Finite Group Databasebeta

← #11760916

Subgroups — #11760916

Order 1056.

136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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×C11×Dic6C211yesmaximal, characteristic
2C2×#63143C211yesmaximal, characteristic
3#10587201C211yesmaximal, characteristic
4C3×Dic11⋊C4C211yesmaximal, characteristic
5#10587158C211yesmaximal, characteristic
6Dic11⋊Dic3C211yesmaximal, characteristic
7Dic3×Dic11C211yesmaximal, characteristic
8#66997—31nomaximal, Hall
9C2×C3×C4×C11C2211yescharacteristic
10C2×Dic33C2211yescharacteristic
11C2×Dic33C2211yescharacteristic
12C2×C11×Dic3C2211yescharacteristic
13C2×C11×Dic3C2211yescharacteristic
14C11×Dic6—22no—
15C2×C3×Dic11C2211yescharacteristic
16C2×C3×Dic11C2211yescharacteristic
17#63143—22no—
18C2×Q8×C11—31no—
19C2×Dic22—31no—
20Dic11⋊C4—31no—
21Dic11⋊C4—31no—
22Dic11⋊C4—31no—
23Dic11⋊C4D311yescharacteristic
24C4×Dic11—31no—
25C22×C3×C11C2311yescharacteristic
26C3×C4×C11—21no—
27Dic33—21no—
28Dic33Q812yescomplemented
29C3×Dic11—21no—
30C3×Dic11Q812yescomplemented
31C11×Dic3—21no—
32C11×Dic3D412yes—
33#888—111nomaximal, Hall
34Q8×C11—62no—
35C2×C4×C11—31no—
36C2×C4×C11—31no—
37C2×C4×C11C2×D311yescharacteristic
38C2×Dic11—31no—
39C2×Dic11—31no—
40C2×Dic11C2×D311yescharacteristic
41C2×Dic11C2×D311yescharacteristic
42Dic22—62no—
43C2×C3×C11C2×D411yescharacteristic
44C2×C3×C11C2×Q811yescharacteristic
45C2×C3×C11C2×Q811yescharacteristic
46C2×Dic6—111no—
47C2×Dic6D1111yescharacteristic
48C3×C4⋊C4—111no—
49C4⋊Dic3—111no—
50Dic3⋊C4—111no—
51Dic3⋊C4—111no—
52C4×Dic3—111no—
53C22×C11C22×D311yescharacteristic
54C4×C11—21no—
55C4×C11—32no—
56C4×C11—61no—
57Dic11—21no—
58Dic11—32no—
59Dic11—61no—
60Dic11Dic612yescomplemented
61C3×C11C4⋊Q811yescharacteristic, complemented, Hall
62C4⋊Q8—331noSylow
63C2×C3×C4—111no—
64C2×C3×C4—111no—
65C2×C3×C4C2×D1111yescharacteristic
66C2×Dic3—111no—
67C2×Dic3—111no—
68C2×Dic3C2×D1111yescharacteristic
69C2×Dic3C2×D1111yescharacteristic
70Dic6—22no—
71Dic6—222no—
72C2×C11C2×Dic611yescharacteristic
73C2×C11D3×D411yescharacteristic
74C2×C11D3×Q811yescharacteristic
75C2×Q8—31no—
76C2×Q8—331no—
77C4⋊C4—111no—
78C4⋊C4—331no—
79C4⋊C4—331no—
80C4⋊C4—331no—
81C42—331no—
82C22×C3C22×D1111yescharacteristic
83C3×C4—21no—
84C3×C4—112no—
85C3×C4—221no—
86Dic3—21no—
87Dic3—112no—
88Dic3—221no—
89Dic3C22⋊D1112yes—
90C11#88811yescharacteristic, complemented, Sylow
91Q8—62no—
92Q8—662no—
93C2×C4—31no—
94C2×C4—31no—
95C2×C4—111no—
96C2×C4—111no—
97C2×C4—331no—
98C2×C4—331no—
99C2×C4D3×D1111yescharacteristic
100C2×C3Q8×D1111yescharacteristic
101C2×C3Q8×D1111yescharacteristic
102C2×C3C2×C22⋊D1111yescharacteristic
103C22C2×D3×D1111yescharacteristic
104C4—21no—
105C4—32no—
106C4—61no—
107C4—112no—
108C4—221no—
109C4—332no—
110C4—661no—
111C3#6699711yescharacteristic, complemented, Sylow
112C2D11×Dic611yescharacteristic
113C2D33⋊Q811yescharacteristic
114C2D3×C22⋊D1111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D11
commutator, socle, prime radical, cosocleC22×C3×C11C23
FittingC2×C3×C4×C11C22
hypercenterC2×C4D3×D11
hypocenterC3×C11C4⋊Q8
LCSG ▷ C22×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
28. Dic33Q8semidirect
30. C3×Dic11Q8semidirect
60. Dic11Dic6semidirect
61. C3×C11C4⋊Q8semidirect
90. C11#888semidirect
111. C3#66997semidirect

Maximal subgroups

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

subgroupindex
C2×C11×Dic62
C2×#631432
#105872012
C3×Dic11⋊C42
#105871582
Dic11⋊Dic32
Dic3×Dic112
#669973
#88811