Finite Group Databasebeta

← C7×D11×C3⋊D33 #44479232

Subgroups — C7×D11×C3⋊D33 #44479232

Order 30492.

360 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C7×C11×D11C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊D33C211yesmaximal, characteristic, complemented
3C7×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4C7×D11×D33—34nomaximal
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C7×C3⋊(C11⋊D11)—34no—
7C7×C11×D33—34no—
8C3×C7×C11×D11D314yescomplemented
9D11×C3⋊D33C711yesmaximal, characteristic, direct product factor, Hall
10C7×D112—91noHall
11C2×C7×C3⋊D33—111nomaximal
12C7×C3⋊D3×D11—111nomaximal
13C3×C7×C112C2×D314yescomplemented
14C3⋊(C3⋊(C11⋊D11))C2×C711yescharacteristic, complemented
15C11×C3⋊D33C2×C711yescharacteristic, complemented
16C32×C11×D11C2×C711yescharacteristic, complemented
17C7×C11⋊D11—91no—
18C7×C11×D11—91no—
19C7×C11×D11C3⋊D311yescharacteristic, complemented
20D11×D33—34no—
21C2×C32×C7×C11—111no—
22C7×C3⋊D33—111no—
23C7×C3⋊D33—111no—
24C7×C3⋊D33—225no—
25C7×C3⋊D33D1111yescharacteristic, direct product factor
26C7×C11×C3⋊D3—111no—
27C32×C7×D11D1111yescharacteristic, complemented
28C32×C112C22×C711yescharacteristic, complemented, Hall
29C2×C7×D33—334no—
30D3×C7×D11—334no—
31C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
32C3⋊(C11⋊D11)—34no—
33C11×D33—34no—
34C3×C11×D11D3×C714yescomplemented
35C32×C7×C11—25no—
36C32×C7×C11C2×D1111yescharacteristic, complemented
37C32×C7×C11C2×D1111yescharacteristic, complemented
38D112—91noHall
39C2×C3×C7×C11—114no—
40C7×D33—34no—
41C7×D33—334no—
42C7×D33—334no—
43C7×D33—6620no—
44D3×C7×C11—334no—
45C3×C7×D11D3314yescomplemented
46C2×C3⋊D33—111no—
47C3⋊D3×D11—111no—
48C3×C112C2×D3×C714yescomplemented
49C2×C7×D11—991no—
50C2×C7×D11—991no—
51C2×C7×C3⋊D3—1211noHall
52C11⋊D11—91no—
53C11×D11—91no—
54C11×D11C7×C3⋊D311yescharacteristic, complemented
55C3×C7×C11—220no—
56C3×C7×C11D3×D1114yescomplemented
57C3×C7×C11C2×D3314yescomplemented
58C2×C32×C11—111no—
59C3⋊D33—111no—
60C3⋊D33—111no—
61C3⋊D33—225no—
62C3⋊D33C7×D1111yescharacteristic, direct product factor
63C11×C3⋊D3—111no—
64C32×D11C7×D1111yescharacteristic, complemented
65C2×C7×C11—111no—
66C2×C7×C11—991no—
67C7×D11—91no—
68C7×D11—991no—
69C7×D11—991no—
70C7×D11—1985no—
71C7×D11C3⋊D3311yescharacteristic, direct product factor
72C2×D33—334no—
73D3×D11—334no—
74C2×C32×C7—111no—
75C7×C3⋊D3—111no—
76C7×C3⋊D3—1211no—
77C112C2×C7×C3⋊D311yescharacteristic, complemented, Sylow
78C32×C11—25no—
79C32×C11C2×C7×D1111yescharacteristic, complemented
80C32×C11C2×C7×D1111yescharacteristic, complemented
81C2×D3×C7—3634no—
82C7×C11—25no—
83C7×C11C3⋊D3×D1111yescharacteristic, complemented
84C7×C11C2×C3⋊D3311yescharacteristic, complemented
85C2×C3×C11—114no—
86D33—34no—
87D33—334no—
88D33—334no—
89D33—6620no—
90C3×D11C7×D3314yescomplemented
91D3×C11—334no—
92C32×C7D11211yescharacteristic, complemented, Hall
93C2×D11—991no—
94C2×D11—991no—
95C2×C3×C7—114no—
96D3×C7—334no—
97D3×C7—3634no—
98C2×C3⋊D3—1211noHall
99C3×C11—220no—
100C3×C11D3×C7×D1114yescomplemented
101C3×C11C2×C7×D3314yescomplemented
102C22×C7—10891noHall
103C2×C11—111no—
104C2×C11—991no—
105D11—91no—
106D11—991no—
107D11—991no—
108D11—1985no—
109D11C7×C3⋊D3311yescharacteristic, direct product factor
110C3×C7D11×D3314yescomplemented
111C2×C32—111no—
112C3⋊D3—111no—
113C3⋊D3—1211no—
114C2×C7—111no—
115C2×C7—10891no—
116C2×C7—991no—
117C2×D3—3634no—
118C11—25no—
119C11C7×C3⋊D3×D1111yescharacteristic, complemented
120C11C2×C7×C3⋊D3311yescharacteristic, complemented
121C32C7×D11211yescharacteristic, complemented, Sylow
122C7D11×C3⋊D3311yescharacteristic, direct product factor, Sylow
123C2×C3—114no—
124D3—334no—
125D3—3634no—
126C22—10891noSylow
127C3C7×D11×D3314yescomplemented
128C2—111no—
129C2—10891no—
130C2—991no—
subgroupG/H
center, hypercenterC7D11×C3⋊D33
commutator, cosocle, hypocenterC32×C112C22×C7
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D11C2semidirect
2. C7×C11×C3⋊D33C2semidirect
3. C7×C3⋊(C3⋊(C11⋊D11))C2semidirect
5. C32×C7×C112C22semidirect
8. C3×C7×C11×D11D3semidirect
9. D11×C3⋊D33C7direct (N × H)
13. C3×C7×C112C2×D3semidirect
14. C3⋊(C3⋊(C11⋊D11))C2×C7semidirect
15. C11×C3⋊D33C2×C7semidirect
16. C32×C11×D11C2×C7semidirect
19. C7×C11×D11C3⋊D3semidirect
25. C7×C3⋊D33D11direct (N × H)
27. C32×C7×D11D11semidirect
28. C32×C112C22×C7semidirect
31. C7×C112C2×C3⋊D3semidirect
34. C3×C11×D11D3×C7semidirect
36. C32×C7×C11C2×D11semidirect
37. C32×C7×C11C2×D11semidirect
45. C3×C7×D11D33semidirect
48. C3×C112C2×D3×C7semidirect
54. C11×D11C7×C3⋊D3semidirect
56. C3×C7×C11D3×D11semidirect
57. C3×C7×C11C2×D33semidirect
62. C3⋊D33C7×D11direct (N × H)
64. C32×D11C7×D11semidirect
71. C7×D11C3⋊D33direct (N × H)
77. C112C2×C7×C3⋊D3semidirect
79. C32×C11C2×C7×D11semidirect
80. C32×C11C2×C7×D11semidirect
83. C7×C11C3⋊D3×D11semidirect
84. C7×C11C2×C3⋊D33semidirect
90. C3×D11C7×D33semidirect
92. C32×C7D112semidirect
100. C3×C11D3×C7×D11semidirect
101. C3×C11C2×C7×D33semidirect
109. D11C7×C3⋊D33direct (N × H)
110. C3×C7D11×D33semidirect
119. C11C7×C3⋊D3×D11semidirect
120. C11C2×C7×C3⋊D33semidirect
121. C32C7×D112semidirect
122. C7D11×C3⋊D33direct (N × H)
127. C3C7×D11×D33semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D112
C7×C11×C3⋊D332
C7×C3⋊(C3⋊(C11⋊D11))2
C7×D11×D333
D11×C3⋊D337
C2×C7×C3⋊D3311
C7×C3⋊D3×D1111