Finite Group Databasebeta

← C11×D7×C3⋊D39 #49114985

Subgroups — C11×D7×C3⋊D39 #49114985

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×C11×C13×D7C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊D39C211yesmaximal, characteristic, complemented
3C11×C3⋊D273C211yesmaximal, characteristic, complemented
4C11×D7×D39—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×D273—34no—
7C7×C11×D39—34no—
8C3×C11×C13×D7D314yescomplemented
9C2×C11×C3⋊D39—71nomaximal, Hall
10C11×D7×D13—91noHall
11D7×C3⋊D39C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C11×D7×C3⋊D3—131nomaximal, Hall
14C11×C3⋊D39—71no—
15C11×C3⋊D39D711yescharacteristic, direct product factor
16C2×C32×C11×C13—71no—
17C11×D91—91no—
18C11×C13×D7C3⋊D311yescharacteristic, complemented
19C7×C11×D13—91no—
20C2×C11×D39—214no—
21C3⋊D273C2×C1111yescharacteristic, complemented
22C7×C3⋊D39C2×C1111yescharacteristic, complemented
23C32×C13×D7C2×C1111yescharacteristic, complemented
24C11×C3⋊D21—131no—
25C7×C11×C3⋊D3—131no—
26C32×C11×D7D1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D7×D39—34no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C11×D7—394no—
31C2×C3×C11×C13—74no—
32C11×D39—34no—
33C11×D39—214no—
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—631noHall
37D273—34no—
38C7×D39—34no—
39C3×C13×D7D3×C1114yescomplemented
40C2×C3⋊D39—71noHall
41C11×D21—394no—
42D3×C7×C11—394no—
43C3×C11×D7D3914yescomplemented
44C3×C11×C13D3×D714yescomplemented
45C2×C11×C3⋊D3—911noHall
46D7×D13—91noHall
47C2×C11×D7—1171noHall
48C2×C11×C13—71no—
49C11×D13—91no—
50C11×D13—631no—
51C3×C7×C13C2×D3×C1114yescomplemented
52D7×C3⋊D3—131noHall
53C2×C32×C13—71no—
54C3⋊D39—71no—
55C3⋊D39C11×D711yescharacteristic, direct product factor
56C3×C7×C11C2×D3914yescomplemented
57C2×C32×C11—71no—
58C11×C3⋊D3—131no—
59C11×C3⋊D3—911no—
60D91—91no—
61C7×D13—91no—
62C13×D7C11×C3⋊D311yescharacteristic, complemented
63C2×D39—214no—
64C2×C7×C11—1171no—
65C11×D7—1171no—
66C11×D7C3⋊D3911yescharacteristic, direct product factor
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D3×C11—2734no—
69C3⋊D21—131no—
70C7×C3⋊D3—131no—
71C32×D7C11×D1311yescharacteristic, complemented
72C32×C13C2×C11×D711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
75D3×D7—394no—
76C2×C3×C13—74no—
77D39—34no—
78D39—214no—
79C7×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
80C2×C3×C11—74no—
81D3×C11—2734no—
82D3×C11—394no—
83C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—631noHall
85C22×C11—8191noHall
86D21—394no—
87C3×D7C11×D3914yescomplemented
88D3×C7—394no—
89C3×C13D3×C11×D714yescomplemented
90C2×C3⋊D3—911noHall
91C3×C11D7×D3914yescomplemented
92C2×D7—1171noHall
93C2×C13—71no—
94D13—91no—
95D13—631no—
96C2×C11—71no—
97C2×C11—8191no—
98C2×C11—1171no—
99C3×C7C2×C11×D3914yescomplemented
100C2×C32—71no—
101C3⋊D3—131no—
102C3⋊D3—911no—
103C2×C7—1171no—
104D7—1171no—
105D7C11×C3⋊D3911yescharacteristic, direct product factor
106C13C11×D7×C3⋊D311yescharacteristic, complemented, Sylow
107C2×D3—2734no—
108C11D7×C3⋊D3911yescharacteristic, direct product factor, Sylow
109C32C11×D7×D1311yescharacteristic, complemented, Sylow
110C7C2×C11×C3⋊D3911yescharacteristic, complemented, Sylow
111C2×C3—74no—
112D3—2734no—
113D3—394no—
114C22—8191noSylow
115C3C11×D7×D3914yescomplemented
116C2—71no—
117C2—8191no—
118C2—1171no—
subgroupG/H
center, hypercenterC11D7×C3⋊D39
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×C13×D7C2semidirect
2. C7×C11×C3⋊D39C2semidirect
3. C11×C3⋊D273C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×C13×D7D3semidirect
11. D7×C3⋊D39C11direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
15. C11×C3⋊D39D7direct (N × H)
18. C11×C13×D7C3⋊D3semidirect
21. C3⋊D273C2×C11semidirect
22. C7×C3⋊D39C2×C11semidirect
23. C32×C13×D7C2×C11semidirect
26. C32×C11×D7D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C22×C11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C13×D7D3×C11semidirect
43. C3×C11×D7D39semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13C2×D3×C11semidirect
55. C3⋊D39C11×D7direct (N × H)
56. C3×C7×C11C2×D39semidirect
62. C13×D7C11×C3⋊D3semidirect
66. C11×D7C3⋊D39direct (N × H)
67. C11×C13D7×C3⋊D3semidirect
71. C32×D7C11×D13semidirect
72. C32×C13C2×C11×D7semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C11×C3⋊D3semidirect
79. C7×C11C2×C3⋊D39semidirect
83. C32×C7C2×C11×D13semidirect
87. C3×D7C11×D39semidirect
89. C3×C13D3×C11×D7semidirect
91. C3×C11D7×D39semidirect
99. C3×C7C2×C11×D39semidirect
105. D7C11×C3⋊D39direct (N × H)
106. C13C11×D7×C3⋊D3semidirect
108. C11D7×C3⋊D39direct (N × H)
109. C32C11×D7×D13semidirect
110. C7C2×C11×C3⋊D39semidirect
115. C3C11×D7×D39semidirect

Maximal subgroups

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

subgroupindex
C32×C11×C13×D72
C7×C11×C3⋊D392
C11×C3⋊D2732
C11×D7×D393
C2×C11×C3⋊D397
D7×C3⋊D3911
C11×D7×C3⋊D313