Finite Group Databasebeta

← #23781854

Subgroups — #23781854

Order 10432.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 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#19104780C211yesmaximal, characteristic
2#19104718C212yesmaximal, complemented
3#19104650C211yesmaximal, characteristic, complemented
4#19104649C212yesmaximal, complemented
5#123×C163C211yesmaximal, characteristic, complemented
6#14579699—21no—
7#14579698—22no—
8C2×C22⋊D163—21no—
9C2×C22⋊D163C2212yes—
10D4×D163—22no—
11Dic163⋊C4—22no—
12C22⋊Dic163C2212yescomplemented
13(C2×D163)⋊C4—22no—
14C2×D4×C163C2211yescharacteristic
15C22×C4×C163C2211yescharacteristic, complemented
16C4⋊C4×C163—21no—
17C22⋊C4×C163—21no—
18C22⋊C4×C163C2211yescharacteristic, complemented
19C22×D163—21no—
20C22×D163D412yes—
21Dic326—21no—
22D652—21no—
23C22⋊D163—22no—
24C22⋊D163—22no—
25C22⋊D163—22no—
26C2×Dic163—21no—
27C2×Dic163—22no—
28C2×Dic163D412yes—
29C4×D163—22no—
30C23×C163D411yescharacteristic
31C23×C163C2311yescharacteristic
32D4×C163—22no—
33C2×C4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163—22no—
36C2×C4×C163D411yescharacteristic
37C22×C163—21no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163C2×D412yes—
41C22×C163C2×D411yescharacteristic
42C2×D163—22no—
43C2×D163—42no—
44C2×D163—81no—
45C4×C163—21no—
46C4×C163—41no—
47C4×C163—41no—
48Dic163—22no—
49Dic163—42no—
50C2×C163—22no—
51C2×C163—21no—
52C2×C163—41no—
53C2×C163#12011yescharacteristic
54D163—42no—
55C163#45811yescharacteristic, complemented, Sylow
56#458—1631nomaximal, Sylow
57H(5,𝔽2)—1631no—
58#123—1632no—
59#123D16311yescharacteristic, complemented
60#99—1631no—
61#99—1632no—
62#41—3262no—
63#41—3261no—
64C2×D4—3262no—
65C2×D4—3261no—
66C2×D4—1632no—
67C2×D4C2×D16311yescharacteristic
68C22×C4C2×D16311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—3262no—
71C22⋊C4—21no—
72C22⋊C4—3262no—
73C22⋊C4—1632no—
74C22⋊C4C2×D16311yescharacteristic, complemented
75C23—3261no—
76C23—1632no—
77C23C22⋊D16311yescharacteristic
78C23C22×D16311yescharacteristic
79Q8—3261no—
80D4—22no—
81D4—3261no—
82D4—3262no—
83D4—3262no—
84D4—3262no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—3262no—
89C2×C4—3261no—
90C2×C4—3262no—
91C2×C4—1632no—
92C2×C4C22⋊D16311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—13041no—
97C22—3262no—
98C22—6522no—
99C22D4×D16312yes—
100C22C2×C22⋊D16311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—3262no—
105C4—6522no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—6522no—
110C2#1910470311yescharacteristic
subgroupG/H
centerC2#19104703
commutator, cosocleC23×C163C23
FrattiniC23C22×D163
Fitting#123×C163C2
socleC2×C163#120
prime radical#19104780C2
hypercenter#123D163
hypocenterC163#458
LCSG ▷ C23×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #19104718C2semidirect
3. #19104650C2semidirect
4. #19104649C2semidirect
5. #123×C163C2semidirect
12. C22⋊Dic163C22semidirect
15. C22×C4×C163C22semidirect
18. C22⋊C4×C163C22semidirect
55. C163#458semidirect
59. #123D163semidirect
68. C22×C4C2×D163semidirect
74. C22⋊C4C2×D163semidirect