Finite Group Databasebeta

← C2×C11×C3⋊D231 #44479272

Subgroups — C2×C11×C3⋊D231 #44479272

Order 30492.

360 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C11×C3⋊D231C212yesmaximal, direct product factor
2C2×C32×C7×C112C211yesmaximal, characteristic, complemented
3C2×C11×D231—34nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C11×D231—38no—
6C2×C3×C7×C112D314yescomplemented
7C2×C11×C3⋊D33—71nomaximal, Hall
8C2×C11×D77—91noHall
9C2×C11×C3⋊D21—111nomaximal
10C2×C3⋊D231C1111yesmaximal, characteristic, direct product factor
11C3×C7×C112C2×D314yescomplemented
12C11×C3⋊D33—72no—
13C2×C32×C112D711yescharacteristic, complemented
14C2×C7×C112C3⋊D311yescharacteristic, complemented
15C11×D77—92no—
16C2×C11×D33—214no—
17C2×C32×C7×C11—25no—
18C2×C32×C7×C11D1111yescharacteristic, complemented
19C2×C32×C7×C11C2×C1111yescharacteristic, complemented
20C3⋊D231C2×C1112yesdirect product factor
21C11×C3⋊D21—112no—
22C32×C112C2×D711yescharacteristic, complemented, Hall
23C2×D231—34no—
24C2×C11×D21—334no—
25C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
26C2×C3×C112D2114yescomplemented
27C11×D33—218no—
28C32×C7×C11—25no—
29C32×C7×C11C2×D1111yescharacteristic, complemented
30C32×C7×C11C22×C1111yescharacteristic, complemented
31C2×C11×D11—631noHall
32C2×C3×C7×C11—220no—
33C2×C3×C7×C11D3×C1114yescomplemented
34C2×C3×C7×C11D3314yescomplemented
35D231—38no—
36C11×D21—338no—
37C2×C3⋊D33—71no—
38C2×C11×C3⋊D3—771no—
39C3×C112C2×D2114yescomplemented
40C2×D77—91no—
41C2×C11×D7—991no—
42C2×C3⋊D21—111noHall
43C2×C112C3⋊D2111yescharacteristic, complemented
44C11×D11—632no—
45C3×C7×C11—220no—
46C3×C7×C11C2×D3×C1114yescomplemented
47C3×C7×C11C2×D3314yescomplemented
48C2×C32×C11—25no—
49C2×C32×C11C11×D711yescharacteristic, complemented
50C2×C32×C11D7711yescharacteristic, complemented
51C3⋊D33—72no—
52C11×C3⋊D3—772no—
53C2×C7×C11—25no—
54C2×C7×C11C11×C3⋊D311yescharacteristic, complemented
55C2×C7×C11C3⋊D3311yescharacteristic, complemented
56D77—92no—
57C11×D7—992no—
58C2×D33—214no—
59C2×D3×C11—2314no—
60C2×C32×C7C11×D1111yescharacteristic, complemented
61C3⋊D21—112no—
62C112C2×C3⋊D2111yescharacteristic, complemented, Sylow
63C32×C11—25no—
64C32×C11C2×C11×D711yescharacteristic, complemented
65C32×C11C2×D7711yescharacteristic, complemented
66C2×D21—334no—
67C7×C11—25no—
68C7×C11C2×C11×C3⋊D311yescharacteristic, complemented
69C7×C11C2×C3⋊D3311yescharacteristic, complemented
70C2×C3×C11—220no—
71C2×C3×C11C11×D2114yescomplemented
72C2×C3×C11D23114yescomplemented
73D33—218no—
74D3×C11—2318no—
75C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
76C22×C11—6931no—
77C2×D11—631no—
78C2×C3×C7C11×D3314yescomplemented
79D21—338no—
80C2×C3⋊D3—771noHall
81C3×C11—220no—
82C3×C11C2×C11×D2114yescomplemented
83C3×C11C2×D23114yescomplemented
84C2×D7—991noHall
85C2×C11—25no—
86C2×C11—6932no—
87C2×C11C11×C3⋊D2111yescharacteristic, complemented
88C2×C11C3⋊D23111yescharacteristic, direct product factor
89D11—632no—
90C3×C7C2×C11×D3314yescomplemented
91C2×C32C11×D7711yescharacteristic, complemented
92C3⋊D3—772no—
93C2×C7C11×C3⋊D3311yescharacteristic, complemented
94D7—992no—
95C2×D3—2314no—
96C11—25no—
97C11C2×C3⋊D23111yescharacteristic, direct product factor
98C11C2×C11×C3⋊D2111yescharacteristic, complemented
99C32C2×C11×D7711yescharacteristic, complemented, Sylow
100C7C2×C11×C3⋊D3311yescharacteristic, complemented, Sylow
101C2×C3C11×D23114yescomplemented
102D3—2318no—
103C22—6931noSylow
104C3C2×C11×D23114yescomplemented
105C2—6932no—
106C2C11×C3⋊D23111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11C3⋊D231
commutator, cosocle, hypocenterC32×C7×C11C22×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×C3⋊D231C2direct (N × H)
2. C2×C32×C7×C112C2semidirect
4. C32×C7×C112C22semidirect
6. C2×C3×C7×C112D3semidirect
10. C2×C3⋊D231C11direct (N × H)
11. C3×C7×C112C2×D3semidirect
13. C2×C32×C112D7semidirect
14. C2×C7×C112C3⋊D3semidirect
18. C2×C32×C7×C11D11semidirect
19. C2×C32×C7×C11C2×C11semidirect
20. C3⋊D231C2×C11direct (N × H)
22. C32×C112C2×D7semidirect
25. C7×C112C2×C3⋊D3semidirect
26. C2×C3×C112D21semidirect
29. C32×C7×C11C2×D11semidirect
30. C32×C7×C11C22×C11semidirect
33. C2×C3×C7×C11D3×C11semidirect
34. C2×C3×C7×C11D33semidirect
39. C3×C112C2×D21semidirect
43. C2×C112C3⋊D21semidirect
46. C3×C7×C11C2×D3×C11semidirect
47. C3×C7×C11C2×D33semidirect
49. C2×C32×C11C11×D7semidirect
50. C2×C32×C11D77semidirect
54. C2×C7×C11C11×C3⋊D3semidirect
55. C2×C7×C11C3⋊D33semidirect
60. C2×C32×C7C11×D11semidirect
62. C112C2×C3⋊D21semidirect
64. C32×C11C2×C11×D7semidirect
65. C32×C11C2×D77semidirect
68. C7×C11C2×C11×C3⋊D3semidirect
69. C7×C11C2×C3⋊D33semidirect
71. C2×C3×C11C11×D21semidirect
72. C2×C3×C11D231semidirect
75. C32×C7C2×C11×D11semidirect
78. C2×C3×C7C11×D33semidirect
82. C3×C11C2×C11×D21semidirect
83. C3×C11C2×D231semidirect
87. C2×C11C11×C3⋊D21semidirect
88. C2×C11C3⋊D231direct (N × H)
90. C3×C7C2×C11×D33semidirect
91. C2×C32C11×D77semidirect
93. C2×C7C11×C3⋊D33semidirect
97. C11C2×C3⋊D231direct (N × H)
98. C11C2×C11×C3⋊D21semidirect
99. C32C2×C11×D77semidirect
100. C7C2×C11×C3⋊D33semidirect
101. C2×C3C11×D231semidirect
104. C3C2×C11×D231semidirect
106. C2C11×C3⋊D231direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C3⋊D2312
C2×C32×C7×C1122
C2×C11×D2313
C2×C11×C3⋊D337
C2×C11×C3⋊D2111
C2×C3⋊D23111