Finite Group Databasebeta

← #11760885

Subgroups — #11760885

Order 1056.

188 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 56 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×D132C211yesmaximal, characteristic, complemented
2C2×C3×C4×D11C211yesmaximal, characteristic, complemented
3C2×#63141C212yesmaximal, complemented
4C11×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10587156C212yesmaximal, complemented
6#66948—31nomaximal, Hall
7C22×D33C2212yes—
8C22×C3×D11C2211yescharacteristic
9C2×C3×C4×C11C2211yescharacteristic
10D132—22no—
11C2×C11×Dic3C2212yes—
12C2×C3×Dic11C2211yescharacteristic
13C3×C4×D11—22no—
14#63141—24no—
15C2×D44—32no—
16C2×D44—31no—
17C2×C4×D11D311yescharacteristic, complemented
18C11×C4⋊C4—31no—
19(C2×D11)⋊C4—32no—
20C22×C3×C11C2311yescharacteristic
21C2×D33—22no—
22C2×D33—22no—
23C2×D33—22no—
24C2×C3×D11—21no—
25C2×C3×D11—21no—
26C2×C3×D11D412yescomplemented
27C3×C4×C11D412yescomplemented
28C3×Dic11—21no—
29C11×Dic3—22no—
30#930—111nomaximal, Hall
31C22×D11—32no—
32C22×D11C2×D311yescharacteristic
33C2×C4×C11—32no—
34C2×C4×C11C2×D311yescharacteristic
35C2×Dic11C2×D311yescharacteristic
36D44—64no—
37D44—62no—
38C4×D11—22no—
39C2×C3×C11C2×D411yescharacteristic
40C2×C3×C11C2×D411yescharacteristic
41C2×C3×C11#4111yescharacteristic
42D33—42no—
43C3×D11—22no—
44C22×C3×C4—111no—
45C2×#67—112no—
46C2×D12—111no—
47(C2×D3)⋊C4—112no—
48C4⋊Dic3D1111yescharacteristic, complemented
49C22×C11C22×D311yescharacteristic
50C2×D11—21no—
51C2×D11—21no—
52C2×D11—62no—
53C2×D11—62no—
54C2×D11—62no—
55C2×D11D1212yescomplemented
56C4×C11—62no—
57C4×C11#6712yescomplemented
58Dic11—21no—
59C3×C11#12111yescharacteristic, complemented, Hall
60#121—331noSylow
61C23×C3—111no—
62C22×D3—112no—
63C2×C3×C4—111no—
64C2×C3×C4—222no—
65C2×C3×C4C2×D1111yescharacteristic
66#67—224no—
67C2×Dic3C2×D1112yes—
68D12—222no—
69C2×C11C2×D1211yescharacteristic
70C2×C11#23511yescharacteristic
71C2×C11C2×#6711yescharacteristic
72D11—22no—
73D11—122no—
74C2×D4—332no—
75C2×D4—331no—
76C22×C4—111no—
77C4⋊C4—31no—
78C22⋊C4—332no—
79C22×C3—112no—
80C22×C3—221no—
81C22×C3—221no—
82C22×C3C22×D1111yescharacteristic
83C2×D3—222no—
84C2×D3—222no—
85C2×D3—222no—
86C3×C4—221no—
87C3×C4D4412yescomplemented
88Dic3—22no—
89C11#93011yescharacteristic, complemented, Sylow
90C23—111no—
91C23—332no—
92D4—664no—
93D4—662no—
94C2×C4—32no—
95C2×C4—111no—
96C2×C4—222no—
97C2×C4D3×D1111yescharacteristic
98C2×C3—222no—
99C2×C3C2×D4411yescharacteristic
100C2×C3D4×D1111yescharacteristic
101C2×C3#434311yescharacteristic
102D3—442no—
103C22—112no—
104C22—221no—
105C22—221no—
106C22—662no—
107C22—662no—
108C22—662no—
109C22C2×D3×D1111yescharacteristic
110C4—62no—
111C4—221no—
112C4#6314112yescomplemented
113C3#6694811yescharacteristic, complemented, Sylow
114C2—222no—
115C2—1322no—
116C2#1058723511yescharacteristic
117C2D11×D1211yescharacteristic
118C2C2×#6314111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D11
commutator, socle, cosocleC22×C3×C11C23
FittingC2×C3×C4×C11C22
hypercenterC2×C4D3×D11
hypocenterC3×C11#121
LCSG ▷ C22×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D132C2semidirect
2. C2×C3×C4×D11C2semidirect
3. C2×#63141C2semidirect
4. C11×C4⋊Dic3C2semidirect
5. #10587156C2semidirect
17. C2×C4×D11D3semidirect
26. C2×C3×D11D4semidirect
27. C3×C4×C11D4semidirect
48. C4⋊Dic3D11semidirect
55. C2×D11D12semidirect
57. C4×C11#67semidirect
59. C3×C11#121semidirect
87. C3×C4D44semidirect
89. C11#930semidirect
112. C4#63141semidirect
113. C3#66948semidirect

Maximal subgroups

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

subgroupindex
C2×D1322
C2×C3×C4×D112
C2×#631412
C11×C4⋊Dic32
#105871562
#669483
#93011