Finite Group Databasebeta

← C11×C3⋊Dic231 #44479035

Subgroups — C11×C3⋊Dic231 #44479035

Order 30492.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C7×C112C211yesmaximal, characteristic
2C11×Dic231—34nomaximal
3C32×C7×C112C411yescharacteristic, complemented, Hall
4C2×C3×C7×C112D314yes—
5C11×C3⋊Dic33—71nomaximal, Hall
6C11×Dic77—91noHall
7C3⋊Dic231C1111yesmaximal, characteristic, direct product factor
8C11×C3⋊Dic21—111nomaximal
9C3×C7×C112Dic314yescomplemented
10C2×C32×C112D711yescharacteristic
11C2×C7×C112C3⋊D311yescharacteristic
12C11×Dic33—214no—
13C2×C32×C7×C11—25no—
14C2×C32×C7×C11D1111yescharacteristic
15C2×C32×C7×C11C2×C1111yescharacteristic
16C32×C112Dic711yescharacteristic, complemented, Hall
17Dic231—34no—
18C11×Dic21—334no—
19C7×C112C3⋊Dic311yescharacteristic, complemented, Hall
20C2×C3×C112D2114yes—
21C32×C7×C11—25no—
22C32×C7×C11Dic1111yescharacteristic, complemented
23C32×C7×C11C4×C1111yescharacteristic, complemented
24C11×Dic11—631noHall
25C2×C3×C7×C11—220no—
26C2×C3×C7×C11D3×C1114yes—
27C2×C3×C7×C11D3314yes—
28C3⋊Dic33—71no—
29C11×C3⋊Dic3—771no—
30C3×C112Dic2114yescomplemented
31Dic77—91no—
32C11×Dic7—991no—
33C3⋊Dic21—111noHall
34C2×C112C3⋊D2111yescharacteristic
35C3×C7×C11—220no—
36C3×C7×C11C11×Dic314yescomplemented
37C3×C7×C11Dic3314yescomplemented
38C2×C32×C11—25no—
39C2×C32×C11C11×D711yescharacteristic
40C2×C32×C11D7711yescharacteristic
41C2×C7×C11—25no—
42C2×C7×C11C11×C3⋊D311yescharacteristic
43C2×C7×C11C3⋊D3311yescharacteristic
44Dic33—214no—
45C11×Dic3—2314no—
46C2×C32×C7C11×D1111yescharacteristic
47C112C3⋊Dic2111yescharacteristic, complemented, Sylow
48C32×C11—25no—
49C32×C11C11×Dic711yescharacteristic, complemented
50C32×C11Dic7711yescharacteristic, complemented
51Dic21—334no—
52C7×C11—25no—
53C7×C11C11×C3⋊Dic311yescharacteristic, complemented
54C7×C11C3⋊Dic3311yescharacteristic, complemented
55C2×C3×C11—220no—
56C2×C3×C11C11×D2114yes—
57C2×C3×C11D23114yes—
58C32×C7C11×Dic1111yescharacteristic, complemented, Hall
59C4×C11—6931no—
60Dic11—631no—
61C2×C3×C7C11×D3314yes—
62C3⋊Dic3—771noHall
63C3×C11—220no—
64C3×C11C11×Dic2114yescomplemented
65C3×C11Dic23114yescomplemented
66Dic7—991noHall
67C2×C11—25no—
68C2×C11C11×C3⋊D2111yescharacteristic
69C2×C11C3⋊D23111yescharacteristic
70C3×C7C11×Dic3314yescomplemented
71C2×C32C11×D7711yescharacteristic
72C2×C7C11×C3⋊D3311yescharacteristic
73Dic3—2314no—
74C11—25no—
75C11C11×C3⋊Dic2111yescharacteristic, complemented
76C11C3⋊Dic23111yescharacteristic, direct product factor
77C32C11×Dic7711yescharacteristic, complemented, Sylow
78C7C11×C3⋊Dic3311yescharacteristic, complemented, Sylow
79C2×C3C11×D23114yes—
80C4—6931noSylow
81C3C11×Dic23114yescomplemented
82C2C11×C3⋊D23111yescharacteristic
subgroupG/H
center, hypercenterC2×C11C3⋊D231
commutator, hypocenterC32×C7×C11C4×C11
FrattiniC2C11×C3⋊D231
Fitting, socle, prime radicalC2×C32×C7×C112C2
cosocleC2×C32×C7×C11C2×C11
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
3. C32×C7×C112C4semidirect
7. C3⋊Dic231C11direct (N × H)
9. C3×C7×C112Dic3semidirect
16. C32×C112Dic7semidirect
19. C7×C112C3⋊Dic3semidirect
22. C32×C7×C11Dic11semidirect
23. C32×C7×C11C4×C11semidirect
30. C3×C112Dic21semidirect
36. C3×C7×C11C11×Dic3semidirect
37. C3×C7×C11Dic33semidirect
47. C112C3⋊Dic21semidirect
49. C32×C11C11×Dic7semidirect
50. C32×C11Dic77semidirect
53. C7×C11C11×C3⋊Dic3semidirect
54. C7×C11C3⋊Dic33semidirect
58. C32×C7C11×Dic11semidirect
64. C3×C11C11×Dic21semidirect
65. C3×C11Dic231semidirect
70. C3×C7C11×Dic33semidirect
75. C11C11×C3⋊Dic21semidirect
76. C11C3⋊Dic231direct (N × H)
77. C32C11×Dic77semidirect
78. C7C11×C3⋊Dic33semidirect
81. C3C11×Dic231semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C7×C1122
C11×Dic2313
C11×C3⋊Dic337
C3⋊Dic23111
C11×C3⋊Dic2111