Finite Group Databasebeta

← C7×C3⋊D3×D143 #49114974

Subgroups — C7×C3⋊D3×D143 #49114974

Order 36036.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C3⋊D429C211yesmaximal, characteristic, complemented
4D3×C7×D143—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C7×D429—34no—
7D3×C7×C11×C13—34no—
8C3×C7×D143D314yescomplemented
9C3⋊D3×D143C711yesmaximal, characteristic, direct product factor, Hall
10C2×C7×D143—91noHall
11C7×C3⋊D3×D13—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C7×C3⋊D3×D11—131nomaximal, Hall
14C3⋊D429C2×C711yescharacteristic, complemented
15C11×C13×C3⋊D3C2×C711yescharacteristic, complemented
16C32×D143C2×C711yescharacteristic, complemented
17C7×D143—91no—
18C7×D143C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20D3×D143—34no—
21C7×C3⋊D39—111no—
22C7×C13×C3⋊D3D1111yescharacteristic, complemented
23C32×C7×D13—111no—
24C7×C3⋊D33—131no—
25C7×C11×C3⋊D3D1311yescharacteristic, complemented
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—
31D429—34no—
32D3×C11×C13—34no—
33C3×D143D3×C714yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×D143—91noHall
37C7×D39—334no—
38D3×C7×C13—34no—
39C3×C7×D13—114no—
40C3⋊D3×D13—111noHall
41C7×D33—394no—
42D3×C7×C11—34no—
43C3×C7×D11—134no—
44C3×C11×C13C2×D3×C714yescomplemented
45C3⋊D3×D11—131noHall
46C2×C7×D13—991noHall
47C2×C7×D11—1171noHall
48C2×C11×C13—91no—
49D143—91no—
50D143C7×C3⋊D311yescharacteristic, direct product factor
51C3×C7×C13D3×D1114yescomplemented
52C2×C7×C3⋊D3—1431noHall
53C3⋊D39—111no—
54C13×C3⋊D3C7×D1111yescharacteristic, complemented
55C32×D13—111no—
56C3×C7×C11D3×D1314yescomplemented
57C3⋊D33—131no—
58C11×C3⋊D3C7×D1311yescharacteristic, complemented
59C32×D11—131no—
60C2×C7×C13—91no—
61C7×D13—111no—
62C7×D13—991no—
63D3×D13—334no—
64C2×C7×C11—91no—
65C7×D11—131no—
66C7×D11—1171no—
67C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—394no—
69C2×C32×C7—1431no—
70C7×C3⋊D3—1431no—
71C7×C3⋊D3D14311yescharacteristic, direct product factor
72C32×C13C2×C7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75C2×D3×C7—4294no—
76D39—334no—
77C3×D13—114no—
78D3×C13—34no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80D33—394no—
81C3×D11—134no—
82D3×C11—34no—
83C32×C7C2×D14311yescharacteristic, complemented, Hall
84C2×D13—991noHall
85C2×D11—1171noHall
86C2×C3×C7—1434no—
87D3×C7—34no—
88D3×C7—4294no—
89C3×C13D3×C7×D1114yescomplemented
90C2×C3⋊D3—1431noHall
91C3×C11D3×C7×D1314yescomplemented
92C22×C7—12871noHall
93C2×C13—91no—
94D13—111no—
95D13—991no—
96C2×C11—91no—
97D11—131no—
98D11—1171no—
99C3×C7D3×D14314yescomplemented
100C2×C32—1431no—
101C3⋊D3—1431no—
102C3⋊D3C7×D14311yescharacteristic, direct product factor
103C2×C7—12871no—
104C2×C7—91no—
105C2×C7—1431no—
106C13C7×C3⋊D3×D1111yescharacteristic, complemented, Sylow
107C2×D3—4294no—
108C11C7×C3⋊D3×D1311yescharacteristic, complemented, Sylow
109C32C2×C7×D14311yescharacteristic, complemented, Sylow
110C7C3⋊D3×D14311yescharacteristic, direct product factor, Sylow
111C2×C3—1434no—
112D3—34no—
113D3—4294no—
114C22—12871noSylow
115C3D3×C7×D14314yescomplemented
116C2—12871no—
117C2—91no—
118C2—1431no—
subgroupG/H
center, hypercenterC7C3⋊D3×D143
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×C13×C3⋊D3C2semidirect
3. C7×C3⋊D429C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×D143D3semidirect
9. C3⋊D3×D143C7direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
14. C3⋊D429C2×C7semidirect
15. C11×C13×C3⋊D3C2×C7semidirect
16. C32×D143C2×C7semidirect
18. C7×D143C3⋊D3direct (N × H)
22. C7×C13×C3⋊D3D11semidirect
25. C7×C11×C3⋊D3D13semidirect
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
50. D143C7×C3⋊D3direct (N × H)
51. C3×C7×C13D3×D11semidirect
54. C13×C3⋊D3C7×D11semidirect
56. C3×C7×C11D3×D13semidirect
58. C11×C3⋊D3C7×D13semidirect
67. C11×C13C2×C7×C3⋊D3semidirect
71. C7×C3⋊D3D143direct (N × H)
72. C32×C13C2×C7×D11semidirect
73. C32×C11C2×C7×D13semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7C2×D143semidirect
89. C3×C13D3×C7×D11semidirect
91. C3×C11D3×C7×D13semidirect
99. C3×C7D3×D143semidirect
102. C3⋊D3C7×D143direct (N × H)
106. C13C7×C3⋊D3×D11semidirect
108. C11C7×C3⋊D3×D13semidirect
109. C32C2×C7×D143semidirect
110. C7C3⋊D3×D143direct (N × H)
115. C3D3×C7×D143semidirect

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×C13×C3⋊D32
C7×C3⋊D4292
D3×C7×D1433
C3⋊D3×D1437
C7×C3⋊D3×D1311
C7×C3⋊D3×D1113