Finite Group Databasebeta

← C9×C11×D7×D13 #49114458

Subgroups — C9×C11×D7×D13 #49114458

Order 36036.

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C9×C11×D91C211yesmaximal, characteristic, complemented
2C9×C11×C13×D7C211yesmaximal, characteristic, complemented
3C7×C9×C11×D13C211yesmaximal, characteristic, complemented
4C3×C11×D7×D13C311yesmaximal, characteristic
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C3×C11×D91C2×C311yescharacteristic
7C3×C11×C13×D7C2×C311yescharacteristic
8C3×C7×C11×D13C2×C311yescharacteristic
9C2×C9×C11×D13—71nomaximal, Hall
10C11×D7×D13C911yescharacteristic, direct product factor, Hall
11C9×D7×D13C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C22×C311yescharacteristic
13C2×C9×C11×D7—131nomaximal, Hall
14C9×C11×D13—71no—
15C9×C11×D13D711yescharacteristic, direct product factor
16C2×C9×C11×C13—71no—
17C11×D91C2×C911yescharacteristic, complemented
18C11×C13×D7C2×C911yescharacteristic, complemented
19C7×C11×D13C2×C911yescharacteristic, complemented
20C2×C3×C11×D13—71no—
21C9×D91C2×C1111yescharacteristic, complemented
22C9×C13×D7C2×C1111yescharacteristic, complemented
23C7×C9×D13C2×C1111yescharacteristic, complemented
24C2×C7×C9×C11—131no—
25C9×C11×D7—131no—
26C9×C11×D7D1311yescharacteristic, direct product factor
27C9×C11×C13C2×D711yescharacteristic, complemented, Hall
28C3×D7×D13C3×C1111yescharacteristic
29C7×C11×C13C22×C911yescharacteristic, complemented, Hall
30C2×C3×C11×D7—131no—
31C2×C3×C11×C13—71no—
32C3×C11×D13—71no—
33C3×C11×D13C3×D711yescharacteristic
34C7×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C7×C9×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—71noHall
37C3×D91C2×C3×C1111yescharacteristic
38C3×C13×D7C2×C3×C1111yescharacteristic
39C3×C7×D13C2×C3×C1111yescharacteristic
40C2×C9×D13—71noHall
41C2×C3×C7×C11—131no—
42C3×C11×D7—131no—
43C3×C11×D7C3×D1311yescharacteristic
44C3×C11×C13C2×C3×D711yescharacteristic
45C22×C9×C11—911noHall
46D7×D13C9×C1111yescharacteristic, direct product factor, Hall
47C2×C11×D7—131noHall
48C2×C11×C13—71no—
49C11×D13—71no—
50C11×D13C9×D711yescharacteristic, direct product factor
51C3×C7×C13C22×C3×C1111yescharacteristic
52C2×C9×D7—131noHall
53C2×C9×C13—71no—
54C9×D13—71no—
55C9×D13C11×D711yescharacteristic, direct product factor
56C3×C7×C11C2×C3×D1311yescharacteristic
57C2×C9×C11—71no—
58C2×C9×C11—131no—
59C2×C9×C11—911no—
60D91C2×C9×C1111yescharacteristic, complemented
61C7×D13C2×C9×C1111yescharacteristic, complemented
62C13×D7C2×C9×C1111yescharacteristic, complemented
63C2×C3×D13—71no—
64C2×C7×C11—131no—
65C11×D7—131no—
66C11×D7C9×D1311yescharacteristic, direct product factor
67C11×C13C2×C9×D711yescharacteristic, complemented, Hall
68C22×C3×C11—911no—
69C2×C7×C9—131no—
70C9×D7—131no—
71C9×D7C11×D1311yescharacteristic, direct product factor
72C9×C13C2×C11×D711yescharacteristic, complemented, Hall
73C9×C11D7×D1311yescharacteristic, direct product factor, Hall
74C7×C13C22×C9×C1111yescharacteristic, complemented, Hall
75C2×C3×D7—131no—
76C2×C3×C13—71no—
77C3×D13—71no—
78C3×D13C3×C11×D711yescharacteristic
79C7×C11C2×C9×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—71no—
81C2×C3×C11—131no—
82C2×C3×C11—911no—
83C7×C9C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—71noHall
85C22×C11—911noHall
86C2×C3×C7—131no—
87C3×D7—131no—
88C3×D7C3×C11×D1311yescharacteristic
89C3×C13C2×C3×C11×D711yescharacteristic
90C22×C9—911noHall
91C3×C11C3×D7×D1311yescharacteristic
92C2×D7—131noHall
93C2×C13—71no—
94D13—71no—
95D13C9×C11×D711yescharacteristic, direct product factor
96C2×C11—71no—
97C2×C11—131no—
98C2×C11—911no—
99C3×C7C2×C3×C11×D1311yescharacteristic
100C2×C9—71no—
101C2×C9—131no—
102C2×C9—911no—
103C2×C7—131no—
104D7—131no—
105D7C9×C11×D1311yescharacteristic, direct product factor
106C13C2×C9×C11×D711yescharacteristic, complemented, Sylow
107C22×C3—911no—
108C11C9×D7×D1311yescharacteristic, direct product factor, Sylow
109C9C11×D7×D1311yescharacteristic, direct product factor, Sylow
110C7C2×C9×C11×D1311yescharacteristic, complemented, Sylow
111C2×C3—71no—
112C2×C3—131no—
113C2×C3—911no—
114C22—911noSylow
115C3C3×C11×D7×D1311yescharacteristic
116C2—71no—
117C2—131no—
118C2—911no—
subgroupG/H
center, hypercenterC9×C11D7×D13
commutator, hypocenterC7×C13C22×C9×C11
FrattiniC3C3×C11×D7×D13
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C22×C3
prime radicalC3×C11×D7×D13C3
cosocleC3×C7×C13C22×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C9×C11

Complements

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

NH ≅ G/Ntype
1. C9×C11×D91C2semidirect
2. C9×C11×C13×D7C2semidirect
3. C7×C9×C11×D13C2semidirect
5. C7×C9×C11×C13C22semidirect
10. C11×D7×D13C9direct (N × H)
11. C9×D7×D13C11direct (N × H)
15. C9×C11×D13D7direct (N × H)
17. C11×D91C2×C9semidirect
18. C11×C13×D7C2×C9semidirect
19. C7×C11×D13C2×C9semidirect
21. C9×D91C2×C11semidirect
22. C9×C13×D7C2×C11semidirect
23. C7×C9×D13C2×C11semidirect
26. C9×C11×D7D13direct (N × H)
27. C9×C11×C13C2×D7semidirect
29. C7×C11×C13C22×C9semidirect
34. C7×C9×C13C22×C11semidirect
35. C7×C9×C11C2×D13semidirect
46. D7×D13C9×C11direct (N × H)
50. C11×D13C9×D7direct (N × H)
55. C9×D13C11×D7direct (N × H)
60. D91C2×C9×C11semidirect
61. C7×D13C2×C9×C11semidirect
62. C13×D7C2×C9×C11semidirect
66. C11×D7C9×D13direct (N × H)
67. C11×C13C2×C9×D7semidirect
71. C9×D7C11×D13direct (N × H)
72. C9×C13C2×C11×D7semidirect
73. C9×C11D7×D13direct (N × H)
74. C7×C13C22×C9×C11semidirect
79. C7×C11C2×C9×D13semidirect
83. C7×C9C2×C11×D13semidirect
95. D13C9×C11×D7direct (N × H)
105. D7C9×C11×D13direct (N × H)
106. C13C2×C9×C11×D7semidirect
108. C11C9×D7×D13direct (N × H)
109. C9C11×D7×D13direct (N × H)
110. C7C2×C9×C11×D13semidirect

Maximal subgroups

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

subgroupindex
C9×C11×D912
C9×C11×C13×D72
C7×C9×C11×D132
C3×C11×D7×D133
C2×C9×C11×D137
C9×D7×D1311
C2×C9×C11×D713