Finite Group Databasebeta

← #11760932

Subgroups — #11760932

Order 1056.

136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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#10587281C211yesmaximal, characteristic, complemented
2#10587239C211yesmaximal, characteristic, complemented
3C11×#213C211yesmaximal, characteristic, complemented
4C3×#4323C211yesmaximal, characteristic, complemented
5#10587148C211yesmaximal, characteristic, complemented
6#10587146C211yesmaximal, characteristic, complemented
7#10587140C211yesmaximal, characteristic, complemented
8#66964—31nomaximal, Hall
9C2×D3×D11—21no—
10C3×D4×C11C2211yescharacteristic, complemented
11#63159—21no—
12C2×Dic33—21no—
13C4×D33C2211yescharacteristic
14Dic66C2211yescharacteristic, complemented
15C11×D12C2211yescharacteristic
16C3×D44C2211yescharacteristic
17#63140—21no—
18C3×C11⋊C8C2211yescharacteristic, complemented
19C11×C3⋊C8C2211yescharacteristic, complemented
20#4341—31no—
21D4×D11—31no—
22C11×D8—31no—
23#4324—31no—
24#4323D311yescharacteristic, complemented
25#4314—31no—
26#4313—31no—
27C22×C3×C11—21no—
28C2×D33D411yescharacteristic
29C2×D3×C11—21no—
30C2×C3×D11—21no—
31D3×D11—42no—
32C3×C4×C11C2311yescharacteristic
33Dic33—21no—
34Dic33D411yescharacteristic
35#911—111nomaximal, Hall
36C22×D11—61no—
37D4×C11—31no—
38D4×C11C2×D311yescharacteristic, complemented
39C22⋊D11—61no—
40C22⋊D11—61no—
41C2×Dic11—61no—
42D44C2×D311yescharacteristic
43C4×D11—31no—
44Dic22—31no—
45C8×C11—31no—
46C11⋊C8C2×D311yescharacteristic, complemented
47C2×C3×C11—41no—
48C2×C3×C11C2×D411yescharacteristic
49D33—21no—
50C3×D11—41no—
51D3×C11—41no—
52#237—111no—
53D3×D4—111no—
54C3×D8—111no—
55#214—111no—
56#213D1111yescharacteristic, complemented
57#204—111no—
58ΓL(1,𝔽25)—111no—
59C22×C11—21no—
60C22×C11—61no—
61C2×D11—21no—
62C2×D11—31no—
63C2×D11—122no—
64C4×C11C22×D311yescharacteristic
65Dic11—31no—
66Dic11—61no—
67C3×C11AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
68AGL(1,ℤ/8)—331noSylow
69C22×D3—221no—
70C3×D4—111no—
71C3×D4C2×D1111yescharacteristic, complemented
72#67—221no—
73#67—221no—
74C2×Dic3—221no—
75D12C2×D1111yescharacteristic
76C4×D3—111no—
77Dic6—111no—
78C3×C8—111no—
79C3⋊C8C2×D1111yescharacteristic, complemented
80C2×C11—41no—
81C2×C11—121no—
82C2×C11D3×D411yescharacteristic
83D11—41no—
84D11—61no—
85#41—331no—
86C2×D4—331no—
87SD16—331no—
88SD16—331no—
89D8—31no—
90D8—111no—
91M16—331no—
92C22×C3—21no—
93C22×C3—221no—
94C2×D3—21no—
95C2×D3—111no—
96C2×D3—442no—
97C3×C4C22×D1111yescharacteristic
98Dic3—111no—
99Dic3—221no—
100C11#91111yescharacteristic, complemented, Sylow
101C23—661no—
102Q8—331no—
103D4—31no—
104D4—111no—
105D4—661no—
106D4—661no—
107D4D3×D1111yescharacteristic, complemented
108C2×C4—331no—
109C2×C4—661no—
110C8—31no—
111C8—111no—
112C2×C3—41no—
113C2×C3—441no—
114C2×C3D4×D1111yescharacteristic
115D3—41no—
116D3—221no—
117C22—21no—
118C22—61no—
119C22—221no—
120C22—331no—
121C22—1322no—
122C4—331no—
123C4—661no—
124C4C2×D3×D1111yescharacteristic
125C3#6696411yescharacteristic, complemented, Sylow
126C2—41no—
127C2—121no—
128C2—441no—
129C2—661no—
130C2#1058725211yescharacteristic
subgroupG/H
centerC2#10587252
commutator, cosocleC3×C4×C11C23
FrattiniC4C2×D3×D11
FittingC3×D4×C11C22
socleC2×C3×C11C2×D4
hypercenterD4D3×D11
hypocenterC3×C11AGL(1,ℤ/8)
LCSG ▷ C3×C4×C11 ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #10587281C2semidirect
2. #10587239C2semidirect
3. C11×#213C2semidirect
4. C3×#4323C2semidirect
5. #10587148C2semidirect
6. #10587146C2semidirect
7. #10587140C2semidirect
10. C3×D4×C11C22semidirect
14. Dic66C22semidirect
18. C3×C11⋊C8C22semidirect
19. C11×C3⋊C8C22semidirect
24. #4323D3semidirect
38. D4×C11C2×D3semidirect
46. C11⋊C8C2×D3semidirect
56. #213D11semidirect
67. C3×C11AGL(1,ℤ/8)semidirect
71. C3×D4C2×D11semidirect
79. C3⋊C8C2×D11semidirect
100. C11#911semidirect
107. D4D3×D11semidirect
125. C3#66964semidirect

Maximal subgroups

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

subgroupindex
#105872812
#105872392
C11×#2132
C3×#43232
#105871482
#105871462
#105871402
#669643
#91111