Finite Group Databasebeta

← #23781911

Subgroups — #23781911

Order 10432.

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

normal subgroups only

This group has 120 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×#14579688C211yesmaximal, characteristic, complemented
2#19104714C211yesmaximal, characteristic, complemented
3#19104709C211yesmaximal, characteristic
4#19104669C211yesmaximal, characteristic, complemented
5#19104660C211yesmaximal, characteristic, complemented
6#19104657C211yesmaximal, characteristic, complemented
7C2×M16×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—21no—
11#14579688—22no—
12C4⋊Dic163C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15C22⋊Dic163—21no—
16(C2×D163)⋊C4—21no—
17C22×C4×C163C2211yescharacteristic
18M16×C163—22no—
19C2×C8×C163C2211yescharacteristic
20C2×C8×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326—21no—
24D652—21no—
25D652—21no—
26C22⋊D163—42no—
27C2×Dic163—21no—
28C2×Dic163—21no—
29C2×Dic163—21no—
30C23×C163D411yescharacteristic
31C2×C4×C163—21no—
32C2×C4×C163—21no—
33C2×C4×C163D411yescharacteristic
34C2×C4×C163C2311yescharacteristic
35C8×C163—21no—
36C8×C163D412yescomplemented
37C22×C163—21no—
38C22×C163—21no—
39C22×C163—21no—
40C22×C163C2×D411yescharacteristic
41C2×D163—41no—
42C2×D163—41no—
43C2×D163—41no—
44C4×C163—21no—
45C4×C163C2×D411yescharacteristic
46C4×C163#4111yescharacteristic
47Dic163—41no—
48Dic163—41no—
49Dic163—41no—
50C2×C163—41no—
51C2×C163#12111yescharacteristic
52C2×C163AGL(1,ℤ/8)11yescharacteristic
53C2×C163#13711yescharacteristic
54D163—81no—
55C163#46811yescharacteristic, complemented, Sylow
56#468—1631nomaximal, Sylow
57C2×SD16—1631no—
58C2×M16D16311yescharacteristic, complemented
59C22⋊Q8—1631no—
60#121—1631no—
61#107—1631no—
62#103—1631no—
63#102—1631no—
64C2×Q8—1631no—
65C2×D4—3261no—
66C2×D4—1631no—
67C22×C4C2×D16311yescharacteristic
68SD16—3262no—
69M16—22no—
70C2×C8C2×D16311yescharacteristic
71C2×C8C2×D16311yescharacteristic
72C4⋊C4—3261no—
73C4⋊C4—1631no—
74C4⋊C4—1631no—
75C22⋊C4—3261no—
76C22⋊C4—3261no—
77C23—3261no—
78C23D65211yescharacteristic
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×C4D65211yescharacteristic
90C2×C4C22×D16311yescharacteristic
91C8—21no—
92C8C22⋊D16312yescomplemented
93C22—21no—
94C22—21no—
95C22—21no—
96C22—6521no—
97C22—6521no—
98C22—6521no—
99C22C2×D65211yescharacteristic
100C4—21no—
101C4—6521no—
102C4—6521no—
103C4—6521no—
104C4C2×C22⋊D16311yescharacteristic
105C4#1457969911yescharacteristic
106C2—41no—
107C2—13041no—
108C2#1910470911yescharacteristic
109C2#1910476311yescharacteristic
110C2#1910476811yescharacteristic
subgroupG/H
centerC22C2×D652
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×M16×C163C2
socleC22×C163C2×D4
prime radical#19104709C2
hypercenterC2×M16D163
hypocenterC163#468
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14579688C2semidirect
2. #19104714C2semidirect
4. #19104669C2semidirect
5. #19104660C2semidirect
6. #19104657C2semidirect
7. C2×M16×C163C2semidirect
36. C8×C163D4semidirect
55. C163#468semidirect
58. C2×M16D163semidirect
92. C8C22⋊D163semidirect