C22×D163—21no—
24Dic326—21no—
25Dic326D412yescomplemented
26D652—21no—
27D652D412yescomplemented
28C22⋊D163—24no—
29C2×Dic163—21no—
30C4×D163—24no—
31C163⋊C8—21no—
32C163⋊C8—21no—
33C23×C163—21no—
34C23×C163D411yescharacteristic
35D4×C163—21no—
36D4×C163—21no—
37D4×C163—42no—
38C2×C4×C163—21no—
39C2×C4×C163—21no—
40C2×C4×C163—21no—
41C2×C4×C163D411yescharacteristic
42C2×C4×C163C2311yescharacteristic
43C22×C163—21no—
44C22×C163—21no—
45C22×C163—21no—
46C22×C163—41no—
47C22×C163—41no—
48C22×C163—41no—
49C22×C163C2×D411yescharacteristic
50C2×D163—22no—
51C2×D163—41no—
52C2×D163—41no—
53C4×C163—21no—
54C4×C163—41no—
55C4×C163C2×D411yescharacteristic
56C4×C163C2×D411yescharacteristic
57Dic163—22no—
58C2×C163—41no—
59C2×C163—81no—
60C2×C163#12011yescharacteristic
61C2×C163#13511yescharacteristic
62C2×C163AGL(1,ℤ/8)11yescharacteristic
63D163—42no—
64C163#44911yescharacteristic, complemented, Sylow
65#449—1631nomaximal, Sylow
66C2×#41—1631no—
67C2×SD16—1631no—
68C2×D8—1631no—
69#121D16311yescharacteristic, complemented
70#103—1631no—
71#102—1631no—
72C22⋊C8—1631no—
73#41—3262no—
74#41—3262no—
75C2×Q8—1631no—
76C2×D4—21no—
77C2×D4—3261no—
78C2×D4—1631no—
79C2×D4C2×D16311yescharacteristic
80C22×C4—3261no—
81C22×C4C2×D16311yescharacteristic
82SD16—3262no—
83D8—3262no—
84C2×C8—1631no—
85C2×C8—1631no—
86C4⋊C4C2×D16311yescharacteristic
87C22⋊C4—21no—
88C23—21no—
89C23—3261no—
90C23C22⋊D16311yescharacteristic
91Q8—3261no—
92Q8—1632no—
93D4—21no—
94D4—21no—
95D4—42no—
96D4—3264no—
97D4—3261no—
98D4—1632no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—3264no—
103C2×C4—3261no—
104C2×C4C22⋊D16311yescharacteristic
105C2×C4C22×D16311yescharacteristic
106C8—3261no—
107C8—3261no—
108C22—21no—
109C22—21no—
110C22—21no—
111C22—41no—
112C22—41no—
113C22—41no—
114C22—3262no—
115C22—6521no—
116C22—6521no—
117C22C2×C22⋊D16311yescharacteristic
118C4—21no—
119C4—41no—
120C4—3262no—
121C4D4×D16311yescharacteristic
122C4D4×D16311yescharacteristic
123C2—41no—
124C2—81no—
125C2—6522no—
126C2#1910470311yescharacteristic
127C2#1910475511yescharacteristic
128C2#1910476111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#121×C163C2
socleC22×C163C2×D4
hypercenter#121D163
hypocenterC163#449
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#14579699C2semidirect
2. C2×#14579687C2semidirect
3. C2×#14579684C2semidirect
4. #19104658C2semidirect
5. #19104655C2semidirect
6. C22⋊(C163⋊C8)C2semidirect
7. #121×C163C2semidirect
25. Dic326D4semidirect
27. D652D4semidirect
64. C163#449semidirect
69. #121D163semidirect