Finite Group Databasebeta

← #44470778

Subgroups — #44470778

Order 29888.

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#28417950C211yesmaximal, characteristic, complemented
2#28417947C211yesmaximal, characteristic, complemented
3#28417938C213yesmaximal, complemented
4#28417928C213yesmaximal, complemented
5#28417926C213yesmaximal, complemented
6#28417923C213yesmaximal, complemented
7#126×C467C211yesmaximal, characteristic, complemented
8C23×D467C2211yescharacteristic
9C2×D1868C2213yes—
10C2×D1868C2213yes—
11C2×D1868C2213yescomplemented
12C2×C22⋊D467C2213yes—
13C2×C4×D467C2213yescomplemented
14Dic467⋊C4C2213yescomplemented
15(C2×D467)⋊C4C2213yes—
16(C2×D467)⋊C4C2213yes—
17(C2×D467)⋊C4C2213yescomplemented
18C4⋊C4×C467C2213yescomplemented
19C22⋊C4×C467C2213yes—
20C42×C467C2211yescharacteristic, complemented
21C22×D467—43no—
22C22×D467C2311yescharacteristic
23C22×D467C2311yescharacteristic
24C22×D467C2313yes—
25D1868—43no—
26D1868—43no—
27D1868—43no—
28C22⋊D467—43no—
29C2×Dic467C2313yes—
30C4×D467—43no—
31C23×C467C2311yescharacteristic
32C2×C4×C467C2313yes—
33C2×C4×C467C2313yes—
34C22×C467—23no—
35C22×C467C2411yescharacteristic
36C2×D467—23no—
37C2×D467—23no—
38C2×D467—23no—
39C2×D467—23no—
40C2×D467—23no—
41C2×D467—44no—
42C4×C467—23no—
43C4×C467—23no—
44Dic467—23no—
45C2×C467—41no—
46C2×C467H(5,𝔽2)13yes—
47D467—43no—
48D467—41no—
49D467—41no—
50C467#56011yescharacteristic, complemented, Sylow
51#560—4671nomaximal, Sylow
52#127—4671no—
53#126—4671no—
54#126D46711yescharacteristic, complemented
55#123—4673no—
56#121—4673no—
57#121—4673no—
58#120—4673no—
59C24—4671no—
60C2×D4—4673no—
61C2×D4—4673no—
62C2×D4—4673no—
63C2×D4—4673no—
64C22×C4—4673no—
65C4⋊C4—4673no—
66C4⋊C4C2×D46713yescomplemented
67C22⋊C4—4673no—
68C22⋊C4—4673no—
69C22⋊C4—4673no—
70C22⋊C4C2×D46713yes—
71C42C2×D46711yescharacteristic, complemented
72C23—18683no—
73C23—4671no—
74C23—4671no—
75C23—4673no—
76C23C22×D46711yescharacteristic
77D4—18683no—
78D4—18683no—
79D4—18683no—
80D4—18683no—
81C2×C4—18683no—
82C2×C4—4673no—
83C2×C4C22×D46713yes—
84C2×C4C22×D46713yes—
85C22—23no—
86C22—18684no—
87C22—9343no—
88C22—9343no—
89C22—9343no—
90C22—9343no—
91C22—9343no—
92C22C23×D46711yescharacteristic
93C4—23no—
94C4—23no—
95C4—9343no—
96C2—41no—
97C2—18681no—
98C2—18681no—
99C2—18683no—
100C2#2841799913yes—
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
Fitting#126×C467C2
hypercenter#126D467
hypocenterC467#560
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #28417950C2semidirect
2. #28417947C2semidirect
3. #28417938C2semidirect
4. #28417928C2semidirect
5. #28417926C2semidirect
6. #28417923C2semidirect
7. #126×C467C2semidirect
11. C2×D1868C22semidirect
13. C2×C4×D467C22semidirect
14. Dic467⋊C4C22semidirect
17. (C2×D467)⋊C4C22semidirect
18. C4⋊C4×C467C22semidirect
20. C42×C467C22semidirect
50. C467#560semidirect
54. #126D467semidirect
66. C4⋊C4C2×D467semidirect
71. C42C2×D467semidirect

Maximal subgroups

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

subgroupindex
#284179502
#284179472
#284179382
#284179282
#284179262
#284179232
#126×C4672
#560467