Finite Group Databasebeta

← #11760910

Subgroups — #11760910

Order 1056.

140 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 62 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×#63143C211yesmaximal, characteristic
2#10587201C211yesmaximal, characteristic
3C4×C11×Dic3C211yesmaximal, characteristic
4C3×Dic11⋊C4C211yesmaximal, characteristic
5Dic3⋊Dic11C211yesmaximal, characteristic
6Dic3×Dic11C211yesmaximal, characteristic
7Dic3×Dic11C211yesmaximal, characteristic
8C4×Dic22—31nomaximal, Hall
9C2×C3×C4×C11C2211yescharacteristic
10C2×Dic33C2211yescharacteristic
11C2×Dic33C2211yescharacteristic
12C2×C11×Dic3C2211yescharacteristic
13C2×C11×Dic3C2211yescharacteristic
14C2×C3×Dic11C2211yescharacteristic
15C2×C3×Dic11C2211yescharacteristic
16#63143C414yescomplemented
17C2×Dic22—31no—
18C42×C11—31no—
19C4⋊Dic11—31no—
20Dic11⋊C4—31no—
21Dic11⋊C4D311yescharacteristic
22C4×Dic11—31no—
23C4×Dic11—31no—
24C22×C3×C11C2311yescharacteristic
25C3×C4×C11—21no—
26Dic33—21no—
27Dic33C2×C412yes—
28C3×Dic11—21no—
29C3×Dic11C2×C412yes—
30C11×Dic3C2×C412yes—
31C11×Dic3Q812yescomplemented
32#887—111nomaximal, Hall
33C2×C4×C11—31no—
34C2×C4×C11—31no—
35C2×C4×C11C2×D311yescharacteristic
36C2×Dic11—31no—
37C2×Dic11—31no—
38C2×Dic11C2×D311yescharacteristic
39C2×Dic11C2×D311yescharacteristic
40Dic22—34no—
41C2×C3×C11C22×C411yescharacteristic
42C2×C3×C11C2×Q811yescharacteristic
43C2×C3×C11#4111yescharacteristic
44C2×Dic6—111no—
45C3×C4⋊C4—111no—
46Dic3⋊C4—111no—
47Dic3⋊C4—111no—
48C4×Dic3—111no—
49C4×Dic3—111no—
50C4×Dic3D1111yescharacteristic
51C22×C11C22×D311yescharacteristic
52C4×C11—21no—
53C4×C11—32no—
54C4×C11—32no—
55Dic11—21no—
56Dic11—32no—
57Dic11—61no—
58Dic11C4×D312yes—
59C3×C11C4×Q811yescharacteristic, complemented, Hall
60C4×Q8—331noSylow
61C2×C3×C4—111no—
62C2×C3×C4—111no—
63C2×C3×C4C2×D1111yescharacteristic
64C2×Dic3—111no—
65C2×Dic3—111no—
66C2×Dic3C2×D1111yescharacteristic
67C2×Dic3C2×D1111yescharacteristic
68Dic6—114no—
69C2×C11C2×C4×D311yescharacteristic
70C2×C11#23711yescharacteristic
71C2×C11D3×Q811yescharacteristic
72C2×Q8—331no—
73C4⋊C4—111no—
74C4⋊C4—331no—
75C4⋊C4—331no—
76C42—31no—
77C42—331no—
78C42—331no—
79C22×C3C22×D1111yescharacteristic
80C3×C4—21no—
81C3×C4—112no—
82C3×C4—221no—
83Dic3—112no—
84Dic3—221no—
85Dic3Dic2212yescomplemented
86Dic3C4×D1112yes—
87C11#88711yescharacteristic, complemented, Sylow
88Q8—334no—
89C2×C4—31no—
90C2×C4—31no—
91C2×C4—111no—
92C2×C4—111no—
93C2×C4—331no—
94C2×C4—331no—
95C2×C4D3×D1111yescharacteristic
96C2×C3C2×Dic2211yescharacteristic
97C2×C3C2×C4×D1111yescharacteristic
98C2×C3#433911yescharacteristic
99C22C2×D3×D1111yescharacteristic
100C4—21no—
101C4—32no—
102C4—32no—
103C4—112no—
104C4—221no—
105C4—332no—
106C4—661no—
107C3C4×Dic2211yescharacteristic, complemented, Sylow
108C2D3×Dic2211yescharacteristic
109C2C4×D3×D1111yescharacteristic
110C2#1058724111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D11
commutatorC2×C3×C11C22×C4
FittingC2×C3×C4×C11C22
socle, prime radical, cosocleC22×C3×C11C23
hypercenterC2×C4D3×D11
hypocenterC3×C11C4×Q8
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
16. #63143C4semidirect
31. C11×Dic3Q8semidirect
59. C3×C11C4×Q8semidirect
85. Dic3Dic22semidirect
87. C11#887semidirect
107. C3C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C2×#631432
#105872012
C4×C11×Dic32
C3×Dic11⋊C42
Dic3⋊Dic112
Dic3×Dic112
C4×Dic223
#88711