Finite Group Databasebeta

← #23781991

Subgroups — #23781991

Order 10432.

106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#19104710C211yesmaximal, characteristic
2#19104693C211yesmaximal, characteristic, complemented
3#19104668C211yesmaximal, characteristic, complemented
4#19104657C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7#106×C163C211yesmaximal, characteristic, complemented
8C2×D652—21no—
9C2×D652C2211yescharacteristic
10C2×C4×D163C2211yescharacteristic
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13(C2×D163)⋊C4—21no—
14(C2×D163)⋊C4—21no—
15C4×Dic163—21no—
16C2×C8×C163C2211yescharacteristic
17C4⋊C4×C163C2211yescharacteristic
18C4⋊C4×C163C2211yescharacteristic
19C22×D163—21no—
20C22×D163D411yescharacteristic
21D652—21no—
22D652—21no—
23D652—42no—
24C2×Dic163—21no—
25C2×Dic163D411yescharacteristic
26C4×D163—21no—
27C4×D163—21no—
28C163⋊C8—21no—
29C2×C4×C163—21no—
30C2×C4×C163—21no—
31C2×C4×C163C2311yescharacteristic
32C8×C163—21no—
33C22×C163C2×D411yescharacteristic
34C2×D163—21no—
35C2×D163—21no—
36C2×D163—21no—
37C2×D163—41no—
38C2×D163—41no—
39C2×D163—41no—
40C4×C163—41no—
41C4×C163—41no—
42C4×C163#4111yescharacteristic
43C4×C163#4111yescharacteristic
44Dic163—21no—
45Dic163—41no—
46C2×C163#12311yescharacteristic
47C2×C163#13511yescharacteristic
48C2×C163AGL(1,ℤ/8)11yescharacteristic
49D163—41no—
50D163—81no—
51C163#48211yescharacteristic, complemented, Sylow
52#482—1631nomaximal, Sylow
53#121—1631no—
54#117—1631no—
55#107—1631no—
56#106D16311yescharacteristic, complemented
57#102—1631no—
58#102—1631no—
59C22⋊C8—1631no—
60C2×D4—3261no—
61C2×D4—1631no—
62C22×C4—1631no—
63C2×C8—1631no—
64C2×C8C2×D16311yescharacteristic
65C4⋊C4—1631no—
66C4⋊C4C2×D16311yescharacteristic
67C4⋊C4C2×D16311yescharacteristic
68C22⋊C4—3261no—
69C22⋊C4—3261no—
70C42—3261no—
71C23—3261no—
72C23—1631no—
73D4—3261no—
74D4—3261no—
75D4—6522no—
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—3261no—
79C2×C4—3261no—
80C2×C4—3261no—
81C2×C4—1631no—
82C2×C4C22×D16311yescharacteristic
83C8—21no—
84C8—3261no—
85C22—3261no—
86C22—3261no—
87C22—3261no—
88C22—6521no—
89C22—6521no—
90C22—6521no—
91C22D4×D16311yescharacteristic
92C4—41no—
93C4—41no—
94C4—3261no—
95C4—6521no—
96C4#1457969911yescharacteristic
97C4#1457970011yescharacteristic
98C2—13041no—
99C2—6521no—
100C2#1910472011yescharacteristic
101C2#1910475611yescharacteristic
102C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#106×C163C2
socleC22×C163C2×D4
prime radical#19104710C2
hypercenter#106D163
hypocenterC163#482
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #19104693C2semidirect
3. #19104668C2semidirect
4. #19104657C2semidirect
5. #19104655C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #106×C163C2semidirect
51. C163#482semidirect
56. #106D163semidirect