Finite Group Databasebeta

← #23781985

Subgroups — #23781985

Order 10432.

114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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
2C4⋊C4×D163C211yesmaximal, characteristic, complemented
3#19104666C211yesmaximal, 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×D163—21no—
11C2×C4×D163C2211yescharacteristic
12C2×C163⋊C8C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15(C2×D163)⋊C4—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—
28C4×D163—42no—
29C163⋊C8—21no—
30C2×C4×C163—21no—
31C2×C4×C163—21no—
32C2×C4×C163C2311yescharacteristic
33C8×C163—21no—
34C22×C163C2×D411yescharacteristic
35C2×D163—21no—
36C2×D163—21no—
37C2×D163—41no—
38C2×D163—41no—
39C2×D163—41no—
40C2×D163SD1612yes—
41C4×C163—41no—
42C4×C163—41no—
43C4×C163#4111yescharacteristic
44C4×C163#4111yescharacteristic
45Dic163—21no—
46Dic163—41no—
47C2×C163#12311yescharacteristic
48C2×C163C2×SD1611yescharacteristic
49C2×C163AGL(1,ℤ/8)11yescharacteristic
50D163—22no—
51D163—81no—
52C163#48111yescharacteristic, complemented, Sylow
53#481—1631nomaximal, Sylow
54#121—1631no—
55C2×C4⋊C4—1631no—
56#106—1631no—
57#106D16311yescharacteristic, complemented
58#102—1631no—
59#102—1631no—
60C22⋊C8—1631no—
61C2×D4—3261no—
62C2×D4—1631no—
63C22×C4—3261no—
64C22×C4—1631no—
65C2×C8—1631no—
66C2×C8C2×D16311yescharacteristic
67C4⋊C4—3261no—
68C4⋊C4—1631no—
69C4⋊C4C2×D16311yescharacteristic
70C4⋊C4C2×D16311yescharacteristic
71C22⋊C4—3261no—
72C23—3261no—
73C23—1631no—
74D4—3261no—
75D4—3261no—
76D4—6522no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—3261no—
80C2×C4—3261no—
81C2×C4—3261no—
82C2×C4—6522no—
83C2×C4—1631no—
84C2×C4C22×D16311yescharacteristic
85C8—21no—
86C8—3261no—
87C22—3261no—
88C22—3261no—
89C22—6521no—
90C22—6521no—
91C22—6521no—
92C22—1632no—
93C22D4×D16311yescharacteristic
94C4—41no—
95C4—41no—
96C4—3261no—
97C4—6521no—
98C4#1457969911yescharacteristic
99C4#1457970011yescharacteristic
100C2—13041no—
101C2—3262no—
102C2#1910472011yescharacteristic
103C2SD16×D16311yescharacteristic
104C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#106×C163C2
socleC22×C163C2×D4
prime radical#19104710C2
hypercenter#106D163
hypocenterC163#481
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. C4⋊C4×D163C2semidirect
3. #19104666C2semidirect
4. #19104657C2semidirect
5. #19104655C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #106×C163C2semidirect
52. C163#481semidirect
57. #106D163semidirect