Finite Group Databasebeta

← C9×D11×D91 #49114462

Subgroups — C9×D11×D91 #49114462

Order 36036.

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 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×D1001C211yesmaximal, characteristic, complemented
2C9×C11×D91C211yesmaximal, characteristic, complemented
3C7×C9×C13×D11C211yesmaximal, characteristic, complemented
4C3×D11×D91C311yesmaximal, characteristic
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C3×D1001C2×C311yescharacteristic
7C3×C11×D91C2×C311yescharacteristic
8C3×C7×C13×D11C2×C311yescharacteristic
9C9×D11×D13—71nomaximal, Hall
10D11×D91C911yescharacteristic, direct product factor, Hall
11C2×C9×D91—111nomaximal, Hall
12C3×C7×C11×C13C22×C311yescharacteristic
13C9×D7×D11—131nomaximal, Hall
14C9×D143—71no—
15C9×C13×D11D711yescharacteristic, complemented
16C9×C11×D13—71no—
17D1001C2×C911yescharacteristic, complemented
18C11×D91C2×C911yescharacteristic, complemented
19C7×C13×D11C2×C911yescharacteristic, complemented
20C3×D11×D13—71no—
21C2×C7×C9×C13—111no—
22C9×D91—111no—
23C9×D91D1111yescharacteristic, direct product factor
24C9×D77—131no—
25C9×C11×D7—131no—
26C7×C9×D11D1311yescharacteristic, complemented
27C9×C11×C13C2×D711yescharacteristic, complemented, Hall
28C2×C3×D91—111no—
29C7×C11×C13C22×C911yescharacteristic, complemented, Hall
30C3×D7×D11—131no—
31C3×D143—71no—
32C3×C13×D11C3×D711yescharacteristic
33C3×C11×D13—71no—
34C7×C9×C13C2×D1111yescharacteristic, complemented, Hall
35C7×C9×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—71noHall
37C2×C3×C7×C13—111no—
38C3×D91—111no—
39C3×D91C3×D1111yescharacteristic
40C2×C9×D13—771noHall
41C3×D77—131no—
42C3×C11×D7—131no—
43C3×C7×D11C3×D1311yescharacteristic
44C3×C11×C13C2×C3×D711yescharacteristic
45C2×C9×D11—911noHall
46C2×D91—111noHall
47D7×D11—131noHall
48D143—71no—
49C11×D13—71no—
50C13×D11C9×D711yescharacteristic, complemented
51C3×C7×C13C2×C3×D1111yescharacteristic
52C2×C9×D7—1431noHall
53C2×C9×C13—111no—
54C9×D13—71no—
55C9×D13—771no—
56C3×C7×C11C2×C3×D1311yescharacteristic
57C2×C9×C11—911no—
58C9×D11—911no—
59C9×D11D9111yescharacteristic, direct product factor
60C2×C7×C13—111no—
61D91—111no—
62D91C9×D1111yescharacteristic, direct product factor
63C2×C3×D13—771no—
64D77—131no—
65C7×D11C9×D1311yescharacteristic, complemented
66C11×D7—131no—
67C11×C13C2×C9×D711yescharacteristic, complemented, Hall
68C2×C3×D11—911no—
69C2×C7×C9—111no—
70C9×D7—131no—
71C9×D7—1431no—
72C9×C13D7×D1111yescharacteristic, complemented, Hall
73C9×C11C2×D9111yescharacteristic, complemented, Hall
74C7×C13C2×C9×D1111yescharacteristic, complemented, Hall
75C2×C3×D7—1431no—
76C2×C3×C13—111no—
77C3×D13—71no—
78C3×D13—771no—
79C7×C11C2×C9×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—911no—
81C3×D11—911no—
82C3×D11C3×D9111yescharacteristic
83C7×C9D11×D1311yescharacteristic, complemented, Hall
84C2×D13—771noHall
85C2×D11—911noHall
86C2×C3×C7—111no—
87C3×D7—131no—
88C3×D7—1431no—
89C3×C13C3×D7×D1111yescharacteristic
90C22×C9—10011noHall
91C3×C11C2×C3×D9111yescharacteristic
92C2×D7—1431noHall
93C2×C13—111no—
94D13—71no—
95D13—771no—
96C2×C11—911no—
97D11—911no—
98D11C9×D9111yescharacteristic, direct product factor
99C3×C7C3×D11×D1311yescharacteristic
100C2×C9—111no—
101C2×C9—911no—
102C2×C9—10011no—
103C2×C7—111no—
104D7—131no—
105D7—1431no—
106C13C9×D7×D1111yescharacteristic, complemented, Sylow
107C22×C3—10011no—
108C11C2×C9×D9111yescharacteristic, complemented, Sylow
109C9D11×D9111yescharacteristic, direct product factor, Sylow
110C7C9×D11×D1311yescharacteristic, complemented, Sylow
111C2×C3—111no—
112C2×C3—911no—
113C2×C3—10011no—
114C22—10011noSylow
115C3C3×D11×D9111yescharacteristic
116C2—111no—
117C2—911no—
118C2—10011no—
subgroupG/H
center, hypercenterC9D11×D91
commutator, hypocenterC7×C11×C13C22×C9
FrattiniC3C3×D11×D91
FittingC7×C9×C11×C13C22
socle, cosocleC3×C7×C11×C13C22×C3
prime radicalC3×D11×D91C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C9×D1001C2semidirect
2. C9×C11×D91C2semidirect
3. C7×C9×C13×D11C2semidirect
5. C7×C9×C11×C13C22semidirect
10. D11×D91C9direct (N × H)
15. C9×C13×D11D7semidirect
17. D1001C2×C9semidirect
18. C11×D91C2×C9semidirect
19. C7×C13×D11C2×C9semidirect
23. C9×D91D11direct (N × H)
26. C7×C9×D11D13semidirect
27. C9×C11×C13C2×D7semidirect
29. C7×C11×C13C22×C9semidirect
34. C7×C9×C13C2×D11semidirect
35. C7×C9×C11C2×D13semidirect
50. C13×D11C9×D7semidirect
59. C9×D11D91direct (N × H)
62. D91C9×D11direct (N × H)
65. C7×D11C9×D13semidirect
67. C11×C13C2×C9×D7semidirect
72. C9×C13D7×D11semidirect
73. C9×C11C2×D91semidirect
74. C7×C13C2×C9×D11semidirect
79. C7×C11C2×C9×D13semidirect
83. C7×C9D11×D13semidirect
98. D11C9×D91direct (N × H)
106. C13C9×D7×D11semidirect
108. C11C2×C9×D91semidirect
109. C9D11×D91direct (N × H)
110. C7C9×D11×D13semidirect

Maximal subgroups

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

subgroupindex
C9×D10012
C9×C11×D912
C7×C9×C13×D112
C3×D11×D913
C9×D11×D137
C2×C9×D9111
C9×D7×D1113