Finite Group Databasebeta

← #23781908

Subgroups — #23781908

Order 10432.

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

normal subgroups only

This group has 120 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
1C2×#14579682C211yesmaximal, characteristic, complemented
2#19104711C211yesmaximal, characteristic, complemented
3#19104706C211yesmaximal, characteristic
4#19104669C211yesmaximal, characteristic, complemented
5#19104659C211yesmaximal, characteristic, complemented
6#19104656C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic, complemented
8C2×C22⋊D163—21no—
9C2×C4×D163C2211yescharacteristic
10#14579682—22no—
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15C22⋊Dic163—21no—
16(C2×D163)⋊C4—21no—
17C2×Q8×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19SD16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21C22×D163D411yescharacteristic
22C22⋊D163—42no—
23C2×Dic163—21no—
24C2×Dic163—21no—
25C2×Dic163D411yescharacteristic
26C4×D163—21no—
27C4×D163—21no—
28C163⋊C8—21no—
29C23×C163—21no—
30Q8×C163—21no—
31Q8×C163—21no—
32D4×C163—21no—
33D4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163D412yescomplemented
37C22×C163—41no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163C2×D411yescharacteristic
41C2×D163—21no—
42C2×D163—21no—
43C2×D163—21no—
44C4×C163—41no—
45C4×C163C2×D411yescharacteristic
46C4×C163#4111yescharacteristic
47Dic163—21no—
48Dic163—41no—
49Dic163—41no—
50C2×C163—81no—
51C2×C163#12111yescharacteristic
52C2×C163AGL(1,ℤ/8)11yescharacteristic
53C2×C163#13711yescharacteristic
54D163—41no—
55C163#46811yescharacteristic, complemented, Sylow
56#468—1631nomaximal, Sylow
57C2×SD16D16311yescharacteristic, complemented
58C2×M16—1631no—
59C22⋊Q8—1631no—
60#121—1631no—
61#107—1631no—
62#103—1631no—
63#102—1631no—
64C2×Q8C2×D16311yescharacteristic
65C2×D4—3261no—
66C2×D4C2×D16311yescharacteristic
67C22×C4—1631no—
68SD16—22no—
69M16—3262no—
70C2×C8—1631no—
71C2×C8C2×D16311yescharacteristic
72C4⋊C4—3261no—
73C4⋊C4—1631no—
74C4⋊C4—1631no—
75C22⋊C4—3261no—
76C22⋊C4—3261no—
77C23—21no—
78C23—1631no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—21no—
83D4—6522no—
84C2×C4—21no—
85C2×C4—3261no—
86C2×C4—3261no—
87C2×C4—3261no—
88C2×C4—3261no—
89C2×C4—1631no—
90C2×C4C22×D16311yescharacteristic
91C8—3261no—
92C8C22⋊D16312yescomplemented
93C22—41no—
94C22—41no—
95C22—41no—
96C22—3261no—
97C22—3261no—
98C22—3261no—
99C22D4×D16311yescharacteristic
100C4—41no—
101C4—3261no—
102C4—6521no—
103C4—6521no—
104C4C2×C22⋊D16311yescharacteristic
105C4#1457969811yescharacteristic
106C2—81no—
107C2—6521no—
108C2#1910470611yescharacteristic
109C2#1910476211yescharacteristic
110C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radical#19104706C2
hypercenterC2×SD16D163
hypocenterC163#468
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14579682C2semidirect
2. #19104711C2semidirect
4. #19104669C2semidirect
5. #19104659C2semidirect
6. #19104656C2semidirect
7. C2×SD16×C163C2semidirect
36. C8×C163D4semidirect
55. C163#468semidirect
57. C2×SD16D163semidirect
92. C8C22⋊D163semidirect