Finite Group Databasebeta

← C11×(C3⋊D3)⋊D77 #44479225

Subgroups — C11×(C3⋊D3)⋊D77 #44479225

Order 30492.

296 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C11×D231C212yesmaximal, complemented
2C7×C112×C3⋊D3C211yesmaximal, characteristic, complemented
3D3×C11×D77—32nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C11×D231D312yescomplemented
6D3×C7×C112—32no—
7D3×C7×C112—61no—
8C3×C11×D77—32no—
9C11×(C3⋊D3)⋊D11—71nomaximal, Hall
10C2×C11×D77—91noHall
11(C3⋊D3)⋊D77C1111yesmaximal, characteristic, direct product factor
12C11×(C3⋊D3)⋊D7—111nomaximal
13C3×C7×C112—21no—
14C3×C7×C112C2×D312yescomplemented
15C112×C3⋊D3D711yescharacteristic, complemented
16C3×C11×D33—72no—
17C2×C7×C112—91no—
18C11×D77—32no—
19D3×C11×D11—212no—
20C7×C11×C3⋊D3—25no—
21C7×C11×C3⋊D3D1111yescharacteristic, complemented
22C7×C11×C3⋊D3C2×C1111yescharacteristic, complemented
23C3×D231C2×C1112yescomplemented
24C3×C11×D21—112no—
25C32×C112C2×D711yescharacteristic, complemented, Hall
26D3×D77—32no—
27D3×C11×D7—332no—
28C7×C112D3211yescharacteristic, complemented, Hall
29C11×D33—72no—
30D3×C112—32no—
31D3×C112—61no—
32C3×C11×D11—212no—
33C32×C7×C11—25no—
34C32×C7×C11C2×D1111yescharacteristic, complemented
35C32×C7×C11C22×C1111yescharacteristic, complemented
36C2×C11×D11—631noHall
37D231D3×C1112yescomplemented
38C11×D21—112no—
39D3×C7×C11—32no—
40D3×C7×C11—32no—
41D3×C7×C11—61no—
42D3×C7×C11—61no—
43D3×C7×C11—610no—
44D3×C7×C11—610no—
45C3×D77—32no—
46C3×C11×D7—332no—
47(C3⋊D3)⋊D11—71no—
48D32×C11—771no—
49C3×C112—21no—
50C3×C112D3×D712yescomplemented
51C2×D77—91no—
52C2×C11×D7—991no—
53(C3⋊D3)⋊D7—111noHall
54C2×C112—91no—
55C11×D11—212no—
56C3×C7×C11—210no—
57C3×C7×C11—21no—
58C3×C7×C11—21no—
59C3×C7×C11—210no—
60C3×C7×C11D3×D1112yescomplemented
61C3×C7×C11C2×D3×C1112yescomplemented
62C11×C3⋊D3—25no—
63C11×C3⋊D3C11×D711yescharacteristic, complemented
64C11×C3⋊D3D7711yescharacteristic, complemented
65C3×D33—72no—
66C3×D3×C11—772no—
67C2×C7×C11—91no—
68C2×C7×C11—91no—
69C2×C7×C11—185no—
70D77—32no—
71C11×D7—332no—
72C2×D3×C11—2312no—
73D3×D11—212no—
74C7×C3⋊D3C11×D1111yescharacteristic, complemented
75C3×D21—112no—
76C112(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
77C32×C11—25no—
78C32×C11C2×C11×D711yescharacteristic, complemented
79C32×C11C2×D7711yescharacteristic, complemented
80D3×D7—332no—
81C7×C11—25no—
82C7×C11D32×C1111yescharacteristic, complemented
83C7×C11(C3⋊D3)⋊D1111yescharacteristic, complemented
84C2×C3×C11—2312no—
85D33—72no—
86C3×D11—212no—
87D3×C11—32no—
88D3×C11—32no—
89D3×C11—610no—
90D3×C11—61no—
91D3×C11—61no—
92D3×C11—610no—
93D3×C11—772no—
94C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
95C22×C11—6931no—
96C2×D11—631no—
97D21—112no—
98C3×D7—332no—
99D3×C7—32no—
100D3×C7—61no—
101D32—771noHall
102C3×C11—210no—
103C3×C11—21no—
104C3×C11—21no—
105C3×C11—210no—
106C3×C11D3×C11×D712yescomplemented
107C3×C11D3×D7712yescomplemented
108C2×D7—991noHall
109C2×C11—91no—
110C2×C11—91no—
111C2×C11—185no—
112C2×C11—2312no—
113D11—212no—
114C3×C7—21no—
115C3×C7D3×C11×D1112yescomplemented
116C3⋊D3C11×D7711yescharacteristic, complemented
117C3×D3—772no—
118C2×C7—91no—
119D7—332no—
120C2×D3—2312no—
121C11—25no—
122C11C11×(C3⋊D3)⋊D711yescharacteristic, complemented
123C11(C3⋊D3)⋊D7711yescharacteristic, direct product factor
124C32C2×C11×D7711yescharacteristic, complemented, Sylow
125C7C11×(C3⋊D3)⋊D1111yescharacteristic, complemented, Sylow
126C2×C3—2312no—
127D3—32no—
128D3—61no—
129D3—772no—
130C22—6931noSylow
131C3—21no—
132C3D3×C11×D7712yescomplemented
133C2—91no—
134C2—2312no—
subgroupG/H
center, hypercenterC11(C3⋊D3)⋊D77
commutator, cosocle, hypocenterC32×C7×C11C22×C11
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×D231C2semidirect
2. C7×C112×C3⋊D3C2semidirect
4. C32×C7×C112C22semidirect
5. C11×D231D3semidirect
11. (C3⋊D3)⋊D77C11direct (N × H)
14. C3×C7×C112C2×D3semidirect
15. C112×C3⋊D3D7semidirect
21. C7×C11×C3⋊D3D11semidirect
22. C7×C11×C3⋊D3C2×C11semidirect
23. C3×D231C2×C11semidirect
25. C32×C112C2×D7semidirect
28. C7×C112D32semidirect
34. C32×C7×C11C2×D11semidirect
35. C32×C7×C11C22×C11semidirect
37. D231D3×C11semidirect
50. C3×C112D3×D7semidirect
60. C3×C7×C11D3×D11semidirect
61. C3×C7×C11C2×D3×C11semidirect
63. C11×C3⋊D3C11×D7semidirect
64. C11×C3⋊D3D77semidirect
74. C7×C3⋊D3C11×D11semidirect
76. C112(C3⋊D3)⋊D7semidirect
78. C32×C11C2×C11×D7semidirect
79. C32×C11C2×D77semidirect
82. C7×C11D32×C11semidirect
83. C7×C11(C3⋊D3)⋊D11semidirect
94. C32×C7C2×C11×D11semidirect
106. C3×C11D3×C11×D7semidirect
107. C3×C11D3×D77semidirect
115. C3×C7D3×C11×D11semidirect
116. C3⋊D3C11×D77semidirect
122. C11C11×(C3⋊D3)⋊D7semidirect
123. C11(C3⋊D3)⋊D77direct (N × H)
124. C32C2×C11×D77semidirect
125. C7C11×(C3⋊D3)⋊D11semidirect
132. C3D3×C11×D77semidirect

Maximal subgroups

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

subgroupindex
C3×C11×D2312
C7×C112×C3⋊D32
D3×C11×D773
C11×(C3⋊D3)⋊D117
(C3⋊D3)⋊D7711
C11×(C3⋊D3)⋊D711