Finite Group Databasebeta

← C11×C13×D7×D9 #49114481

Subgroups — C11×C13×D7×D9 #49114481

Order 36036.

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C11×C13×D63C211yesmaximal, characteristic, complemented
2C7×C11×C13×D9C211yesmaximal, characteristic, complemented
3C9×C11×C13×D7C211yesmaximal, characteristic, complemented
4D3×C11×C13×D7—31nomaximal
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C13×D21—31no—
7D3×C7×C11×C13—31no—
8C3×C11×C13×D7D311yescharacteristic
9C2×C11×C13×D9—71nomaximal, Hall
10C2×C11×C13×D7—91noHall
11C13×D7×D9C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D311yescharacteristic
13C11×D7×D9C1311yesmaximal, characteristic, direct product factor, Hall
14C11×C13×D9—71no—
15C11×C13×D9D711yescharacteristic, direct product factor
16C2×C9×C11×C13—71no—
17C11×C13×D7—91no—
18C11×C13×D7D911yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20C2×D3×C11×C13—211no—
21C13×D63C2×C1111yescharacteristic, complemented
22C7×C13×D9C2×C1111yescharacteristic, complemented
23C9×C13×D7C2×C1111yescharacteristic, complemented
24C11×D63C2×C1311yescharacteristic, complemented
25C7×C11×D9C2×C1311yescharacteristic, complemented
26C9×C11×D7C2×C1311yescharacteristic, complemented
27C9×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×C13×D7—31no—
29C7×C11×C13C2×D911yescharacteristic, complemented, Hall
30D3×C11×D7—31no—
31C2×C3×C11×C13—71no—
32D3×C11×C13—31no—
33D3×C11×C13—211no—
34C7×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C7×C9×C11C22×C1311yescharacteristic, complemented, Hall
36C22×C11×C13—631noHall
37C13×D21—31no—
38D3×C7×C13—31no—
39C3×C13×D7D3×C1111yescharacteristic
40C2×C13×D9—71noHall
41C11×D21—31no—
42D3×C7×C11—31no—
43C3×C11×D7D3×C1311yescharacteristic
44C3×C11×C13D3×D711yescharacteristic
45C2×C11×D9—71noHall
46C2×C13×D7—91noHall
47C2×C11×D7—91noHall
48C2×C11×C13—71no—
49C2×C11×C13—91no—
50C2×C11×C13—631no—
51C3×C7×C13C2×D3×C1111yescharacteristic
52D7×D9C11×C1311yescharacteristic, direct product factor, Hall
53C2×C9×C13—71no—
54C13×D9—71no—
55C13×D9C11×D711yescharacteristic, direct product factor
56C3×C7×C11C2×D3×C1311yescharacteristic
57C2×C9×C11—71no—
58C11×D9—71no—
59C11×D9C13×D711yescharacteristic, direct product factor
60C2×C7×C13—91no—
61C13×D7—91no—
62C13×D7C11×D911yescharacteristic, direct product factor
63C2×D3×C13—211no—
64C2×C7×C11—91no—
65C11×D7—91no—
66C11×D7C13×D911yescharacteristic, direct product factor
67C11×C13D7×D911yescharacteristic, direct product factor, Hall
68C2×D3×C11—211no—
69D63C2×C11×C1311yescharacteristic, complemented
70C9×D7C2×C11×C1311yescharacteristic, complemented
71C7×D9C2×C11×C1311yescharacteristic, complemented
72C9×C13C2×C11×D711yescharacteristic, complemented, Hall
73C9×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C2×C11×D911yescharacteristic, complemented, Hall
75D3×D7—31no—
76C2×C3×C13—71no—
77D3×C13—31no—
78D3×C13—211no—
79C7×C11C2×C13×D911yescharacteristic, complemented, Hall
80C2×C3×C11—71no—
81D3×C11—31no—
82D3×C11—211no—
83C7×C9C22×C11×C1311yescharacteristic, complemented, Hall
84C22×C13—631noHall
85C22×C11—631noHall
86D21—31no—
87C3×D7D3×C11×C1311yescharacteristic
88D3×C7—31no—
89C3×C13D3×C11×D711yescharacteristic
90C2×D9—71noHall
91C3×C11D3×C13×D711yescharacteristic
92C2×D7—91noHall
93C2×C13—71no—
94C2×C13—91no—
95C2×C13—631no—
96C2×C11—71no—
97C2×C11—91no—
98C2×C11—631no—
99C3×C7C2×D3×C11×C1311yescharacteristic
100C2×C9—71no—
101D9—71no—
102D9C11×C13×D711yescharacteristic, direct product factor
103C2×C7—91no—
104D7—91no—
105D7C11×C13×D911yescharacteristic, direct product factor
106C13C11×D7×D911yescharacteristic, direct product factor, Sylow
107C2×D3—211no—
108C11C13×D7×D911yescharacteristic, direct product factor, Sylow
109C9C2×C11×C13×D711yescharacteristic, complemented, Sylow
110C7C2×C11×C13×D911yescharacteristic, complemented, Sylow
111C2×C3—71no—
112D3—31no—
113D3—211no—
114C22—631noSylow
115C3D3×C11×C13×D711yescharacteristic
116C2—71no—
117C2—91no—
118C2—631no—
subgroupG/H
center, hypercenterC11×C13D7×D9
commutator, cosocle, hypocenterC7×C9C22×C11×C13
FrattiniC3D3×C11×C13×D7
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C2×D3
LCSG ▷ C7×C9
UCSC1 ◁ C11×C13

Complements

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

NH ≅ G/Ntype
1. C11×C13×D63C2semidirect
2. C7×C11×C13×D9C2semidirect
3. C9×C11×C13×D7C2semidirect
5. C7×C9×C11×C13C22semidirect
11. C13×D7×D9C11direct (N × H)
13. C11×D7×D9C13direct (N × H)
15. C11×C13×D9D7direct (N × H)
18. C11×C13×D7D9direct (N × H)
21. C13×D63C2×C11semidirect
22. C7×C13×D9C2×C11semidirect
23. C9×C13×D7C2×C11semidirect
24. C11×D63C2×C13semidirect
25. C7×C11×D9C2×C13semidirect
26. C9×C11×D7C2×C13semidirect
27. C9×C11×C13C2×D7semidirect
29. C7×C11×C13C2×D9semidirect
34. C7×C9×C13C22×C11semidirect
35. C7×C9×C11C22×C13semidirect
52. D7×D9C11×C13direct (N × H)
55. C13×D9C11×D7direct (N × H)
59. C11×D9C13×D7direct (N × H)
62. C13×D7C11×D9direct (N × H)
66. C11×D7C13×D9direct (N × H)
67. C11×C13D7×D9direct (N × H)
69. D63C2×C11×C13semidirect
70. C9×D7C2×C11×C13semidirect
71. C7×D9C2×C11×C13semidirect
72. C9×C13C2×C11×D7semidirect
73. C9×C11C2×C13×D7semidirect
74. C7×C13C2×C11×D9semidirect
79. C7×C11C2×C13×D9semidirect
83. C7×C9C22×C11×C13semidirect
102. D9C11×C13×D7direct (N × H)
105. D7C11×C13×D9direct (N × H)
106. C13C11×D7×D9direct (N × H)
108. C11C13×D7×D9direct (N × H)
109. C9C2×C11×C13×D7semidirect
110. C7C2×C11×C13×D9semidirect

Maximal subgroups

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

subgroupindex
C11×C13×D632
C7×C11×C13×D92
C9×C11×C13×D72
D3×C11×C13×D73
C2×C11×C13×D97
C13×D7×D911
C11×D7×D913