Finite Group Databasebeta

← #31827206

Subgroups — #31827206

Order 18112.

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#22583607C211yesmaximal, characteristic, complemented
2#22583604C211yesmaximal, characteristic, complemented
3#22583595C213yesmaximal, complemented
4#22583585C213yesmaximal, complemented
5#22583583C213yesmaximal, complemented
6#22583580C213yesmaximal, complemented
7#126×C283C211yesmaximal, characteristic, complemented
8C23×D283C2211yescharacteristic
9C2×D1132C2213yes—
10C2×D1132C2213yes—
11C2×D1132C2213yescomplemented
12C2×C22⋊D283C2213yes—
13C2×C4×D283C2213yescomplemented
14Dic283⋊C4C2213yescomplemented
15(C2×D283)⋊C4C2213yes—
16(C2×D283)⋊C4C2213yes—
17(C2×D283)⋊C4C2213yescomplemented
18C4⋊C4×C283C2213yescomplemented
19C22⋊C4×C283C2213yes—
20C42×C283C2211yescharacteristic, complemented
21C22×D283—43no—
22C22×D283C2311yescharacteristic
23C22×D283C2311yescharacteristic
24C22×D283C2313yes—
25D1132—43no—
26D1132—43no—
27D1132—43no—
28C22⋊D283—43no—
29C2×Dic283C2313yes—
30C4×D283—43no—
31C23×C283C2311yescharacteristic
32C2×C4×C283C2313yes—
33C2×C4×C283C2313yes—
34C22×C283—23no—
35C22×C283C2411yescharacteristic
36C2×D283—23no—
37C2×D283—23no—
38C2×D283—23no—
39C2×D283—23no—
40C2×D283—23no—
41C2×D283—44no—
42C4×C283—23no—
43C4×C283—23no—
44Dic283—23no—
45C2×C283—41no—
46C2×C283H(5,𝔽2)13yes—
47D283—43no—
48D283—41no—
49D283—41no—
50C283#56011yescharacteristic, complemented, Sylow
51#560—2831nomaximal, Sylow
52#127—2831no—
53#126—2831no—
54#126D28311yescharacteristic, complemented
55#123—2833no—
56#121—2833no—
57#121—2833no—
58#120—2833no—
59C24—2831no—
60C2×D4—2833no—
61C2×D4—2833no—
62C2×D4—2833no—
63C2×D4—2833no—
64C22×C4—2833no—
65C4⋊C4—2833no—
66C4⋊C4C2×D28313yescomplemented
67C22⋊C4—2833no—
68C22⋊C4—2833no—
69C22⋊C4—2833no—
70C22⋊C4C2×D28313yes—
71C42C2×D28311yescharacteristic, complemented
72C23—2831no—
73C23—2831no—
74C23—2833no—
75C23—11323no—
76C23C22×D28311yescharacteristic
77D4—11323no—
78D4—11323no—
79D4—11323no—
80D4—11323no—
81C2×C4—2833no—
82C2×C4—11323no—
83C2×C4C22×D28313yes—
84C2×C4C22×D28313yes—
85C22—23no—
86C22—5663no—
87C22—5663no—
88C22—5663no—
89C22—5663no—
90C22—5663no—
91C22—11324no—
92C22C23×D28311yescharacteristic
93C4—23no—
94C4—23no—
95C4—5663no—
96C2—41no—
97C2—11321no—
98C2—11321no—
99C2—11323no—
100C2#2258365613yes—
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
Fitting#126×C283C2
hypercenter#126D283
hypocenterC283#560
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #22583607C2semidirect
2. #22583604C2semidirect
3. #22583595C2semidirect
4. #22583585C2semidirect
5. #22583583C2semidirect
6. #22583580C2semidirect
7. #126×C283C2semidirect
11. C2×D1132C22semidirect
13. C2×C4×D283C22semidirect
14. Dic283⋊C4C22semidirect
17. (C2×D283)⋊C4C22semidirect
18. C4⋊C4×C283C22semidirect
20. C42×C283C22semidirect
50. C283#560semidirect
54. #126D283semidirect
66. C4⋊C4C2×D283semidirect
71. C42C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836072
#225836042
#225835952
#225835852
#225835832
#225835802
#126×C2832
#560283