Finite Group Databasebeta

← #23781858

Subgroups — #23781858

Order 10432.

140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14579684C211yesmaximal, characteristic, complemented
2#19104731C211yesmaximal, characteristic, complemented
3D4×Dic163C211yesmaximal, characteristic, complemented
4Dic163⋊C8C211yesmaximal, characteristic, complemented
5#19104657C211yesmaximal, characteristic, complemented
6#19104656C211yesmaximal, characteristic, complemented
7C2×D8×C163C211yesmaximal, characteristic, complemented
8C2×D652C2211yescharacteristic
9C2×C22⋊D163—21no—
10C2×C22⋊D163—21no—
11C22×Dic163—21no—
12#14579684—22no—
13C2×C163⋊C8C2211yescharacteristic
14C4⋊Dic163C2211yescharacteristic
15C22⋊Dic163—21no—
16C4×Dic163C2211yescharacteristic
17C2×D4×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19D8×C163—22no—
20C2×C8×C163C2211yescharacteristic
21C22×D163—21no—
22D652—21no—
23D652—21no—
24C22⋊D163—42no—
25C22⋊D163—42no—
26C2×Dic163—21no—
27C2×Dic163—42no—
28C2×Dic163D411yescharacteristic
29C2×Dic163D411yescharacteristic
30C163⋊C8—21no—
31C23×C163—21no—
32C23×C163—21no—
33D4×C163—21no—
34D4×C163—21no—
35D4×C163—21no—
36D4×C163D412yescomplemented
37C2×C4×C163C2311yescharacteristic
38C8×C163—21no—
39C22×C163—22no—
40C22×C163—41no—
41C22×C163—41no—
42C22×C163—41no—
43C22×C163—41no—
44C22×C163—41no—
45C22×C163C2×D411yescharacteristic
46C2×D163—41no—
47C2×D163—41no—
48C2×D163—41no—
49C4×C163C2×D411yescharacteristic
50C4×C163#4111yescharacteristic
51Dic163—21no—
52Dic163—41no—
53Dic163D812yescomplemented
54C2×C163—42no—
55C2×C163—81no—
56C2×C163#12111yescharacteristic
57C2×C163C2×D811yescharacteristic
58C2×C163AGL(1,ℤ/8)11yescharacteristic
59D163—81no—
60C163#45911yescharacteristic, complemented, Sylow
61#459—1631nomaximal, Sylow
62C2×D8—1631no—
63C2×D8D16311yescharacteristic, complemented
64#127—1631no—
65C4×D4—1631no—
66C4⋊C8—1631no—
67#102—1631no—
68#102—1631no—
69C2×D4—3261no—
70C2×D4—3261no—
71C2×D4—1631no—
72C2×D4C2×D16311yescharacteristic
73C2×D4C2×D16311yescharacteristic
74C22×C4—3261no—
75D8—22no—
76D8—3262no—
77C2×C8—1631no—
78C2×C8C2×D16311yescharacteristic
79C4⋊C4—1631no—
80C22⋊C4—3261no—
81C42—1631no—
82C23—21no—
83C23—21no—
84C23—3261no—
85D4—21no—
86D4—21no—
87D4—21no—
88D4—3261no—
89D4—3261no—
90D4—6522no—
91D4—6522no—
92D4C22⋊D16312yescomplemented
93C2×C4—3261no—
94C2×C4—6522no—
95C2×C4—1631no—
96C2×C4—1631no—
97C2×C4C22×D16311yescharacteristic
98C8—21no—
99C8—3261no—
100C22—22no—
101C22—41no—
102C22—41no—
103C22—41no—
104C22—41no—
105C22—41no—
106C22—6521no—
107C22—6521no—
108C22—6521no—
109C22D4×D16311yescharacteristic
110C4—3261no—
111C4—6521no—
112C4—1632no—
113C4C2×C22⋊D16311yescharacteristic
114C4#1457969811yescharacteristic
115C2—42no—
116C2—81no—
117C2—13041no—
118C2#1910470711yescharacteristic
119C2D8×D16311yescharacteristic
120C2#1910475911yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×D8×C163C2
socleC22×C163C2×D4
hypercenterC2×D8D163
hypocenterC163#459
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14579684C2semidirect
2. #19104731C2semidirect
3. D4×Dic163C2semidirect
4. Dic163⋊C8C2semidirect
5. #19104657C2semidirect
6. #19104656C2semidirect
7. C2×D8×C163C2semidirect
36. D4×C163D4semidirect
53. Dic163D8semidirect
60. C163#459semidirect
63. C2×D8D163semidirect
92. D4C22⋊D163semidirect