Finite Group Databasebeta

← #23781912

Subgroups — #23781912

Order 10432.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#14579688C211yesmaximal, characteristic, complemented
2C2×#14579682C211yesmaximal, characteristic, complemented
3#19104715C211yesmaximal, characteristic, complemented
4#19104710C211yesmaximal, characteristic
5#19104658C211yesmaximal, characteristic, complemented
6#19104655C211yesmaximal, characteristic, complemented
7#107×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652—21no—
10C2×D652C2211yescharacteristic
11C2×C4×D163C2211yescharacteristic
12#14579688—22no—
13#14579682—22no—
14C2×C163⋊C8C2211yescharacteristic
15C4⋊Dic163—21no—
16(C2×D163)⋊C4—21no—
17(C2×D163)⋊C4—21no—
18C2×C8×C163C2211yescharacteristic
19C4⋊C4×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163—21no—
22C22×D163D411yescharacteristic
23Dic326—21no—
24Dic326—21no—
25D652—21no—
26D652—21no—
27D652—42no—
28C2×Dic163—21no—
29C2×Dic163D411yescharacteristic
30C4×D163—21no—
31C4×D163—21no—
32C163⋊C8—21no—
33C2×C4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163D412yescomplemented
37C22×C163C2×D411yescharacteristic
38C2×D163—21no—
39C2×D163—21no—
40C2×D163—21no—
41C2×D163—41no—
42C2×D163—41no—
43C2×D163—41no—
44C4×C163—41no—
45C4×C163—41no—
46C4×C163C2×D411yescharacteristic
47C4×C163#4111yescharacteristic
48Dic163—21no—
49Dic163—41no—
50C2×C163#12111yescharacteristic
51C2×C163AGL(1,ℤ/8)11yescharacteristic
52C2×C163#13711yescharacteristic
53D163—41no—
54D163—81no—
55C163#46811yescharacteristic, complemented, Sylow
56#468—1631nomaximal, Sylow
57C2×SD16—1631no—
58C2×M16—1631no—
59C22⋊Q8—1631no—
60#121—1631no—
61#107D16311yescharacteristic, complemented
62#103—1631no—
63#102—1631no—
64C2×Q8—1631no—
65C2×D4—3261no—
66C2×D4—1631no—
67C22×C4—1631no—
68SD16—3262no—
69M16—3262no—
70C2×C8—1631no—
71C2×C8C2×D16311yescharacteristic
72C4⋊C4—3261no—
73C4⋊C4C2×D16311yescharacteristic
74C4⋊C4C2×D16311yescharacteristic
75C22⋊C4—3261no—
76C22⋊C4—3261no—
77C23—3261no—
78C23—1631no—
79Q8—3261no—
80Q8—3261no—
81D4—3261no—
82D4—3261no—
83D4—6522no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—3261no—
87C2×C4—3261no—
88C2×C4—3261no—
89C2×C4—1631no—
90C2×C4C22×D16311yescharacteristic
91C8—3261no—
92C8D65212yescomplemented
93C22—3261no—
94C22—3261no—
95C22—3261no—
96C22—6521no—
97C22—6521no—
98C22—6521no—
99C22D4×D16311yescharacteristic
100C4—41no—
101C4—41no—
102C4—3261no—
103C4—6521no—
104C4C2×D65211yescharacteristic
105C4#1457970011yescharacteristic
106C2—13041no—
107C2—6521no—
108C2#1910471011yescharacteristic
109C2#1910475911yescharacteristic
110C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#107×C163C2
socleC22×C163C2×D4
prime radical#19104710C2
hypercenter#107D163
hypocenterC163#468
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#14579688C2semidirect
2. C2×#14579682C2semidirect
3. #19104715C2semidirect
5. #19104658C2semidirect
6. #19104655C2semidirect
7. #107×C163C2semidirect
36. C8×C163D4semidirect
55. C163#468semidirect
61. #107D163semidirect
92. C8D652semidirect