Finite Group Databasebeta

← #50306631

Subgroups — #50306631

Order 38336.

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#34062712C211yesmaximal, characteristic, complemented
2#34062709C211yesmaximal, characteristic, complemented
3#34062700C213yesmaximal, complemented
4#34062690C213yesmaximal, complemented
5#34062688C213yesmaximal, complemented
6#34062685C213yesmaximal, complemented
7#126×C599C211yesmaximal, characteristic, complemented
8C23×D599C2211yescharacteristic
9C2×D2396C2213yes—
10C2×D2396C2213yes—
11C2×D2396C2213yescomplemented
12C2×C22⋊D599C2213yes—
13C2×C4×D599C2213yescomplemented
14Dic599⋊C4C2213yescomplemented
15(C2×D599)⋊C4C2213yes—
16(C2×D599)⋊C4C2213yes—
17(C2×D599)⋊C4C2213yescomplemented
18C4⋊C4×C599C2213yescomplemented
19C22⋊C4×C599C2213yes—
20C42×C599C2211yescharacteristic, complemented
21C22×D599—43no—
22C22×D599C2311yescharacteristic
23C22×D599C2311yescharacteristic
24C22×D599C2313yes—
25D2396—43no—
26D2396—43no—
27D2396—43no—
28C22⋊D599—43no—
29C2×Dic599C2313yes—
30C4×D599—43no—
31C23×C599C2311yescharacteristic
32C2×C4×C599C2313yes—
33C2×C4×C599C2313yes—
34C22×C599—23no—
35C22×C599C2411yescharacteristic
36C2×D599—23no—
37C2×D599—23no—
38C2×D599—23no—
39C2×D599—23no—
40C2×D599—23no—
41C2×D599—44no—
42C4×C599—23no—
43C4×C599—23no—
44Dic599—23no—
45C2×C599—41no—
46C2×C599H(5,𝔽2)13yes—
47D599—43no—
48D599—41no—
49D599—41no—
50C599#56011yescharacteristic, complemented, Sylow
51#560—5991nomaximal, Sylow
52#127—5991no—
53#126—5991no—
54#126D59911yescharacteristic, complemented
55#123—5993no—
56#121—5993no—
57#121—5993no—
58#120—5993no—
59C24—5991no—
60C2×D4—5993no—
61C2×D4—5993no—
62C2×D4—5993no—
63C2×D4—5993no—
64C22×C4—5993no—
65C4⋊C4—5993no—
66C4⋊C4C2×D59913yescomplemented
67C22⋊C4—5993no—
68C22⋊C4—5993no—
69C22⋊C4—5993no—
70C22⋊C4C2×D59913yes—
71C42C2×D59911yescharacteristic, complemented
72C23—5991no—
73C23—5991no—
74C23—5993no—
75C23—23963no—
76C23C22×D59911yescharacteristic
77D4—23963no—
78D4—23963no—
79D4—23963no—
80D4—23963no—
81C2×C4—5993no—
82C2×C4—23963no—
83C2×C4C22×D59913yes—
84C2×C4C22×D59913yes—
85C22—23no—
86C22—23964no—
87C22—11983no—
88C22—11983no—
89C22—11983no—
90C22—11983no—
91C22—11983no—
92C22C23×D59911yescharacteristic
93C4—23no—
94C4—23no—
95C4—11983no—
96C2—41no—
97C2—23961no—
98C2—23961no—
99C2—23963no—
100C2#3406276113yes—
subgroupG/H
center, FrattiniC22C23×D599
commutator, socle, cosocleC22×C599C24
Fitting#126×C599C2
hypercenter#126D599
hypocenterC599#560
LCSG ▷ C22×C599 ▷ C599
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #34062712C2semidirect
2. #34062709C2semidirect
3. #34062700C2semidirect
4. #34062690C2semidirect
5. #34062688C2semidirect
6. #34062685C2semidirect
7. #126×C599C2semidirect
11. C2×D2396C22semidirect
13. C2×C4×D599C22semidirect
14. Dic599⋊C4C22semidirect
17. (C2×D599)⋊C4C22semidirect
18. C4⋊C4×C599C22semidirect
20. C42×C599C22semidirect
50. C599#560semidirect
54. #126D599semidirect
66. C4⋊C4C2×D599semidirect
71. C42C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627122
#340627092
#340627002
#340626902
#340626882
#340626852
#126×C5992
#560599