Finite Group Databasebeta

← C7×C13×C3⋊D3×D11 #49114972

Subgroups — C7×C13×C3⋊D3×D11 #49114972

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×C13×D11C211yesmaximal, characteristic, complemented
2C7×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C13×C3⋊D33C211yesmaximal, characteristic, complemented
4D3×C7×C13×D11—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C7×C13×D33—34no—
7D3×C7×C11×C13—34no—
8C3×C7×C13×D11D314yescomplemented
9C13×C3⋊D3×D11C711yesmaximal, characteristic, direct product factor, Hall
10C2×C7×C13×D11—91noHall
11C2×C7×C13×C3⋊D3—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C7×C3⋊D3×D11C1311yesmaximal, characteristic, direct product factor, Hall
14C13×C3⋊D33C2×C711yescharacteristic, complemented
15C11×C13×C3⋊D3C2×C711yescharacteristic, complemented
16C32×C13×D11C2×C711yescharacteristic, complemented
17C7×C13×D11—91no—
18C7×C13×D11C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20D3×C13×D11—34no—
21C2×C32×C7×C13—111no—
22C7×C13×C3⋊D3—111no—
23C7×C13×C3⋊D3D1111yescharacteristic, direct product factor
24C7×C3⋊D33C2×C1311yescharacteristic, complemented
25C7×C11×C3⋊D3C2×C1311yescharacteristic, complemented
26C32×C7×D11C2×C1311yescharacteristic, complemented
27C32×C11×C13C22×C711yescharacteristic, complemented, Hall
28C2×D3×C7×C13—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C7×D11—34no—
31C13×D33—34no—
32D3×C11×C13—34no—
33C3×C13×D11D3×C714yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D11—91noHall
37C2×C3×C7×C13—114no—
38D3×C7×C13—34no—
39D3×C7×C13—334no—
40C2×C13×C3⋊D3—111noHall
41C7×D33—34no—
42D3×C7×C11—34no—
43C3×C7×D11D3×C1314yescomplemented
44C3×C11×C13C2×D3×C714yescomplemented
45C3⋊D3×D11C7×C1311yescharacteristic, direct product factor, Hall
46C22×C7×C13—991noHall
47C2×C7×D11—91noHall
48C2×C11×C13—91no—
49C13×D11—91no—
50C13×D11C7×C3⋊D311yescharacteristic, direct product factor
51C3×C7×C13D3×D1114yescomplemented
52C2×C7×C3⋊D3—111noHall
53C2×C32×C13—111no—
54C13×C3⋊D3—111no—
55C13×C3⋊D3C7×D1111yescharacteristic, direct product factor
56C3×C7×C11C2×D3×C1314yescomplemented
57C3⋊D33C2×C7×C1311yescharacteristic, complemented
58C11×C3⋊D3C2×C7×C1311yescharacteristic, complemented
59C32×D11C2×C7×C1311yescharacteristic, complemented
60C2×C7×C13—91no—
61C2×C7×C13—111no—
62C2×C7×C13—991no—
63C2×D3×C13—334no—
64C2×C7×C11—91no—
65C7×D11—91no—
66C7×D11C13×C3⋊D311yescharacteristic, direct product factor
67C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—34no—
69C2×C32×C7—111no—
70C7×C3⋊D3—111no—
71C7×C3⋊D3C13×D1111yescharacteristic, direct product factor
72C32×C13C2×C7×D1111yescharacteristic, complemented, Hall
73C32×C11C22×C7×C1311yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, direct product factor, Hall
75C2×D3×C7—334no—
76C2×C3×C13—114no—
77D3×C13—34no—
78D3×C13—334no—
79C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
80D33—34no—
81C3×D11D3×C7×C1314yescomplemented
82D3×C11—34no—
83C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
84C22×C13—991noHall
85C2×D11—91noHall
86C2×C3×C7—114no—
87D3×C7—34no—
88D3×C7—334no—
89C3×C13D3×C7×D1114yescomplemented
90C2×C3⋊D3—111noHall
91C3×C11C2×D3×C7×C1314yescomplemented
92C22×C7—991noHall
93C2×C13—91no—
94C2×C13—111no—
95C2×C13—991no—
96C2×C11—91no—
97D11—91no—
98D11C7×C13×C3⋊D311yescharacteristic, direct product factor
99C3×C7D3×C13×D1114yescomplemented
100C2×C32—111no—
101C3⋊D3—111no—
102C3⋊D3C7×C13×D1111yescharacteristic, direct product factor
103C2×C7—91no—
104C2×C7—111no—
105C2×C7—991no—
106C13C7×C3⋊D3×D1111yescharacteristic, direct product factor, Sylow
107C2×D3—334no—
108C11C2×C7×C13×C3⋊D311yescharacteristic, complemented, Sylow
109C32C2×C7×C13×D1111yescharacteristic, complemented, Sylow
110C7C13×C3⋊D3×D1111yescharacteristic, direct product factor, Sylow
111C2×C3—114no—
112D3—34no—
113D3—334no—
114C22—991noSylow
115C3D3×C7×C13×D1114yescomplemented
116C2—91no—
117C2—111no—
118C2—991no—
subgroupG/H
center, hypercenterC7×C13C3⋊D3×D11
commutator, cosocle, hypocenterC32×C11C22×C7×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C11
UCSC1 ◁ C7×C13

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D11C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
3. C7×C13×C3⋊D33C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C13×D11D3semidirect
9. C13×C3⋊D3×D11C7direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
13. C7×C3⋊D3×D11C13direct (N × H)
14. C13×C3⋊D33C2×C7semidirect
15. C11×C13×C3⋊D3C2×C7semidirect
16. C32×C13×D11C2×C7semidirect
18. C7×C13×D11C3⋊D3direct (N × H)
23. C7×C13×C3⋊D3D11direct (N × H)
24. C7×C3⋊D33C2×C13semidirect
25. C7×C11×C3⋊D3C2×C13semidirect
26. C32×C7×D11C2×C13semidirect
27. C32×C11×C13C22×C7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C13×D11D3×C7semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C22×C13semidirect
43. C3×C7×D11D3×C13semidirect
44. C3×C11×C13C2×D3×C7semidirect
45. C3⋊D3×D11C7×C13direct (N × H)
50. C13×D11C7×C3⋊D3direct (N × H)
51. C3×C7×C13D3×D11semidirect
55. C13×C3⋊D3C7×D11direct (N × H)
56. C3×C7×C11C2×D3×C13semidirect
57. C3⋊D33C2×C7×C13semidirect
58. C11×C3⋊D3C2×C7×C13semidirect
59. C32×D11C2×C7×C13semidirect
66. C7×D11C13×C3⋊D3direct (N × H)
67. C11×C13C2×C7×C3⋊D3semidirect
71. C7×C3⋊D3C13×D11direct (N × H)
72. C32×C13C2×C7×D11semidirect
73. C32×C11C22×C7×C13semidirect
74. C7×C13C3⋊D3×D11direct (N × H)
79. C7×C11C2×C13×C3⋊D3semidirect
81. C3×D11D3×C7×C13semidirect
83. C32×C7C2×C13×D11semidirect
89. C3×C13D3×C7×D11semidirect
91. C3×C11C2×D3×C7×C13semidirect
98. D11C7×C13×C3⋊D3direct (N × H)
99. C3×C7D3×C13×D11semidirect
102. C3⋊D3C7×C13×D11direct (N × H)
106. C13C7×C3⋊D3×D11direct (N × H)
108. C11C2×C7×C13×C3⋊D3semidirect
109. C32C2×C7×C13×D11semidirect
110. C7C13×C3⋊D3×D11direct (N × H)
115. C3D3×C7×C13×D11semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C13×D112
C7×C11×C13×C3⋊D32
C7×C13×C3⋊D332
D3×C7×C13×D113
C13×C3⋊D3×D117
C2×C7×C13×C3⋊D311
C7×C3⋊D3×D1113