Finite Group Databasebeta

← #13097101

Subgroups — #13097101

Order 1584.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#634C211yesmaximal, characteristic, complemented
2C3×D132C211yesmaximal, characteristic
3C3×C3⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
4#10587149—31nomaximal
5#10587144—31nomaximal
6C2×C3×D33—21no—
7C32×C4×C11C2211yescharacteristic
8C11×C3⋊Dic3—21no—
9D132D311yescharacteristic
10C11×Dic6—31no—
11C11×Dic6—31no—
12C11×Dic6—61no—
13C3×D44—31no—
14C3⋊(C11⋊C8)D311yescharacteristic, complemented
15C3×C11⋊C8—31no—
16C2×C32×C11D411yescharacteristic
17C3×D33—41no—
18#4325—91noHall
19#3716—111nomaximal, Hall
20C2×D33—21no—
21C2×C3×D11—61no—
22C3×C4×C11—21no—
23C3×C4×C11C2×D311yescharacteristic
24C3×C4×C11C2×D311yescharacteristic
25C11×Dic3—62no—
26C11×Dic3—61no—
27C11×Dic3—61no—
28C32×C11SD1611yescharacteristic, complemented, Hall
29Q8×C11—91no—
30D44—31no—
31C11⋊C8—31no—
32#634D1111yescharacteristic, complemented
33C3×D12—111no—
34C3×C3⋊C8—111no—
35C2×C3×C11—21no—
36C2×C3×C11D1211yescharacteristic
37C2×C3×C11#6711yescharacteristic
38D33—41no—
39C3×D11—121no—
40#214—331no—
41#204—331no—
42C2×D11—61no—
43C4×C11—181no—
44C4×C11D3211yescharacteristic
45C2×C3×D3—221no—
46C32×C4C2×D1111yescharacteristic
47C3⋊Dic3—21no—
48C3×C11—21no—
49C3×C11#20411yescharacteristic, complemented
50C3×C11#21411yescharacteristic, complemented
51C3×D4—331no—
52D12—111no—
53Dic6—31no—
54Dic6—31no—
55Dic6—61no—
56C3×C8—331no—
57C3⋊C8—111no—
58C2×C11#62611yescharacteristic
59D11—121no—
60C2×C32C22⋊D1111yescharacteristic
61C3×D3—441no—
62SD16—991noSylow
63C22×C3—661no—
64C2×D3—221no—
65C3×C4—21no—
66C3×C4D3×D1111yescharacteristic
67C3×C4D3×D1111yescharacteristic
68Dic3—62no—
69Dic3—61no—
70Dic3—61no—
71C11#371611yescharacteristic, complemented, Sylow
72C32#432511yescharacteristic, complemented, Sylow
73Q8—91no—
74D4—331no—
75C8—331no—
76C2×C3—21no—
77C2×C3—1321no—
78C2×C3#6314011yescharacteristic
79C2×C3#6314211yescharacteristic
80D3—441no—
81C22—661no—
82C4—181no—
83C4(C3⋊D3)⋊D1111yescharacteristic
84C3—21no—
85C3#1058714411yescharacteristic, complemented
86C3#1058714911yescharacteristic, complemented
87C2—1321no—
88C2#1171624611yescharacteristic
subgroupG/H
centerC2#11716246
commutator, Fitting, cosocleC32×C4×C11C22
Frattini, hypercenterC4(C3⋊D3)⋊D11
socleC2×C32×C11D4
prime radicalC3×D132C2
hypocenterC32×C11SD16
LCSG ▷ C32×C4×C11 ▷ C2×C32×C11 ▷ C32×C11
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C11×#634C2semidirect
3. C3×C3⋊(C11⋊C8)C2semidirect
14. C3⋊(C11⋊C8)D3semidirect
28. C32×C11SD16semidirect
32. #634D11semidirect
49. C3×C11#204semidirect
50. C3×C11#214semidirect
71. C11#3716semidirect
72. C32#4325semidirect
85. C3#10587144semidirect
86. C3#10587149semidirect

Maximal subgroups

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

subgroupindex
C11×#6342
C3×D1322
C3×C3⋊(C11⋊C8)2
#105871493
#105871443
#371611