Finite Group Databasebeta

← C7×D5×C11×C3⋊D3 #28357708

Subgroups — C7×D5×C11×C3⋊D3 #28357708

Order 13860.

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
1C7×C11×C3⋊D15C211yesmaximal, characteristic, complemented
2C5×C7×C11×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C7×D5×C11C211yesmaximal, characteristic, complemented
4D3×C7×D5×C11—34nomaximal
5C32×C5×C7×C11C2211yescharacteristic, complemented, Hall
6C2×C7×C11×C3⋊D3—51nomaximal, Hall
7C7×C11×D15—34no—
8C5×D3×C7×C11—34no—
9C3×C7×D5×C11D314yescomplemented
10D5×C11×C3⋊D3C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C11—91noHall
12C2×C32×C7×C11—51no—
13C7×C11×C3⋊D3—51no—
14C7×C11×C3⋊D3D511yescharacteristic, direct product factor
15C7×D5×C3⋊D3C1111yesmaximal, characteristic, direct product factor, Hall
16C3×C5×C7×C11C2×D314yescomplemented
17C11×C3⋊D15C2×C711yescharacteristic, complemented
18C5×C11×C3⋊D3C2×C711yescharacteristic, complemented
19C32×D5×C11C2×C711yescharacteristic, complemented
20C2×D3×C7×C11—154no—
21C2×C5×C7×C11—91no—
22C7×D5×C11—91no—
23C7×D5×C11C3⋊D311yescharacteristic, direct product factor
24C32×C7×C11C2×D511yescharacteristic, complemented, Hall
25D3×D5×C11—34no—
26C7×C3⋊D15C2×C1111yescharacteristic, complemented
27C5×C7×C3⋊D3C2×C1111yescharacteristic, complemented
28C32×C7×D5C2×C1111yescharacteristic, complemented
29C32×C5×C11C22×C711yescharacteristic, complemented, Hall
30C2×C3×C7×C11—54no—
31D3×C7×C11—34no—
32D3×C7×C11—154no—
33D3×C7×D5—34no—
34C2×C11×C3⋊D3—51noHall
35C5×C7×C11C2×C3⋊D311yescharacteristic, complemented, Hall
36C11×D15—34no—
37C5×D3×C11—34no—
38C3×D5×C11D3×C714yescomplemented
39C32×C5×C7C22×C1111yescharacteristic, complemented, Hall
40C22×C7×C11—451noHall
41C2×C7×C3⋊D3—51noHall
42C3×C7×C11D3×D514yescomplemented
43C2×D5×C11—91noHall
44C7×D15—34no—
45C5×D3×C7—34no—
46C3×C7×D5D3×C1114yescomplemented
47C2×C32×C11—51no—
48C11×C3⋊D3—51no—
49C11×C3⋊D3C7×D511yescharacteristic, direct product factor
50D5×C3⋊D3C7×C1111yescharacteristic, direct product factor, Hall
51C3×C5×C11C2×D3×C714yescomplemented
52C2×C7×C11—51no—
53C2×C7×C11—91no—
54C2×C7×C11—451no—
55C2×C7×D5—91noHall
56C2×D3×C11—154no—
57C2×C32×C7—51no—
58C7×C3⋊D3—51no—
59C7×C3⋊D3D5×C1111yescharacteristic, direct product factor
60C2×C5×C11—91no—
61D5×C11—91no—
62D5×C11C7×C3⋊D311yescharacteristic, direct product factor
63C3×C5×C7C2×D3×C1114yescomplemented
64C32×C11C2×C7×D511yescharacteristic, complemented, Hall
65C3⋊D15C2×C7×C1111yescharacteristic, complemented
66C5×C3⋊D3C2×C7×C1111yescharacteristic, complemented
67C32×D5C2×C7×C1111yescharacteristic, complemented
68C2×D3×C7—154no—
69C7×C11D5×C3⋊D311yescharacteristic, direct product factor, Hall
70C2×C5×C7—91no—
71C7×D5—91no—
72C7×D5C11×C3⋊D311yescharacteristic, direct product factor
73C2×C3×C11—54no—
74D3×C11—34no—
75D3×C11—154no—
76C32×C7C2×D5×C1111yescharacteristic, complemented, Hall
77D3×D5—34no—
78C5×C11C2×C7×C3⋊D311yescharacteristic, complemented, Hall
79C32×C5C22×C7×C1111yescharacteristic, complemented, Hall
80C22×C11—451noHall
81C2×C3×C7—54no—
82D3×C7—34no—
83D3×C7—154no—
84C2×C3⋊D3—51noHall
85C5×C7C2×C11×C3⋊D311yescharacteristic, complemented, Hall
86C3×C11D3×C7×D514yescomplemented
87D15—34no—
88C3×D5D3×C7×C1114yescomplemented
89C5×D3—34no—
90C22×C7—451noHall
91C2×C11—51no—
92C2×C11—91no—
93C2×C11—451no—
94C3×C7D3×D5×C1114yescomplemented
95C2×D5—91noHall
96C2×C32—51no—
97C3⋊D3—51no—
98C3⋊D3C7×D5×C1111yescharacteristic, direct product factor
99C3×C5C2×D3×C7×C1114yescomplemented
100C2×C7—51no—
101C2×C7—91no—
102C2×C7—451no—
103C2×D3—154no—
104C11C7×D5×C3⋊D311yescharacteristic, direct product factor, Sylow
105C2×C5—91no—
106D5—91no—
107D5C7×C11×C3⋊D311yescharacteristic, direct product factor
108C32C2×C7×D5×C1111yescharacteristic, complemented, Sylow
109C7D5×C11×C3⋊D311yescharacteristic, direct product factor, Sylow
110C2×C3—54no—
111D3—34no—
112D3—154no—
113C5C2×C7×C11×C3⋊D311yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×C7×D5×C1114yescomplemented
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC7×C11D5×C3⋊D3
commutator, cosocle, hypocenterC32×C5C22×C7×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C32×C5
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×C3⋊D15C2semidirect
2. C5×C7×C11×C3⋊D3C2semidirect
3. C32×C7×D5×C11C2semidirect
5. C32×C5×C7×C11C22semidirect
9. C3×C7×D5×C11D3semidirect
10. D5×C11×C3⋊D3C7direct (N × H)
14. C7×C11×C3⋊D3D5direct (N × H)
15. C7×D5×C3⋊D3C11direct (N × H)
16. C3×C5×C7×C11C2×D3semidirect
17. C11×C3⋊D15C2×C7semidirect
18. C5×C11×C3⋊D3C2×C7semidirect
19. C32×D5×C11C2×C7semidirect
23. C7×D5×C11C3⋊D3direct (N × H)
24. C32×C7×C11C2×D5semidirect
26. C7×C3⋊D15C2×C11semidirect
27. C5×C7×C3⋊D3C2×C11semidirect
28. C32×C7×D5C2×C11semidirect
29. C32×C5×C11C22×C7semidirect
35. C5×C7×C11C2×C3⋊D3semidirect
38. C3×D5×C11D3×C7semidirect
39. C32×C5×C7C22×C11semidirect
42. C3×C7×C11D3×D5semidirect
46. C3×C7×D5D3×C11semidirect
49. C11×C3⋊D3C7×D5direct (N × H)
50. D5×C3⋊D3C7×C11direct (N × H)
51. C3×C5×C11C2×D3×C7semidirect
59. C7×C3⋊D3D5×C11direct (N × H)
62. D5×C11C7×C3⋊D3direct (N × H)
63. C3×C5×C7C2×D3×C11semidirect
64. C32×C11C2×C7×D5semidirect
65. C3⋊D15C2×C7×C11semidirect
66. C5×C3⋊D3C2×C7×C11semidirect
67. C32×D5C2×C7×C11semidirect
69. C7×C11D5×C3⋊D3direct (N × H)
72. C7×D5C11×C3⋊D3direct (N × H)
76. C32×C7C2×D5×C11semidirect
78. C5×C11C2×C7×C3⋊D3semidirect
79. C32×C5C22×C7×C11semidirect
85. C5×C7C2×C11×C3⋊D3semidirect
86. C3×C11D3×C7×D5semidirect
88. C3×D5D3×C7×C11semidirect
94. C3×C7D3×D5×C11semidirect
98. C3⋊D3C7×D5×C11direct (N × H)
99. C3×C5C2×D3×C7×C11semidirect
104. C11C7×D5×C3⋊D3direct (N × H)
107. D5C7×C11×C3⋊D3direct (N × H)
108. C32C2×C7×D5×C11semidirect
109. C7D5×C11×C3⋊D3direct (N × H)
113. C5C2×C7×C11×C3⋊D3semidirect
115. C3D3×C7×D5×C11semidirect

Maximal subgroups

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

subgroupindex
C7×C11×C3⋊D152
C5×C7×C11×C3⋊D32
C32×C7×D5×C112
D3×C7×D5×C113
C2×C7×C11×C3⋊D35
D5×C11×C3⋊D37
C7×D5×C3⋊D311