Finite Group Databasebeta

← #23782146

Subgroups — #23782146

Order 10432.

294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14579699C211yesmaximal, characteristic
2#19104700C212yesmaximal, complemented
3#19104697C212yesmaximal, complemented
4C4×C22⋊D163C214yesmaximal, complemented
5#19104694C211yesmaximal, characteristic, complemented
6#19104693C212yesmaximal, complemented
7C4⋊C4×D163C212yesmaximal, complemented
8C2×C4⋊C4×C163C211yesmaximal, characteristic, complemented
9#14579699C418yescomplemented
10C2×Dic326C2211yescharacteristic
11C2×D652C2211yescharacteristic
12C2×C22⋊D163C2212yes—
13C2×C4×D163C2214yes—
14C2×C4×D163C2212yes—
15C4⋊Dic163C2211yescharacteristic
16C4⋊Dic163C2211yescharacteristic
17Dic163⋊C4C2214yes—
18C22⋊Dic163C2212yes—
19(C2×D163)⋊C4C2214yes—
20C4×Dic163C2214yes—
21C4×Dic163C2212yes—
22C22×C4×C163C2212yes—
23C22×C4×C163C2211yescharacteristic
24C4⋊C4×C163C2212yes—
25C4⋊C4×C163C2212yes—
26C22×D163C2312yes—
27Dic326C2×C414yescomplemented
28D652C2×C414yescomplemented
29C22⋊D163C2×C418yescomplemented
30C2×Dic163C2312yes—
31C2×Dic163C2312yes—
32C2×Dic163C2312yes—
33C4×D163—44no—
34C4×D163C2×C418yescomplemented
35C23×C163C2311yescharacteristic
36C2×C4×C163—42no—
37C2×C4×C163C2×C414yescomplemented
38C2×C4×C163C2314yes—
39C2×C4×C163C2311yescharacteristic
40C2×C4×C163C2311yescharacteristic
41C22×C163—21no—
42C22×C163—21no—
43C22×C163C22×C412yes—
44C22×C163C2411yescharacteristic
45C2×D163—22no—
46C2×D163—22no—
47C2×D163C22×C414yes—
48C4×C163—24no—
49C4×C163C22×C412yes—
50C4×C163C22×C412yes—
51Dic163—22no—
52Dic163—22no—
53Dic163C22×C414yes—
54C2×C163—22no—
55C2×C163C23×C411yescharacteristic
56C2×C163H(5,𝔽2)11yescharacteristic
57C2×C1632−1+411yescharacteristic
58D163—24no—
59C163#52011yescharacteristic, complemented, Sylow
60#520—1631nomaximal, Sylow
61C2×#41—1631no—
62C4×Q8—1632no—
63C4×D4—1634no—
64C4×D4—1632no—
65#117—1631no—
66#117—1632no—
67C2×C4⋊C4—1632no—
68C2×C4⋊C4D16311yescharacteristic, complemented
69#41—1638no—
70C2×Q8—1631no—
71C2×D4—1632no—
72C2×D4—1631no—
73C22×C4—1634no—
74C22×C4—1632no—
75C22×C4C2×D16312yes—
76C22×C4C2×D16311yescharacteristic
77C4⋊C4—1631no—
78C4⋊C4—1634no—
79C4⋊C4—1631no—
80C4⋊C4C2×D16312yes—
81C4⋊C4C2×D16312yes—
82C22⋊C4—1632no—
83C22⋊C4—1634no—
84C42—1632no—
85C42—1634no—
86C23—1632no—
87C23C22×D16311yescharacteristic
88Q8—1634no—
89D4—1638no—
90D4—1634no—
91C2×C4—42no—
92C2×C4—6524no—
93C2×C4—1632no—
94C2×C4—1632no—
95C2×C4—1632no—
96C2×C4—1638no—
97C2×C4C4×D16314yescomplemented
98C2×C4C22×D16314yes—
99C2×C4C22×D16311yescharacteristic
100C2×C4C22×D16311yescharacteristic
101C22—21no—
102C22—21no—
103C22—3262no—
104C22—3262no—
105C22—1634no—
106C22C2×C4×D16312yes—
107C22C23×D16311yescharacteristic
108C4—24no—
109C4—3262no—
110C4—3262no—
111C4—1634no—
112C4C2×C4×D16312yes—
113C4C2×C4×D16312yes—
114C2—22no—
115C2—3264no—
116C2C22×C4×D16311yescharacteristic
117C2#1910478011yescharacteristic
118C2#1910478311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutatorC2×C163C23×C4
FittingC2×C4⋊C4×C163C2
socle, cosocleC22×C163C24
prime radicalC2×#14579699C2
hypercenterC2×C4⋊C4D163
hypocenterC163#520
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #19104700C2semidirect
3. #19104697C2semidirect
4. C4×C22⋊D163C2semidirect
5. #19104694C2semidirect
6. #19104693C2semidirect
7. C4⋊C4×D163C2semidirect
8. C2×C4⋊C4×C163C2semidirect
9. #14579699C4semidirect
27. Dic326C2×C4semidirect
28. D652C2×C4semidirect
29. C22⋊D163C2×C4semidirect
34. C4×D163C2×C4semidirect
37. C2×C4×C163C2×C4semidirect
59. C163#520semidirect
68. C2×C4⋊C4D163semidirect
97. C2×C4C4×D163semidirect