Finite Group Databasebeta

← #23781982

Subgroups — #23781982

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#19104706C211yesmaximal, characteristic
2C4⋊C4×D163C211yesmaximal, characteristic, complemented
3#19104667C211yesmaximal, 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×D163—21no—
10C2×C4×D163C2211yescharacteristic
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15C22⋊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—
26C4×D163—42no—
27C163⋊C8—21no—
28C23×C163—21no—
29D4×C163—21no—
30D4×C163—21no—
31C2×C4×C163—21no—
32C2×C4×C163C2311yescharacteristic
33C8×C163—21no—
34C22×C163—41no—
35C22×C163—41no—
36C22×C163—41no—
37C22×C163C2×D411yescharacteristic
38C2×D163—21no—
39C2×D163—21no—
40C2×D163SD1612yes—
41C4×C163—41no—
42C4×C163#4111yescharacteristic
43C4×C163#4111yescharacteristic
44Dic163—21no—
45Dic163—41no—
46Dic163—41no—
47C2×C163—81no—
48C2×C163#12311yescharacteristic
49C2×C163C2×SD1611yescharacteristic
50C2×C163AGL(1,ℤ/8)11yescharacteristic
51D163—22no—
52C163#48111yescharacteristic, complemented, Sylow
53#481—1631nomaximal, Sylow
54#121—1631no—
55C2×C4⋊C4—1631no—
56#106—1631no—
57#106—1631no—
58#102—1631no—
59#102D16311yescharacteristic, complemented
60C22⋊C8—1631no—
61C2×D4—3261no—
62C2×D4C2×D16311yescharacteristic
63C22×C4—3261no—
64C22×C4—1631no—
65C2×C8—1631no—
66C2×C8C2×D16311yescharacteristic
67C4⋊C4—3261no—
68C4⋊C4—1631no—
69C4⋊C4—1631no—
70C4⋊C4C2×D16311yescharacteristic
71C22⋊C4—3261no—
72C23—21no—
73C23—1631no—
74D4—21no—
75D4—21no—
76D4—6522no—
77C2×C4—21no—
78C2×C4—3261no—
79C2×C4—3261no—
80C2×C4—3261no—
81C2×C4—3261no—
82C2×C4—6522no—
83C2×C4—1631no—
84C2×C4C22×D16311yescharacteristic
85C8—21no—
86C8—3261no—
87C22—41no—
88C22—41no—
89C22—41no—
90C22—3261no—
91C22—3261no—
92C22—1632no—
93C22D4×D16311yescharacteristic
94C4—41no—
95C4—3261no—
96C4—6521no—
97C4—6521no—
98C4#1457969811yescharacteristic
99C4#1457969911yescharacteristic
100C2—81no—
101C2—3262no—
102C2#1910471711yescharacteristic
103C2SD16×D16311yescharacteristic
104C2#1910475911yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radical#19104706C2
hypercenter#102D163
hypocenterC163#481
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. C4⋊C4×D163C2semidirect
3. #19104667C2semidirect
4. #19104666C2semidirect
5. #19104656C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #102×C163C2semidirect
52. C163#481semidirect
59. #102D163semidirect