Finite Group Databasebeta

← #23782010

Subgroups — #23782010

Order 10432.

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

normal subgroups only

This group has 118 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
1#19104734C211yesmaximal, characteristic, complemented
2#19104731C211yesmaximal, characteristic
3#19104657C211yesmaximal, characteristic, complemented
4#19104656C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic, complemented
6C8×Dic163C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×Dic326—21no—
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—21no—
11C2×C22⋊D163—21no—
12C2×C163⋊C8C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15C4×Dic163C2211yescharacteristic
16C2×D4×C163C2211yescharacteristic
17C2×C8×C163C2211yescharacteristic
18C4⋊C4×C163C2211yescharacteristic
19C22×D163—21no—
20Dic326—42no—
21D652—21no—
22D652—21no—
23C22⋊D163—42no—
24C22⋊D163—42no—
25C2×Dic163—21no—
26C2×Dic163D411yescharacteristic
27C2×Dic163D411yescharacteristic
28C163⋊C8—21no—
29C23×C163—21no—
30D4×C163—21no—
31D4×C163—21no—
32C2×C4×C163—21no—
33C2×C4×C163C2311yescharacteristic
34C8×C163—21no—
35C22×C163—41no—
36C22×C163—41no—
37C22×C163—41no—
38C22×C163C2×D411yescharacteristic
39C2×D163—41no—
40C2×D163—41no—
41C2×D163—41no—
42C4×C163—41no—
43C4×C163#4111yescharacteristic
44C4×C163#4111yescharacteristic
45Dic163—41no—
46Dic163D812yes—
47Dic163SD1612yes—
48C2×C163—81no—
49C2×C163#12411yescharacteristic
50C2×C163C2×D811yescharacteristic
51C2×C163C2×SD1611yescharacteristic
52D163—81no—
53C163#48611yescharacteristic, complemented, Sylow
54#486—1631nomaximal, Sylow
55C4⋊Q8—1631no—
56#127—1631no—
57#102—1631no—
58#102—1631no—
59#102—1631no—
60#102D16311yescharacteristic, complemented
61C4×C8—1631no—
62C2×Q8—3261no—
63C2×D4—3261no—
64C2×D4—3261no—
65C2×D4—1631no—
66C2×D4C2×D16311yescharacteristic
67C2×C8—1631no—
68C2×C8C2×D16311yescharacteristic
69C4⋊C4—3261no—
70C4⋊C4—1631no—
71C4⋊C4C2×D16311yescharacteristic
72C42—1631no—
73C23—21no—
74C23—3261no—
75Q8—6522no—
76D4—21no—
77D4—21no—
78D4—3261no—
79D4—3261no—
80D4—6522no—
81D4—6522no—
82C2×C4—21no—
83C2×C4—3261no—
84C2×C4—1631no—
85C2×C4—1631no—
86C2×C4C22×D16311yescharacteristic
87C8—21no—
88C8—3261no—
89C22—41no—
90C22—41no—
91C22—41no—
92C22—6521no—
93C22—6521no—
94C22—6521no—
95C22D4×D16311yescharacteristic
96C4—41no—
97C4—6521no—
98C4—1632no—
99C4—1632no—
100C4#1457969811yescharacteristic
101C4#1457969911yescharacteristic
102C2—81no—
103C2—13041no—
104C2#1910472111yescharacteristic
105C2D8×D16311yescharacteristic
106C2SD16×D16311yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radical#19104731C2
hypercenter#102D163
hypocenterC163#486
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
1. #19104734C2semidirect
3. #19104657C2semidirect
4. #19104656C2semidirect
5. #19104655C2semidirect
6. C8×Dic163C2semidirect
7. #102×C163C2semidirect
53. C163#486semidirect
60. #102D163semidirect