Finite Group Databasebeta

← C7×C11×C3⋊D3×D13 #49114969

Subgroups — C7×C11×C3⋊D3×D13 #49114969

Order 36036.

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 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×D13C211yesmaximal, characteristic, complemented
2C7×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C11×C3⋊D39C211yesmaximal, characteristic, complemented
4D3×C7×C11×D13—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C7×C11×D39—34no—
7D3×C7×C11×C13—34no—
8C3×C7×C11×D13D314yescomplemented
9C11×C3⋊D3×D13C711yesmaximal, characteristic, direct product factor, Hall
10C2×C7×C11×D13—91noHall
11C7×C3⋊D3×D13C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C2×C7×C11×C3⋊D3—131nomaximal, Hall
14C11×C3⋊D39C2×C711yescharacteristic, complemented
15C11×C13×C3⋊D3C2×C711yescharacteristic, complemented
16C32×C11×D13C2×C711yescharacteristic, complemented
17C7×C11×D13—91no—
18C7×C11×D13C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20D3×C11×D13—34no—
21C7×C3⋊D39C2×C1111yescharacteristic, complemented
22C7×C13×C3⋊D3C2×C1111yescharacteristic, complemented
23C32×C7×D13C2×C1111yescharacteristic, complemented
24C2×C32×C7×C11—131no—
25C7×C11×C3⋊D3—131no—
26C7×C11×C3⋊D3D1311yescharacteristic, direct product factor
27C32×C11×C13C22×C711yescharacteristic, complemented, Hall
28D3×C7×D13—34no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×D3×C7×C11—394no—
31C11×D39—34no—
32D3×C11×C13—34no—
33C3×C11×D13D3×C714yescomplemented
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—91noHall
37C7×D39—34no—
38D3×C7×C13—34no—
39C3×C7×D13D3×C1114yescomplemented
40C3⋊D3×D13C7×C1111yescharacteristic, direct product factor, Hall
41C2×C3×C7×C11—134no—
42D3×C7×C11—34no—
43D3×C7×C11—394no—
44C3×C11×C13C2×D3×C714yescomplemented
45C2×C11×C3⋊D3—131noHall
46C2×C7×D13—91noHall
47C22×C7×C11—1171noHall
48C2×C11×C13—91no—
49C11×D13—91no—
50C11×D13C7×C3⋊D311yescharacteristic, direct product factor
51C3×C7×C13C2×D3×C1114yescomplemented
52C2×C7×C3⋊D3—131noHall
53C3⋊D39C2×C7×C1111yescharacteristic, complemented
54C13×C3⋊D3C2×C7×C1111yescharacteristic, complemented
55C32×D13C2×C7×C1111yescharacteristic, complemented
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—131no—
58C11×C3⋊D3—131no—
59C11×C3⋊D3C7×D1311yescharacteristic, direct product factor
60C2×C7×C13—91no—
61C7×D13—91no—
62C7×D13C11×C3⋊D311yescharacteristic, direct product factor
63D3×D13—34no—
64C2×C7×C11—91no—
65C2×C7×C11—131no—
66C2×C7×C11—1171no—
67C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D3×C11—394no—
69C2×C32×C7—131no—
70C7×C3⋊D3—131no—
71C7×C3⋊D3C11×D1311yescharacteristic, direct product factor
72C32×C13C22×C7×C1111yescharacteristic, complemented, Hall
73C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
75C2×D3×C7—394no—
76D39—34no—
77C3×D13D3×C7×C1114yescomplemented
78D3×C13—34no—
79C7×C11C3⋊D3×D1311yescharacteristic, direct product factor, Hall
80C2×C3×C11—134no—
81D3×C11—34no—
82D3×C11—394no—
83C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—91noHall
85C22×C11—1171noHall
86C2×C3×C7—134no—
87D3×C7—34no—
88D3×C7—394no—
89C3×C13C2×D3×C7×C1114yescomplemented
90C2×C3⋊D3—131noHall
91C3×C11D3×C7×D1314yescomplemented
92C22×C7—1171noHall
93C2×C13—91no—
94D13—91no—
95D13C7×C11×C3⋊D311yescharacteristic, direct product factor
96C2×C11—91no—
97C2×C11—131no—
98C2×C11—1171no—
99C3×C7D3×C11×D1314yescomplemented
100C2×C32—131no—
101C3⋊D3—131no—
102C3⋊D3C7×C11×D1311yescharacteristic, direct product factor
103C2×C7—91no—
104C2×C7—131no—
105C2×C7—1171no—
106C13C2×C7×C11×C3⋊D311yescharacteristic, complemented, Sylow
107C2×D3—394no—
108C11C7×C3⋊D3×D1311yescharacteristic, direct product factor, Sylow
109C32C2×C7×C11×D1311yescharacteristic, complemented, Sylow
110C7C11×C3⋊D3×D1311yescharacteristic, direct product factor, Sylow
111C2×C3—134no—
112D3—34no—
113D3—394no—
114C22—1171noSylow
115C3D3×C7×C11×D1314yescomplemented
116C2—91no—
117C2—131no—
118C2—1171no—
subgroupG/H
center, hypercenterC7×C11C3⋊D3×D13
commutator, cosocle, hypocenterC32×C13C22×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C13
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D13C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
3. C7×C11×C3⋊D39C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C11×D13D3semidirect
9. C11×C3⋊D3×D13C7direct (N × H)
11. C7×C3⋊D3×D13C11direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
14. C11×C3⋊D39C2×C7semidirect
15. C11×C13×C3⋊D3C2×C7semidirect
16. C32×C11×D13C2×C7semidirect
18. C7×C11×D13C3⋊D3direct (N × H)
21. C7×C3⋊D39C2×C11semidirect
22. C7×C13×C3⋊D3C2×C11semidirect
23. C32×C7×D13C2×C11semidirect
26. C7×C11×C3⋊D3D13direct (N × H)
27. C32×C11×C13C22×C7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C11×D13D3×C7semidirect
34. C32×C7×C13C22×C11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C7×D13D3×C11semidirect
40. C3⋊D3×D13C7×C11direct (N × H)
44. C3×C11×C13C2×D3×C7semidirect
50. C11×D13C7×C3⋊D3direct (N × H)
51. C3×C7×C13C2×D3×C11semidirect
53. C3⋊D39C2×C7×C11semidirect
54. C13×C3⋊D3C2×C7×C11semidirect
55. C32×D13C2×C7×C11semidirect
56. C3×C7×C11D3×D13semidirect
59. C11×C3⋊D3C7×D13direct (N × H)
62. C7×D13C11×C3⋊D3direct (N × H)
67. C11×C13C2×C7×C3⋊D3semidirect
71. C7×C3⋊D3C11×D13direct (N × H)
72. C32×C13C22×C7×C11semidirect
73. C32×C11C2×C7×D13semidirect
74. C7×C13C2×C11×C3⋊D3semidirect
77. C3×D13D3×C7×C11semidirect
79. C7×C11C3⋊D3×D13direct (N × H)
83. C32×C7C2×C11×D13semidirect
89. C3×C13C2×D3×C7×C11semidirect
91. C3×C11D3×C7×D13semidirect
95. D13C7×C11×C3⋊D3direct (N × H)
99. C3×C7D3×C11×D13semidirect
102. C3⋊D3C7×C11×D13direct (N × H)
106. C13C2×C7×C11×C3⋊D3semidirect
108. C11C7×C3⋊D3×D13direct (N × H)
109. C32C2×C7×C11×D13semidirect
110. C7C11×C3⋊D3×D13direct (N × H)
115. C3D3×C7×C11×D13semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C7×C11×C13×C3⋊D32
C7×C11×C3⋊D392
D3×C7×C11×D133
C11×C3⋊D3×D137
C7×C3⋊D3×D1311
C2×C7×C11×C3⋊D313