Finite Group Databasebeta

← C9×C13×D7×D11 #49114461

Subgroups — C9×C13×D7×D11 #49114461

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×C13×D77C211yesmaximal, characteristic, complemented
2C9×C11×C13×D7C211yesmaximal, characteristic, complemented
3C7×C9×C13×D11C211yesmaximal, characteristic, complemented
4C3×C13×D7×D11C311yesmaximal, characteristic
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C3×C13×D77C2×C311yescharacteristic
7C3×C11×C13×D7C2×C311yescharacteristic
8C3×C7×C13×D11C2×C311yescharacteristic
9C2×C9×C13×D11—71nomaximal, Hall
10C13×D7×D11C911yescharacteristic, direct product factor, Hall
11C2×C9×C13×D7—111nomaximal, Hall
12C3×C7×C11×C13C22×C311yescharacteristic
13C9×D7×D11C1311yesmaximal, characteristic, direct product factor, Hall
14C9×C13×D11—71no—
15C9×C13×D11D711yescharacteristic, direct product factor
16C2×C9×C11×C13—71no—
17C13×D77C2×C911yescharacteristic, complemented
18C11×C13×D7C2×C911yescharacteristic, complemented
19C7×C13×D11C2×C911yescharacteristic, complemented
20C2×C3×C13×D11—71no—
21C2×C7×C9×C13—111no—
22C9×C13×D7—111no—
23C9×C13×D7D1111yescharacteristic, direct product factor
24C9×D77C2×C1311yescharacteristic, complemented
25C9×C11×D7C2×C1311yescharacteristic, complemented
26C7×C9×D11C2×C1311yescharacteristic, complemented
27C9×C11×C13C2×D711yescharacteristic, complemented, Hall
28C2×C3×C13×D7—111no—
29C7×C11×C13C22×C911yescharacteristic, complemented, Hall
30C3×D7×D11C3×C1311yescharacteristic
31C2×C3×C11×C13—71no—
32C3×C13×D11—71no—
33C3×C13×D11C3×D711yescharacteristic
34C7×C9×C13C2×D1111yescharacteristic, complemented, Hall
35C7×C9×C11C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D11—71noHall
37C2×C3×C7×C13—111no—
38C3×C13×D7—111no—
39C3×C13×D7C3×D1111yescharacteristic
40C22×C9×C13—771noHall
41C3×D77C2×C3×C1311yescharacteristic
42C3×C11×D7C2×C3×C1311yescharacteristic
43C3×C7×D11C2×C3×C1311yescharacteristic
44C3×C11×C13C2×C3×D711yescharacteristic
45C2×C9×D11—71noHall
46C2×C13×D7—111noHall
47D7×D11C9×C1311yescharacteristic, direct product factor, Hall
48C2×C11×C13—71no—
49C13×D11—71no—
50C13×D11C9×D711yescharacteristic, direct product factor
51C3×C7×C13C2×C3×D1111yescharacteristic
52C2×C9×D7—111noHall
53C2×C9×C13—71no—
54C2×C9×C13—111no—
55C2×C9×C13—771no—
56C3×C7×C11C22×C3×C1311yescharacteristic
57C2×C9×C11—71no—
58C9×D11—71no—
59C9×D11C13×D711yescharacteristic, direct product factor
60C2×C7×C13—111no—
61C13×D7—111no—
62C13×D7C9×D1111yescharacteristic, direct product factor
63C22×C3×C13—771no—
64D77C2×C9×C1311yescharacteristic, complemented
65C7×D11C2×C9×C1311yescharacteristic, complemented
66C11×D7C2×C9×C1311yescharacteristic, complemented
67C11×C13C2×C9×D711yescharacteristic, complemented, Hall
68C2×C3×D11—71no—
69C2×C7×C9—111no—
70C9×D7—111no—
71C9×D7C13×D1111yescharacteristic, direct product factor
72C9×C13D7×D1111yescharacteristic, direct product factor, Hall
73C9×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C2×C9×D1111yescharacteristic, complemented, Hall
75C2×C3×D7—111no—
76C2×C3×C13—71no—
77C2×C3×C13—111no—
78C2×C3×C13—771no—
79C7×C11C22×C9×C1311yescharacteristic, complemented, Hall
80C2×C3×C11—71no—
81C3×D11—71no—
82C3×D11C3×C13×D711yescharacteristic
83C7×C9C2×C13×D1111yescharacteristic, complemented, Hall
84C22×C13—771noHall
85C2×D11—71noHall
86C2×C3×C7—111no—
87C3×D7—111no—
88C3×D7C3×C13×D1111yescharacteristic
89C3×C13C3×D7×D1111yescharacteristic
90C22×C9—771noHall
91C3×C11C2×C3×C13×D711yescharacteristic
92C2×D7—111noHall
93C2×C13—71no—
94C2×C13—111no—
95C2×C13—771no—
96C2×C11—71no—
97D11—71no—
98D11C9×C13×D711yescharacteristic, direct product factor
99C3×C7C2×C3×C13×D1111yescharacteristic
100C2×C9—71no—
101C2×C9—111no—
102C2×C9—771no—
103C2×C7—111no—
104D7—111no—
105D7C9×C13×D1111yescharacteristic, direct product factor
106C13C9×D7×D1111yescharacteristic, direct product factor, Sylow
107C22×C3—771no—
108C11C2×C9×C13×D711yescharacteristic, complemented, Sylow
109C9C13×D7×D1111yescharacteristic, direct product factor, Sylow
110C7C2×C9×C13×D1111yescharacteristic, complemented, Sylow
111C2×C3—71no—
112C2×C3—111no—
113C2×C3—771no—
114C22—771noSylow
115C3C3×C13×D7×D1111yescharacteristic
116C2—71no—
117C2—111no—
118C2—771no—
subgroupG/H
center, hypercenterC9×C13D7×D11
commutator, hypocenterC7×C11C22×C9×C13
FrattiniC3C3×C13×D7×D11
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C22×C3
prime radicalC3×C13×D7×D11C3
cosocleC3×C7×C11C22×C3×C13
LCSG ▷ C7×C11
UCSC1 ◁ C9×C13

Complements

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

NH ≅ G/Ntype
1. C9×C13×D77C2semidirect
2. C9×C11×C13×D7C2semidirect
3. C7×C9×C13×D11C2semidirect
5. C7×C9×C11×C13C22semidirect
10. C13×D7×D11C9direct (N × H)
13. C9×D7×D11C13direct (N × H)
15. C9×C13×D11D7direct (N × H)
17. C13×D77C2×C9semidirect
18. C11×C13×D7C2×C9semidirect
19. C7×C13×D11C2×C9semidirect
23. C9×C13×D7D11direct (N × H)
24. C9×D77C2×C13semidirect
25. C9×C11×D7C2×C13semidirect
26. C7×C9×D11C2×C13semidirect
27. C9×C11×C13C2×D7semidirect
29. C7×C11×C13C22×C9semidirect
34. C7×C9×C13C2×D11semidirect
35. C7×C9×C11C22×C13semidirect
47. D7×D11C9×C13direct (N × H)
50. C13×D11C9×D7direct (N × H)
59. C9×D11C13×D7direct (N × H)
62. C13×D7C9×D11direct (N × H)
64. D77C2×C9×C13semidirect
65. C7×D11C2×C9×C13semidirect
66. C11×D7C2×C9×C13semidirect
67. C11×C13C2×C9×D7semidirect
71. C9×D7C13×D11direct (N × H)
72. C9×C13D7×D11direct (N × H)
73. C9×C11C2×C13×D7semidirect
74. C7×C13C2×C9×D11semidirect
79. C7×C11C22×C9×C13semidirect
83. C7×C9C2×C13×D11semidirect
98. D11C9×C13×D7direct (N × H)
105. D7C9×C13×D11direct (N × H)
106. C13C9×D7×D11direct (N × H)
108. C11C2×C9×C13×D7semidirect
109. C9C13×D7×D11direct (N × H)
110. C7C2×C9×C13×D11semidirect

Maximal subgroups

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

subgroupindex
C9×C13×D772
C9×C11×C13×D72
C7×C9×C13×D112
C3×C13×D7×D113
C2×C9×C13×D117
C2×C9×C13×D711
C9×D7×D1113