Finite Group Databasebeta

← #23781813

Subgroups — #23781813

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×#14579700C211yesmaximal, characteristic, complemented
2C2×#14579686C211yesmaximal, characteristic, complemented
3C2×D1304C211yesmaximal, characteristic, complemented
4#19104710C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7#103×C163C211yesmaximal, characteristic, complemented
8#14579700—22no—
9#14579700—22no—
10C2×D652—21no—
11C2×D652—21no—
12C2×D652C2211yescharacteristic
13C2×D652C2211yescharacteristic
14C2×C4×D163—21no—
15C2×C4×D163C2211yescharacteristic
16#14579686—22no—
17D1304—22no—
18C2×C163⋊C8C2211yescharacteristic
19(C2×D163)⋊C4—21no—
20C2×Q8×C163C2211yescharacteristic
21C2×C8×C163C2211yescharacteristic
22C4⋊C4×C163C2211yescharacteristic
23C22×D163—21no—
24C22×D163—21no—
25C22×D163D411yescharacteristic
26D652—24no—
27D652—21no—
28D652—21no—
29D652—21no—
30D652—42no—
31D652D412yescomplemented
32C2×Dic163D411yescharacteristic
33C4×D163—24no—
34C4×D163—21no—
35C4×D163—21no—
36C163⋊C8—21no—
37Q8×C163—21no—
38Q8×C163D412yescomplemented
39C2×C4×C163—21no—
40C2×C4×C163—21no—
41C2×C4×C163C2311yescharacteristic
42C8×C163—21no—
43C22×C163C2×D411yescharacteristic
44C2×D163—21no—
45C2×D163—22no—
46C2×D163—21no—
47C2×D163—21no—
48C2×D163—41no—
49C2×D163—41no—
50C2×D163—41no—
51C2×D163—41no—
52C2×D163—41no—
53C4×C163—22no—
54C4×C163—41no—
55C4×C163C2×D411yescharacteristic
56C4×C163C2×D411yescharacteristic
57Dic163—21no—
58C2×C163#12011yescharacteristic
59C2×C163#13511yescharacteristic
60C2×C163AGL(1,ℤ/8)11yescharacteristic
61D163—41no—
62D163—42no—
63D163—81no—
64C163#44911yescharacteristic, complemented, Sylow
65#449—1631nomaximal, Sylow
66C2×#41—1631no—
67C2×SD16—1631no—
68C2×D8—1631no—
69#121—1631no—
70#103D16311yescharacteristic, complemented
71#102—1631no—
72C22⋊C8—1631no—
73#41—3262no—
74#41—3262no—
75C2×Q8C2×D16311yescharacteristic
76C2×D4—3261no—
77C2×D4—3261no—
78C2×D4—1631no—
79C2×D4—1631no—
80C22×C4—3261no—
81C22×C4—1631no—
82SD16—3262no—
83D8—3262no—
84C2×C8—1631no—
85C2×C8C2×D16311yescharacteristic
86C4⋊C4C2×D16311yescharacteristic
87C22⋊C4—3261no—
88C23—3261no—
89C23—3261no—
90C23—1631no—
91Q8—21no—
92Q8D65212yescomplemented
93D4—3264no—
94D4—3261no—
95D4—3261no—
96D4—3261no—
97D4—6522no—
98D4—1632no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3264no—
102C2×C4—3261no—
103C2×C4—3261no—
104C2×C4—1631no—
105C2×C4C22×D16311yescharacteristic
106C8—21no—
107C8—3261no—
108C22—3261no—
109C22—3262no—
110C22—3261no—
111C22—3261no—
112C22—6521no—
113C22—6521no—
114C22—6521no—
115C22—6521no—
116C22—6521no—
117C22D4×D16311yescharacteristic
118C4—22no—
119C4—41no—
120C4—3261no—
121C4D4×D16311yescharacteristic
122C4C2×D65211yescharacteristic
123C2—13041no—
124C2—6521no—
125C2—6522no—
126C2#1910470511yescharacteristic
127C2#1910475811yescharacteristic
128C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#103×C163C2
socleC22×C163C2×D4
hypercenter#103D163
hypocenterC163#449
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×#14579700C2semidirect
2. C2×#14579686C2semidirect
3. C2×D1304C2semidirect
4. #19104710C2semidirect
5. #19104655C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #103×C163C2semidirect
31. D652D4semidirect
38. Q8×C163D4semidirect
64. C163#449semidirect
70. #103D163semidirect
92. Q8D652semidirect