Finite Group Databasebeta

← #23781987

Subgroups — #23781987

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#19104706C211yesmaximal, characteristic
2#19104693C211yesmaximal, characteristic, complemented
3#19104669C211yesmaximal, characteristic, complemented
4#19104666C211yesmaximal, characteristic, complemented
5#19104656C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×C22⋊D163—21no—
9C2×C4×D163C2211yescharacteristic
10C2×C163⋊C8C2211yescharacteristic
11C4⋊Dic163C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13C22⋊Dic163—21no—
14(C2×D163)⋊C4—21no—
15C4×Dic163—21no—
16C2×D4×C163C2211yescharacteristic
17C2×C8×C163C2211yescharacteristic
18C4⋊C4×C163C2211yescharacteristic
19C22×D163D411yescharacteristic
20C22⋊D163—42no—
21C2×Dic163—21no—
22C2×Dic163—21no—
23C2×Dic163D411yescharacteristic
24C4×D163—21no—
25C4×D163—21no—
26C163⋊C8—21no—
27C23×C163—21no—
28D4×C163—21no—
29D4×C163—21no—
30C2×C4×C163—21no—
31C2×C4×C163C2311yescharacteristic
32C8×C163—21no—
33C22×C163—41no—
34C22×C163—41no—
35C22×C163—41no—
36C22×C163C2×D411yescharacteristic
37C2×D163—21no—
38C2×D163—21no—
39C2×D163—21no—
40C4×C163—41no—
41C4×C163#4111yescharacteristic
42C4×C163#4111yescharacteristic
43Dic163—21no—
44Dic163—41no—
45Dic163—41no—
46C2×C163—81no—
47C2×C163#12311yescharacteristic
48C2×C163#13511yescharacteristic
49C2×C163AGL(1,ℤ/8)11yescharacteristic
50D163—41no—
51C163#48211yescharacteristic, complemented, Sylow
52#482—1631nomaximal, Sylow
53#121—1631no—
54#117—1631no—
55#107—1631no—
56#106—1631no—
57#102—1631no—
58#102D16311yescharacteristic, complemented
59C22⋊C8—1631no—
60C2×D4—3261no—
61C2×D4C2×D16311yescharacteristic
62C22×C4—1631no—
63C2×C8—1631no—
64C2×C8C2×D16311yescharacteristic
65C4⋊C4—1631no—
66C4⋊C4—1631no—
67C4⋊C4C2×D16311yescharacteristic
68C22⋊C4—3261no—
69C22⋊C4—3261no—
70C42—3261no—
71C23—21no—
72C23—1631no—
73D4—21no—
74D4—21no—
75D4—6522no—
76C2×C4—21no—
77C2×C4—3261no—
78C2×C4—3261no—
79C2×C4—3261no—
80C2×C4—3261no—
81C2×C4—1631no—
82C2×C4C22×D16311yescharacteristic
83C8—21no—
84C8—3261no—
85C22—41no—
86C22—41no—
87C22—41no—
88C22—3261no—
89C22—3261no—
90C22—3261no—
91C22D4×D16311yescharacteristic
92C4—41no—
93C4—3261no—
94C4—6521no—
95C4—6521no—
96C4#1457969811yescharacteristic
97C4#1457969911yescharacteristic
98C2—81no—
99C2—6521no—
100C2#1910471711yescharacteristic
101C2#1910475411yescharacteristic
102C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radical#19104706C2
hypercenter#102D163
hypocenterC163#482
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
2. #19104693C2semidirect
3. #19104669C2semidirect
4. #19104666C2semidirect
5. #19104656C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #102×C163C2semidirect
51. C163#482semidirect
58. #102D163semidirect