Finite Group Databasebeta

← #13097103

Subgroups — #13097103

Order 1584.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D132C211yesmaximal, characteristic
2C3×Dic66C211yesmaximal, characteristic, complemented
3C11×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10587147—31nomaximal
5#10587146—31nomaximal
6C2×C3×D33—21no—
7C32×C4×C11C2211yescharacteristic
8C3×Dic33—21no—
9D132D311yescharacteristic
10Dic66D311yescharacteristic, complemented
11C3×D44—31no—
12C3×Dic22—31no—
13C11×C3⋊C8—31no—
14C11×C3⋊C8—31no—
15C11×C3⋊C8—61no—
16C2×C32×C11D411yescharacteristic
17C3×D33—41no—
18#4314—91noHall
19#3715—111nomaximal, Hall
20C2×D33—21no—
21C2×C3×D11—61no—
22C3×C4×C11—21no—
23C3×C4×C11C2×D311yescharacteristic
24C3×C4×C11C2×D311yescharacteristic
25Dic33—21no—
26C3×Dic11—61no—
27C32×C11SD1611yescharacteristic, complemented, Hall
28D44—31no—
29Dic22—31no—
30C8×C11—91no—
31C3×D12—111no—
32C3×Dic6—111no—
33C3⋊(C3⋊C8)D1111yescharacteristic, complemented
34C2×C3×C11—21no—
35C2×C3×C11#6711yescharacteristic
36C2×C3×C11#6711yescharacteristic
37D33—41no—
38C3×D11—121no—
39#215—331no—
40#214—331no—
41C2×D11—61no—
42C4×C11D3211yescharacteristic
43Dic11—61no—
44C2×C3×D3—221no—
45C32×C4C2×D1111yescharacteristic
46C3×Dic3—221no—
47C3×C11—21no—
48C3×C11#21411yescharacteristic, complemented
49C3×C11#21511yescharacteristic, complemented
50C3×Q8—331no—
51C3×D4—331no—
52D12—111no—
53Dic6—111no—
54C3⋊C8—31no—
55C3⋊C8—31no—
56C3⋊C8—61no—
57C2×C11#62511yescharacteristic
58D11—121no—
59C2×C32D4411yescharacteristic
60C3×D3—441no—
61SD16—991noSylow
62C22×C3—661no—
63C2×D3—221no—
64C3×C4—21no—
65C3×C4—661no—
66C3×C4D3×D1111yescharacteristic
67C3×C4D3×D1111yescharacteristic
68Dic3—221no—
69C11#371511yescharacteristic, complemented, Sylow
70C32#431411yescharacteristic, complemented, Sylow
71Q8—331no—
72D4—331no—
73C8—91no—
74C2×C3—21no—
75C2×C3—1321no—
76C2×C3#6314111yescharacteristic
77C2×C3#6314111yescharacteristic
78D3—441no—
79C22—661no—
80C4—661no—
81C4(C3⋊D3)⋊D1111yescharacteristic
82C3—21no—
83C3#1058714611yescharacteristic, complemented
84C3#1058714711yescharacteristic, complemented
85C2—1321no—
86C2#1171624711yescharacteristic
subgroupG/H
centerC2#11716247
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
2. C3×Dic66C2semidirect
3. C11×C3⋊(C3⋊C8)C2semidirect
10. Dic66D3semidirect
27. C32×C11SD16semidirect
33. C3⋊(C3⋊C8)D11semidirect
48. C3×C11#214semidirect
49. C3×C11#215semidirect
69. C11#3715semidirect
70. C32#4314semidirect
83. C3#10587146semidirect
84. C3#10587147semidirect

Maximal subgroups

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

subgroupindex
C3×D1322
C3×Dic662
C11×C3⋊(C3⋊C8)2
#105871473
#105871463
#371511