Finite Group Databasebeta

← C11×D7×D117 #49114482

Subgroups — C11×D7×D117 #49114482

Order 36036.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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×D819C211yesmaximal, characteristic, complemented
2C7×C11×D117C211yesmaximal, characteristic, complemented
3C9×C11×C13×D7C211yesmaximal, characteristic, complemented
4C11×D7×D39—31nomaximal
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C11×D273—31no—
7C7×C11×D39—31no—
8C3×C11×C13×D7D311yescharacteristic
9C2×C11×D117—71nomaximal, Hall
10C11×D7×D13—91noHall
11D7×D117C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D311yescharacteristic
13C11×D7×D9—131nomaximal, Hall
14C11×D117—71no—
15C11×D117D711yescharacteristic, direct product factor
16C2×C9×C11×C13—71no—
17C11×D91—91no—
18C11×C13×D7D911yescharacteristic, complemented
19C7×C11×D13—91no—
20C2×C11×D39—211no—
21D819C2×C1111yescharacteristic, complemented
22C7×D117C2×C1111yescharacteristic, complemented
23C9×C13×D7C2×C1111yescharacteristic, complemented
24C11×D63—131no—
25C7×C11×D9—131no—
26C9×C11×D7D1311yescharacteristic, complemented
27C9×C11×C13C2×D711yescharacteristic, complemented, Hall
28D7×D39—31no—
29C7×C11×C13C2×D911yescharacteristic, complemented, Hall
30D3×C11×D7—391no—
31C2×C3×C11×C13—71no—
32C11×D39—31no—
33C11×D39—211no—
34C7×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C7×C9×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—631noHall
37D273—31no—
38C7×D39—31no—
39C3×C13×D7D3×C1111yescharacteristic
40C2×D117—71noHall
41C11×D21—391no—
42D3×C7×C11—391no—
43C3×C11×D7D3911yescharacteristic
44C3×C11×C13D3×D711yescharacteristic
45C2×C11×D9—911noHall
46D7×D13—91noHall
47C2×C11×D7—1171noHall
48C2×C11×C13—71no—
49C11×D13—91no—
50C11×D13—631no—
51C3×C7×C13C2×D3×C1111yescharacteristic
52D7×D9—131noHall
53C2×C9×C13—71no—
54D117—71no—
55D117C11×D711yescharacteristic, direct product factor
56C3×C7×C11C2×D3911yescharacteristic
57C2×C9×C11—71no—
58C11×D9—131no—
59C11×D9—911no—
60D91—91no—
61C7×D13—91no—
62C13×D7C11×D911yescharacteristic, complemented
63C2×D39—211no—
64C2×C7×C11—1171no—
65C11×D7—1171no—
66C11×D7D11711yescharacteristic, direct product factor
67C11×C13D7×D911yescharacteristic, complemented, Hall
68C2×D3×C11—2731no—
69D63—131no—
70C9×D7C11×D1311yescharacteristic, complemented
71C7×D9—131no—
72C9×C13C2×C11×D711yescharacteristic, complemented, Hall
73C9×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C11×D911yescharacteristic, complemented, Hall
75D3×D7—391no—
76C2×C3×C13—71no—
77D39—31no—
78D39—211no—
79C7×C11C2×D11711yescharacteristic, complemented, Hall
80C2×C3×C11—71no—
81D3×C11—2731no—
82D3×C11—391no—
83C7×C9C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—631noHall
85C22×C11—8191noHall
86D21—391no—
87C3×D7C11×D3911yescharacteristic
88D3×C7—391no—
89C3×C13D3×C11×D711yescharacteristic
90C2×D9—911noHall
91C3×C11D7×D3911yescharacteristic
92C2×D7—1171noHall
93C2×C13—71no—
94D13—91no—
95D13—631no—
96C2×C11—71no—
97C2×C11—8191no—
98C2×C11—1171no—
99C3×C7C2×C11×D3911yescharacteristic
100C2×C9—71no—
101D9—131no—
102D9—911no—
103C2×C7—1171no—
104D7—1171no—
105D7C11×D11711yescharacteristic, direct product factor
106C13C11×D7×D911yescharacteristic, complemented, Sylow
107C2×D3—2731no—
108C11D7×D11711yescharacteristic, direct product factor, Sylow
109C9C11×D7×D1311yescharacteristic, complemented, Sylow
110C7C2×C11×D11711yescharacteristic, complemented, Sylow
111C2×C3—71no—
112D3—2731no—
113D3—391no—
114C22—8191noSylow
115C3C11×D7×D3911yescharacteristic
116C2—71no—
117C2—8191no—
118C2—1171no—
subgroupG/H
center, hypercenterC11D7×D117
commutator, cosocle, hypocenterC7×C9×C13C22×C11
FrattiniC3C11×D7×D39
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C2×D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D819C2semidirect
2. C7×C11×D117C2semidirect
3. C9×C11×C13×D7C2semidirect
5. C7×C9×C11×C13C22semidirect
11. D7×D117C11direct (N × H)
15. C11×D117D7direct (N × H)
18. C11×C13×D7D9semidirect
21. D819C2×C11semidirect
22. C7×D117C2×C11semidirect
23. C9×C13×D7C2×C11semidirect
26. C9×C11×D7D13semidirect
27. C9×C11×C13C2×D7semidirect
29. C7×C11×C13C2×D9semidirect
34. C7×C9×C13C22×C11semidirect
35. C7×C9×C11C2×D13semidirect
55. D117C11×D7direct (N × H)
62. C13×D7C11×D9semidirect
66. C11×D7D117direct (N × H)
67. C11×C13D7×D9semidirect
70. C9×D7C11×D13semidirect
72. C9×C13C2×C11×D7semidirect
73. C9×C11D7×D13semidirect
74. C7×C13C2×C11×D9semidirect
79. C7×C11C2×D117semidirect
83. C7×C9C2×C11×D13semidirect
105. D7C11×D117direct (N × H)
106. C13C11×D7×D9semidirect
108. C11D7×D117direct (N × H)
109. C9C11×D7×D13semidirect
110. C7C2×C11×D117semidirect

Maximal subgroups

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

subgroupindex
C11×D8192
C7×C11×D1172
C9×C11×C13×D72
C11×D7×D393
C2×C11×D1177
D7×D11711
C11×D7×D913