Finite Group Databasebeta

← C7×D13×C3⋊D33 #49114971

Subgroups — C7×D13×C3⋊D33 #49114971

Order 36036.

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

normal subgroups only

This group has 240 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×D13C211yesmaximal, characteristic, complemented
2C7×C13×C3⋊D33C211yesmaximal, characteristic, complemented
3C7×C3⋊D429C211yesmaximal, characteristic, complemented
4C7×D13×D33—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C7×D429—34no—
7C7×C13×D33—34no—
8C3×C7×C11×D13D314yescomplemented
9D13×C3⋊D33C711yesmaximal, characteristic, direct product factor, Hall
10C7×D11×D13—91noHall
11C7×C3⋊D3×D13—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C2×C7×C3⋊D33—131nomaximal, Hall
14C3⋊D429C2×C711yescharacteristic, complemented
15C13×C3⋊D33C2×C711yescharacteristic, complemented
16C32×C11×D13C2×C711yescharacteristic, complemented
17C7×D143—91no—
18C7×C13×D11—91no—
19C7×C11×D13C3⋊D311yescharacteristic, complemented
20D13×D33—34no—
21C7×C3⋊D39—111no—
22C7×C13×C3⋊D3—111no—
23C32×C7×D13D1111yescharacteristic, complemented
24C2×C32×C7×C11—131no—
25C7×C3⋊D33—131no—
26C7×C3⋊D33D1311yescharacteristic, direct product factor
27C32×C11×C13C22×C711yescharacteristic, complemented, Hall
28D3×C7×D13—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×C7×D33—394no—
31D429—34no—
32C13×D33—34no—
33C3×C11×D13D3×C714yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—91noHall
37C7×D39—334no—
38D3×C7×C13—334no—
39C3×C7×D13D3314yescomplemented
40C3⋊D3×D13—111noHall
41C2×C3×C7×C11—134no—
42C7×D33—34no—
43C7×D33—394no—
44C3×C11×C13C2×D3×C714yescomplemented
45C2×C3⋊D33—131noHall
46C2×C7×D13—991noHall
47C2×C7×D11—1171noHall
48D143—91no—
49C11×D13C7×C3⋊D311yescharacteristic, complemented
50C13×D11—91no—
51C3×C7×C13C2×D3314yescomplemented
52C2×C7×C3⋊D3—1431noHall
53C3⋊D39—111no—
54C13×C3⋊D3—111no—
55C32×D13C7×D1111yescharacteristic, complemented
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—131no—
58C3⋊D33—131no—
59C3⋊D33C7×D1311yescharacteristic, direct product factor
60C2×C7×C13—991no—
61C7×D13—991no—
62C7×D13C3⋊D3311yescharacteristic, direct product factor
63D3×D13—334no—
64C2×C7×C11—131no—
65C7×D11—91no—
66C7×D11—1171no—
67C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D33—394no—
69C2×C32×C7—131no—
70C7×C3⋊D3—111no—
71C7×C3⋊D3—1431no—
72C32×C13C2×C7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
75C2×D3×C7—4294no—
76D39—334no—
77C3×D13C7×D3314yescomplemented
78D3×C13—334no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—134no—
81D33—34no—
82D33—394no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—991noHall
85C2×D11—1171noHall
86C2×C3×C7—134no—
87D3×C7—334no—
88D3×C7—4294no—
89C3×C13C2×C7×D3314yescomplemented
90C2×C3⋊D3—1431noHall
91C3×C11D3×C7×D1314yescomplemented
92C22×C7—12871noHall
93C2×C13—991no—
94D13—991no—
95D13C7×C3⋊D3311yescharacteristic, direct product factor
96C2×C11—131no—
97D11—91no—
98D11—1171no—
99C3×C7D13×D3314yescomplemented
100C2×C32—131no—
101C3⋊D3—111no—
102C3⋊D3—1431no—
103C2×C7—12871no—
104C2×C7—131no—
105C2×C7—991no—
106C13C2×C7×C3⋊D3311yescharacteristic, complemented, Sylow
107C2×D3—4294no—
108C11C7×C3⋊D3×D1311yescharacteristic, complemented, Sylow
109C32C7×D11×D1311yescharacteristic, complemented, Sylow
110C7D13×C3⋊D3311yescharacteristic, direct product factor, Sylow
111C2×C3—134no—
112D3—334no—
113D3—4294no—
114C22—12871noSylow
115C3C7×D13×D3314yescomplemented
116C2—12871no—
117C2—131no—
118C2—991no—
subgroupG/H
center, hypercenterC7D13×C3⋊D33
commutator, cosocle, hypocenterC32×C11×C13C22×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D13C2semidirect
2. C7×C13×C3⋊D33C2semidirect
3. C7×C3⋊D429C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C11×D13D3semidirect
9. D13×C3⋊D33C7direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
14. C3⋊D429C2×C7semidirect
15. C13×C3⋊D33C2×C7semidirect
16. C32×C11×D13C2×C7semidirect
19. C7×C11×D13C3⋊D3semidirect
23. C32×C7×D13D11semidirect
26. C7×C3⋊D33D13direct (N × H)
27. C32×C11×C13C22×C7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C11×D13D3×C7semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C7×D13D33semidirect
44. C3×C11×C13C2×D3×C7semidirect
49. C11×D13C7×C3⋊D3semidirect
51. C3×C7×C13C2×D33semidirect
55. C32×D13C7×D11semidirect
56. C3×C7×C11D3×D13semidirect
59. C3⋊D33C7×D13direct (N × H)
62. C7×D13C3⋊D33direct (N × H)
67. C11×C13C2×C7×C3⋊D3semidirect
72. C32×C13C2×C7×D11semidirect
73. C32×C11C2×C7×D13semidirect
74. C7×C13C2×C3⋊D33semidirect
77. C3×D13C7×D33semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7D11×D13semidirect
89. C3×C13C2×C7×D33semidirect
91. C3×C11D3×C7×D13semidirect
95. D13C7×C3⋊D33direct (N × H)
99. C3×C7D13×D33semidirect
106. C13C2×C7×C3⋊D33semidirect
108. C11C7×C3⋊D3×D13semidirect
109. C32C7×D11×D13semidirect
110. C7D13×C3⋊D33direct (N × H)
115. C3C7×D13×D33semidirect

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×C13×C3⋊D332
C7×C3⋊D4292
C7×D13×D333
D13×C3⋊D337
C7×C3⋊D3×D1311
C2×C7×C3⋊D3313