Finite Group Databasebeta

← C7×D143⋊(C3⋊D3) #49114975

Subgroups — C7×D143⋊(C3⋊D3) #49114975

Order 36036.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×D143C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊D39C211yesmaximal, characteristic, complemented
3C7×C13×C3⋊D33C211yesmaximal, characteristic, complemented
4C7×D33⋊D13—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C7×C13×D33—34no—
7C7×C11×D39—34no—
8C3×C7×D143D314yescomplemented
9D143⋊(C3⋊D3)C711yesmaximal, characteristic, direct product factor, Hall
10C7×D11×D13—91noHall
11C7×C3⋊D3×D13—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C7×C3⋊D3×D11—131nomaximal, Hall
14C13×C3⋊D33C2×C711yescharacteristic, complemented
15C11×C3⋊D39C2×C711yescharacteristic, complemented
16C32×D143C2×C711yescharacteristic, complemented
17C7×D143C3⋊D311yescharacteristic, complemented
18C7×C13×D11—91no—
19C7×C11×D13—91no—
20D33⋊D13—34no—
21C7×C3⋊D39D1111yescharacteristic, complemented
22C7×C13×C3⋊D3—111no—
23C32×C7×D13—111no—
24C7×C3⋊D33D1311yescharacteristic, complemented
25C7×C11×C3⋊D3—131no—
26C32×C7×D11—131no—
27C32×C11×C13C22×C711yescharacteristic, complemented, Hall
28D3×C7×D13—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C7×D11—394no—
31C13×D33—34no—
32C11×D39—34no—
33C3×D143D3×C714yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—91noHall
37C7×D39—34no—
38D3×C7×C13—334no—
39C3×C7×D13—114no—
40C3⋊D3×D13—111noHall
41C7×D33—34no—
42D3×C7×C11—394no—
43C3×C7×D11—134no—
44C3×C11×C13C2×D3×C714yescomplemented
45C3⋊D3×D11—131noHall
46C2×C7×D13—991noHall
47C2×C7×D11—1171noHall
48D143C7×C3⋊D311yescharacteristic, complemented
49C11×D13—91no—
50C13×D11—91no—
51C3×C7×C13D3×D1114yescomplemented
52C2×C7×C3⋊D3—1431noHall
53C3⋊D39C7×D1111yescharacteristic, complemented
54C13×C3⋊D3—111no—
55C32×D13—111no—
56C3×C7×C11D3×D1314yescomplemented
57C3⋊D33C7×D1311yescharacteristic, complemented
58C11×C3⋊D3—131no—
59C32×D11—131no—
60C2×C7×C13—991no—
61C7×D13—91no—
62C7×D13—111no—
63D3×D13—334no—
64C2×C7×C11—1171no—
65C7×D11—91no—
66C7×D11—131no—
67C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—394no—
69C2×C32×C7—1431no—
70C7×C3⋊D3—111no—
71C7×C3⋊D3—131no—
72C32×C13C2×C7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75C2×D3×C7—4294no—
76D39—34no—
77C3×D13—114no—
78D3×C13—334no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80D33—34no—
81C3×D11—134no—
82D3×C11—394no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—991noHall
85C2×D11—1171noHall
86C2×C3×C7—1434no—
87D3×C7—334no—
88D3×C7—394no—
89C3×C13D3×C7×D1114yescomplemented
90C2×C3⋊D3—1431noHall
91C3×C11D3×C7×D1314yescomplemented
92C22×C7—12871noHall
93C2×C13—991no—
94D13—91no—
95D13—111no—
96C2×C11—1171no—
97D11—91no—
98D11—131no—
99C3×C7D33⋊D1314yescomplemented
100C2×C32—1431no—
101C3⋊D3—111no—
102C3⋊D3—131no—
103C2×C7—991no—
104C2×C7—1171no—
105C2×C7—1431no—
106C13C7×C3⋊D3×D1111yescharacteristic, complemented, Sylow
107C2×D3—4294no—
108C11C7×C3⋊D3×D1311yescharacteristic, complemented, Sylow
109C32C7×D11×D1311yescharacteristic, complemented, Sylow
110C7D143⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
111C2×C3—1434no—
112D3—334no—
113D3—394no—
114C22—12871noSylow
115C3C7×D33⋊D1314yescomplemented
116C2—991no—
117C2—1171no—
118C2—1431no—
subgroupG/H
center, hypercenterC7D143⋊(C3⋊D3)
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×D143C2semidirect
2. C7×C11×C3⋊D39C2semidirect
3. C7×C13×C3⋊D33C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×D143D3semidirect
9. D143⋊(C3⋊D3)C7direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
14. C13×C3⋊D33C2×C7semidirect
15. C11×C3⋊D39C2×C7semidirect
16. C32×D143C2×C7semidirect
17. C7×D143C3⋊D3semidirect
21. C7×C3⋊D39D11semidirect
24. C7×C3⋊D33D13semidirect
27. C32×C11×C13C22×C7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×D143D3×C7semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
44. C3×C11×C13C2×D3×C7semidirect
48. D143C7×C3⋊D3semidirect
51. C3×C7×C13D3×D11semidirect
53. C3⋊D39C7×D11semidirect
56. C3×C7×C11D3×D13semidirect
57. C3⋊D33C7×D13semidirect
67. C11×C13C2×C7×C3⋊D3semidirect
72. C32×C13C2×C7×D11semidirect
73. C32×C11C2×C7×D13semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7D11×D13semidirect
89. C3×C13D3×C7×D11semidirect
91. C3×C11D3×C7×D13semidirect
99. C3×C7D33⋊D13semidirect
106. C13C7×C3⋊D3×D11semidirect
108. C11C7×C3⋊D3×D13semidirect
109. C32C7×D11×D13semidirect
110. C7D143⋊(C3⋊D3)direct (N × H)
115. C3C7×D33⋊D13semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1432
C7×C11×C3⋊D392
C7×C13×C3⋊D332
C7×D33⋊D133
D143⋊(C3⋊D3)7
C7×C3⋊D3×D1311
C7×C3⋊D3×D1113