Finite Group Databasebeta

← C11⋊C5×(C3⋊D3)⋊D11 #36345122

Subgroups — C11⋊C5×(C3⋊D3)⋊D11 #36345122

Order 21780.

188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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⋊D3×C11⋊C5C211yesmaximal, characteristic, complemented
2C3×C11⋊C5×D33C212yesmaximal, complemented
3D3×D11×C11⋊C5—32nomaximal
4C32×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5C11×(C3⋊D3)⋊D11C511yesmaximal, characteristic, complemented, Hall
6C11⋊C5×D33D312yescomplemented
7D3×C11×C11⋊C5—32no—
8D3×C11×C11⋊C5—61no—
9C3×D11×C11⋊C5—32no—
10C2×D11×C11⋊C5—91noHall
11C112×C3⋊D3C2×C511yescharacteristic, complemented
12C3×C11×D33C2×C512yescomplemented
13C5×(C3⋊D3)⋊D11—111nomaximal
14D32×C11⋊C5—111nomaximal
15C3×C11×C11⋊C5—21no—
16C3×C11×C11⋊C5C2×D312yescomplemented
17D3×C11×D11—32no—
18C2×C11×C11⋊C5—91no—
19D11×C11⋊C5—32no—
20C32×C112C22×C511yescharacteristic, complemented, Hall
21C5×C11×C3⋊D3—111no—
22C3×C5×D33—112no—
23C3⋊D3×C11⋊C5D1111yescharacteristic, complemented
24C3×D3×C11⋊C5—112no—
25C11×D33C5×D312yescomplemented
26D3×C112—32no—
27D3×C112—61no—
28C3×C11×D11—32no—
29C5×D3×D11—332no—
30C2×D3×C11⋊C5—332no—
31C11×C11⋊C5D3211yescharacteristic, complemented, Hall
32C32×C5×C11—111no—
33C32×C11⋊C5C2×D1111yescharacteristic, complemented
34C2×C11×D11—91noHall
35(C3⋊D3)⋊D11C11⋊C511yescharacteristic, direct product factor
36D32×C11—111no—
37C3×C112—21no—
38C3×C112C2×C5×D312yescomplemented
39C5×D33—112no—
40C5×D3×C11—332no—
41C5×D3×C11—661no—
42C3×C5×D11—332no—
43C2×C3×C11⋊C5—332no—
44D3×C11⋊C5—32no—
45D3×C11⋊C5—61no—
46D3×C11⋊C5—112no—
47C2×C112—91no—
48C11×D11—32no—
49C2×C5×D11—991no—
50C22×C11⋊C5—991no—
51C11×C3⋊D3—101no—
52C11×C3⋊D3C2×C11⋊C511yescharacteristic, complemented
53C11×C3⋊D3C5×D1111yescharacteristic, complemented
54C3×D33C2×C11⋊C512yescomplemented
55C3×D3×C11—112no—
56C5×D32—1211noHall
57C3×C5×C11—112no—
58C3×C5×C11—221no—
59C3×C11⋊C5—21no—
60C3×C11⋊C5D3×D1112yescomplemented
61C2×D3×C11—332no—
62D3×D11—32no—
63C112C5×D3211yescharacteristic, complemented, Sylow
64C2×C5×C11—991no—
65C5×D11—332no—
66C2×C11⋊C5—91no—
67C2×C11⋊C5—332no—
68C32×C11—101no—
69C32×C11C22×C11⋊C511yescharacteristic, complemented
70C32×C11C2×C5×D1111yescharacteristic, complemented
71C5×C3⋊D3—111no—
72C3×C5×D3—1212no—
73C2×C3×C11—332no—
74D33D3×C11⋊C512yescomplemented
75C3×D11—32no—
76D3×C11—32no—
77D3×C11—32no—
78D3×C11—61no—
79D3×C11—61no—
80D3×C11—112no—
81D3×C11—302no—
82D3×C11—302no—
83C2×C5×D3—3632no—
84C5×C11—111no—
85C11⋊C5(C3⋊D3)⋊D1111yescharacteristic, direct product factor
86C32×C5—111noHall
87C22×C11—991no—
88C2×D11—91no—
89D32—111noHall
90C3×C11—21no—
91C3×C11—21no—
92C3×C11—102no—
93C3×C11—102no—
94C3×C11C2×D3×C11⋊C512yescomplemented
95C3×C11C5×D3×D1112yescomplemented
96C2×C3×C5—3632no—
97C5×D3—332no—
98C5×D3—661no—
99C5×D3—1212no—
100C2×C11—91no—
101C2×C11—91no—
102C2×C11—332no—
103C2×C11—901no—
104D11—32no—
105C22×C5—10891noHall
106C3⋊D3D11×C11⋊C511yescharacteristic, complemented
107C3×D3—112no—
108C3×C5—112no—
109C3×C5—221no—
110C2×D3—332no—
111C11—101no—
112C11D32×C11⋊C511yescharacteristic, complemented
113C11C5×(C3⋊D3)⋊D1111yescharacteristic, complemented
114C2×C5—991no—
115C2×C5—3632no—
116C32C2×D11×C11⋊C511yescharacteristic, complemented, Sylow
117C2×C3—332no—
118D3—32no—
119D3—61no—
120D3—112no—
121C5—111noSylow
122C22—991noSylow
123C3—21no—
124C3D3×D11×C11⋊C512yescomplemented
125C2—91no—
126C2—332no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C112C22×C5
LCSG ▷ C32×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11×C3⋊D3×C11⋊C5C2semidirect
2. C3×C11⋊C5×D33C2semidirect
4. C32×C11×C11⋊C5C22semidirect
5. C11×(C3⋊D3)⋊D11C5semidirect
6. C11⋊C5×D33D3semidirect
11. C112×C3⋊D3C2×C5semidirect
12. C3×C11×D33C2×C5semidirect
16. C3×C11×C11⋊C5C2×D3semidirect
20. C32×C112C22×C5semidirect
23. C3⋊D3×C11⋊C5D11semidirect
25. C11×D33C5×D3semidirect
31. C11×C11⋊C5D32semidirect
33. C32×C11⋊C5C2×D11semidirect
35. (C3⋊D3)⋊D11C11⋊C5direct (N × H)
38. C3×C112C2×C5×D3semidirect
52. C11×C3⋊D3C2×C11⋊C5semidirect
53. C11×C3⋊D3C5×D11semidirect
54. C3×D33C2×C11⋊C5semidirect
60. C3×C11⋊C5D3×D11semidirect
63. C112C5×D32semidirect
69. C32×C11C22×C11⋊C5semidirect
70. C32×C11C2×C5×D11semidirect
74. D33D3×C11⋊C5semidirect
85. C11⋊C5(C3⋊D3)⋊D11direct (N × H)
94. C3×C11C2×D3×C11⋊C5semidirect
95. C3×C11C5×D3×D11semidirect
106. C3⋊D3D11×C11⋊C5semidirect
112. C11D32×C11⋊C5semidirect
113. C11C5×(C3⋊D3)⋊D11semidirect
116. C32C2×D11×C11⋊C5semidirect
124. C3D3×D11×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C11×C3⋊D3×C11⋊C52
C3×C11⋊C5×D332
D3×D11×C11⋊C53
C11×(C3⋊D3)⋊D115
C5×(C3⋊D3)⋊D1111
D32×C11⋊C511