Finite Group Databasebeta

← #34094893

Subgroups — #34094893

Order 20032.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#23756494C211yesmaximal, characteristic, complemented
2#23756491C211yesmaximal, characteristic, complemented
3#23756482C213yesmaximal, complemented
4#23756472C213yesmaximal, complemented
5#23756470C213yesmaximal, complemented
6#23756467C213yesmaximal, complemented
7#126×C313C211yesmaximal, characteristic, complemented
8C23×D313C2211yescharacteristic
9C2×D1252C2213yes—
10C2×D1252C2213yes—
11C2×D1252C2213yescomplemented
12C2×C22⋊D313C2213yes—
13C2×C4×D313C2213yescomplemented
14#19097540C2213yescomplemented
15#19097538C2213yes—
16#19097538C2213yes—
17#19097538C2213yescomplemented
18C4⋊C4×C313C2213yescomplemented
19C22⋊C4×C313C2213yes—
20C42×C313C2211yescharacteristic, complemented
21C22×D313—43no—
22C22×D313C2311yescharacteristic
23C22×D313C2311yescharacteristic
24C22×D313C2313yes—
25D1252—43no—
26D1252—43no—
27D1252—43no—
28C22⋊D313—43no—
29C2×Dic313C2313yes—
30C4×D313—43no—
31C23×C313C2311yescharacteristic
32C2×C4×C313C2313yes—
33C2×C4×C313C2313yes—
34C22×C313—23no—
35C22×C313C2411yescharacteristic
36C2×D313—23no—
37C2×D313—23no—
38C2×D313—23no—
39C2×D313—23no—
40C2×D313—23no—
41C2×D313—44no—
42C4×C313—23no—
43C4×C313—23no—
44Dic313—23no—
45C2×C313—41no—
46C2×C313H(5,𝔽2)13yes—
47D313—43no—
48D313—41no—
49D313—41no—
50C313#56011yescharacteristic, complemented, Sylow
51#560—3131nomaximal, Sylow
52#127—3131no—
53#126—3131no—
54#126D31311yescharacteristic, complemented
55#123—3133no—
56#121—3133no—
57#121—3133no—
58#120—3133no—
59C24—3131no—
60C2×D4—3133no—
61C2×D4—3133no—
62C2×D4—3133no—
63C2×D4—3133no—
64C22×C4—3133no—
65C4⋊C4—3133no—
66C4⋊C4C2×D31313yescomplemented
67C22⋊C4—3133no—
68C22⋊C4—3133no—
69C22⋊C4—3133no—
70C22⋊C4C2×D31313yes—
71C42C2×D31311yescharacteristic, complemented
72C23—3131no—
73C23—3131no—
74C23—3133no—
75C23—12523no—
76C23C22×D31311yescharacteristic
77D4—12523no—
78D4—12523no—
79D4—12523no—
80D4—12523no—
81C2×C4—3133no—
82C2×C4—12523no—
83C2×C4C22×D31313yes—
84C2×C4C22×D31313yes—
85C22—23no—
86C22—6263no—
87C22—6263no—
88C22—6263no—
89C22—6263no—
90C22—6263no—
91C22—12524no—
92C22C23×D31311yescharacteristic
93C4—23no—
94C4—23no—
95C4—6263no—
96C2—41no—
97C2—12521no—
98C2—12521no—
99C2—12523no—
100C2#2375654313yes—
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#126×C313C2
hypercenter#126D313
hypocenterC313#560
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #23756494C2semidirect
2. #23756491C2semidirect
3. #23756482C2semidirect
4. #23756472C2semidirect
5. #23756470C2semidirect
6. #23756467C2semidirect
7. #126×C313C2semidirect
11. C2×D1252C22semidirect
13. C2×C4×D313C22semidirect
14. #19097540C22semidirect
17. #19097538C22semidirect
18. C4⋊C4×C313C22semidirect
20. C42×C313C22semidirect
50. C313#560semidirect
54. #126D313semidirect
66. C4⋊C4C2×D313semidirect
71. C42C2×D313semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237564942
#237564912
#237564822
#237564722
#237564702
#237564672
#126×C3132
#560313