Finite Group Databasebeta

← #23781809

Subgroups — #23781809

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×#14579684C211yesmaximal, characteristic, complemented
3#19104706C211yesmaximal, characteristic, complemented
4#19104659C211yesmaximal, characteristic, complemented
5#19104657C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic, complemented
8#14579700—22no—
9#14579700—22no—
10C2×D652—21no—
11C2×D652C2211yescharacteristic
12C2×C22⋊D163—21no—
13C2×C4×D163—21no—
14C2×C4×D163C2211yescharacteristic
15#14579684—22no—
16C2×C163⋊C8C2211yescharacteristic
17C4⋊Dic163C2211yescharacteristic
18C22⋊Dic163—21no—
19C2×Q8×C163C2211yescharacteristic
20C2×D4×C163C2211yescharacteristic
21SD16×C163—22no—
22C2×C8×C163C2211yescharacteristic
23C22×D163—21no—
24C22×D163D411yescharacteristic
25D652—24no—
26D652—21no—
27D652D412yescomplemented
28C22⋊D163—42no—
29C2×Dic163—21no—
30C2×Dic163D411yescharacteristic
31C4×D163—24no—
32C4×D163—21no—
33C4×D163—21no—
34C163⋊C8—21no—
35C23×C163—21no—
36Q8×C163—21no—
37Q8×C163D412yescomplemented
38D4×C163—21no—
39D4×C163—21no—
40C2×C4×C163—21no—
41C2×C4×C163C2311yescharacteristic
42C8×C163—21no—
43C22×C163—41no—
44C22×C163—41no—
45C22×C163—41no—
46C22×C163C2×D411yescharacteristic
47C2×D163—21no—
48C2×D163—22no—
49C2×D163—21no—
50C2×D163—21no—
51C2×D163—41no—
52C2×D163—41no—
53C4×C163—22no—
54C4×C163C2×D411yescharacteristic
55C4×C163C2×D411yescharacteristic
56Dic163—21no—
57Dic163—41no—
58C2×C163—81no—
59C2×C163#12011yescharacteristic
60C2×C163#13511yescharacteristic
61C2×C163AGL(1,ℤ/8)11yescharacteristic
62D163—41no—
63D163—42no—
64C163#44911yescharacteristic, complemented, Sylow
65#449—1631nomaximal, Sylow
66C2×#41—1631no—
67C2×SD16D16311yescharacteristic, complemented
68C2×D8—1631no—
69#121—1631no—
70#103—1631no—
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×D4C2×D16311yescharacteristic
80C22×C4—3261no—
81C22×C4—1631no—
82SD16—22no—
83D8—3262no—
84C2×C8—1631no—
85C2×C8C2×D16311yescharacteristic
86C4⋊C4—1631no—
87C22⋊C4—3261no—
88C23—21no—
89C23—3261no—
90C23—1631no—
91Q8—21no—
92Q8C22⋊D16312yescomplemented
93D4—21no—
94D4—21no—
95D4—3264no—
96D4—3261no—
97D4—6522no—
98D4—1632no—
99C2×C4—21no—
100C2×C4—3264no—
101C2×C4—3261no—
102C2×C4—3261no—
103C2×C4—3261no—
104C2×C4—1631no—
105C2×C4C22×D16311yescharacteristic
106C8—21no—
107C8—3261no—
108C22—41no—
109C22—41no—
110C22—41no—
111C22—3261no—
112C22—3262no—
113C22—3261no—
114C22—3261no—
115C22—6521no—
116C22—6521no—
117C22D4×D16311yescharacteristic
118C4—22no—
119C4—3261no—
120C4—6521no—
121C4D4×D16311yescharacteristic
122C4C2×C22⋊D16311yescharacteristic
123C2—81no—
124C2—6521no—
125C2—6522no—
126C2#1910470311yescharacteristic
127C2#1910475611yescharacteristic
128C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
hypercenterC2×SD16D163
hypocenterC163#449
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14579700C2semidirect
2. C2×#14579684C2semidirect
3. #19104706C2semidirect
4. #19104659C2semidirect
5. #19104657C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. C2×SD16×C163C2semidirect
27. D652D4semidirect
37. Q8×C163D4semidirect
64. C163#449semidirect
67. C2×SD16D163semidirect
92. Q8C22⋊D163semidirect