Finite Group Databasebeta

← C7×D11×C3⋊D39 #49114973

Subgroups — C7×D11×C3⋊D39 #49114973

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×C13×D11C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊D39C211yesmaximal, characteristic, complemented
3C7×C3⋊D429C211yesmaximal, characteristic, complemented
4C7×D11×D39—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C7×D429—34no—
7C7×C11×D39—34no—
8C3×C7×C13×D11D314yescomplemented
9D11×C3⋊D39C711yesmaximal, characteristic, direct product factor, Hall
10C7×D11×D13—91noHall
11C2×C7×C3⋊D39—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C7×C3⋊D3×D11—131nomaximal, Hall
14C3⋊D429C2×C711yescharacteristic, complemented
15C11×C3⋊D39C2×C711yescharacteristic, complemented
16C32×C13×D11C2×C711yescharacteristic, complemented
17C7×D143—91no—
18C7×C13×D11C3⋊D311yescharacteristic, complemented
19C7×C11×D13—91no—
20D11×D39—34no—
21C2×C32×C7×C13—111no—
22C7×C3⋊D39—111no—
23C7×C3⋊D39D1111yescharacteristic, direct product factor
24C7×C3⋊D33—131no—
25C7×C11×C3⋊D3—131no—
26C32×C7×D11D1311yescharacteristic, complemented
27C32×C11×C13C22×C711yescharacteristic, complemented, Hall
28C2×C7×D39—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C7×D11—394no—
31D429—34no—
32C11×D39—34no—
33C3×C13×D11D3×C714yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—91noHall
37C2×C3×C7×C13—114no—
38C7×D39—34no—
39C7×D39—334no—
40C2×C3⋊D39—111noHall
41C7×D33—394no—
42D3×C7×C11—394no—
43C3×C7×D11D3914yescomplemented
44C3×C11×C13C2×D3×C714yescomplemented
45C3⋊D3×D11—131noHall
46C2×C7×D13—991noHall
47C2×C7×D11—1171noHall
48D143—91no—
49C11×D13—91no—
50C13×D11C7×C3⋊D311yescharacteristic, complemented
51C3×C7×C13D3×D1114yescomplemented
52C2×C7×C3⋊D3—1431noHall
53C2×C32×C13—111no—
54C3⋊D39—111no—
55C3⋊D39C7×D1111yescharacteristic, direct product factor
56C3×C7×C11C2×D3914yescomplemented
57C3⋊D33—131no—
58C11×C3⋊D3—131no—
59C32×D11C7×D1311yescharacteristic, complemented
60C2×C7×C13—111no—
61C7×D13—91no—
62C7×D13—991no—
63C2×D39—334no—
64C2×C7×C11—1171no—
65C7×D11—1171no—
66C7×D11C3⋊D3911yescharacteristic, direct product factor
67C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—394no—
69C2×C32×C7—111no—
70C7×C3⋊D3—131no—
71C7×C3⋊D3—1431no—
72C32×C13C2×C7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75C2×D3×C7—4294no—
76C2×C3×C13—114no—
77D39—34no—
78D39—334no—
79C7×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
80D33—394no—
81C3×D11C7×D3914yescomplemented
82D3×C11—394no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—991noHall
85C2×D11—1171noHall
86C2×C3×C7—114no—
87D3×C7—394no—
88D3×C7—4294no—
89C3×C13D3×C7×D1114yescomplemented
90C2×C3⋊D3—1431noHall
91C3×C11C2×C7×D3914yescomplemented
92C22×C7—12871noHall
93C2×C13—111no—
94D13—91no—
95D13—991no—
96C2×C11—1171no—
97D11—1171no—
98D11C7×C3⋊D3911yescharacteristic, direct product factor
99C3×C7D11×D3914yescomplemented
100C2×C32—111no—
101C3⋊D3—131no—
102C3⋊D3—1431no—
103C2×C7—12871no—
104C2×C7—111no—
105C2×C7—1171no—
106C13C7×C3⋊D3×D1111yescharacteristic, complemented, Sylow
107C2×D3—4294no—
108C11C2×C7×C3⋊D3911yescharacteristic, complemented, Sylow
109C32C7×D11×D1311yescharacteristic, complemented, Sylow
110C7D11×C3⋊D3911yescharacteristic, direct product factor, Sylow
111C2×C3—114no—
112D3—394no—
113D3—4294no—
114C22—12871noSylow
115C3C7×D11×D3914yescomplemented
116C2—12871no—
117C2—111no—
118C2—1171no—
subgroupG/H
center, hypercenterC7D11×C3⋊D39
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×C13×D11C2semidirect
2. C7×C11×C3⋊D39C2semidirect
3. C7×C3⋊D429C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C13×D11D3semidirect
9. D11×C3⋊D39C7direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
14. C3⋊D429C2×C7semidirect
15. C11×C3⋊D39C2×C7semidirect
16. C32×C13×D11C2×C7semidirect
18. C7×C13×D11C3⋊D3semidirect
23. C7×C3⋊D39D11direct (N × H)
26. C32×C7×D11D13semidirect
27. C32×C11×C13C22×C7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C13×D11D3×C7semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
43. C3×C7×D11D39semidirect
44. C3×C11×C13C2×D3×C7semidirect
50. C13×D11C7×C3⋊D3semidirect
51. C3×C7×C13D3×D11semidirect
55. C3⋊D39C7×D11direct (N × H)
56. C3×C7×C11C2×D39semidirect
59. C32×D11C7×D13semidirect
66. C7×D11C3⋊D39direct (N × H)
67. C11×C13C2×C7×C3⋊D3semidirect
72. C32×C13C2×C7×D11semidirect
73. C32×C11C2×C7×D13semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C2×C3⋊D39semidirect
81. C3×D11C7×D39semidirect
83. C32×C7D11×D13semidirect
89. C3×C13D3×C7×D11semidirect
91. C3×C11C2×C7×D39semidirect
98. D11C7×C3⋊D39direct (N × H)
99. C3×C7D11×D39semidirect
106. C13C7×C3⋊D3×D11semidirect
108. C11C2×C7×C3⋊D39semidirect
109. C32C7×D11×D13semidirect
110. C7D11×C3⋊D39direct (N × H)
115. C3C7×D11×D39semidirect

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×C3⋊D392
C7×C3⋊D4292
C7×D11×D393
D11×C3⋊D397
C2×C7×C3⋊D3911
C7×C3⋊D3×D1113