Finite Group Databasebeta

← C32×C11×D7×D13 #49114893

Subgroups — C32×C11×D7×D13 #49114893

Order 36036.

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

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C32×C7×C11×D13C211yesmaximal, characteristic, complemented
2C32×C11×C13×D7C211yesmaximal, characteristic, complemented
3C32×C11×D91C211yesmaximal, characteristic, complemented
4C3×C11×D7×D13C314yesmaximal, direct product factor
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C3×C11×D91C2×C314yescomplemented
7C3×C11×C13×D7C2×C314yescomplemented
8C3×C7×C11×D13C2×C314yescomplemented
9C2×C32×C11×D13—71nomaximal, Hall
10C11×D7×D13C3211yescharacteristic, direct product factor, Hall
11C32×D7×D13C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C22×C314yescomplemented
13C2×C32×C11×D7—131nomaximal, Hall
14C32×C11×D13—71no—
15C32×C11×D13D711yescharacteristic, direct product factor
16C2×C32×C11×C13—71no—
17C11×D91C2×C3211yescharacteristic, complemented
18C11×C13×D7C2×C3211yescharacteristic, complemented
19C7×C11×D13C2×C3211yescharacteristic, complemented
20C2×C3×C11×D13—74no—
21C32×D91C2×C1111yescharacteristic, complemented
22C32×C13×D7C2×C1111yescharacteristic, complemented
23C32×C7×D13C2×C1111yescharacteristic, complemented
24C2×C32×C7×C11—131no—
25C32×C11×D7—131no—
26C32×C11×D7D1311yescharacteristic, direct product factor
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28C3×D7×D13C3×C1114yesdirect product factor
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C2×C3×C11×D7—134no—
31C2×C3×C11×C13—74no—
32C3×C11×D13—74no—
33C3×C11×D13C3×D714yesdirect product factor
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—71noHall
37C3×D91C2×C3×C1114yescomplemented
38C3×C13×D7C2×C3×C1114yescomplemented
39C3×C7×D13C2×C3×C1114yescomplemented
40C2×C32×D13—71noHall
41C2×C3×C7×C11—134no—
42C3×C11×D7—134no—
43C3×C11×D7C3×D1314yesdirect product factor
44C3×C11×C13C2×C3×D714yescomplemented
45C22×C32×C11—911noHall
46D7×D13C32×C1111yescharacteristic, direct product factor, Hall
47C2×C11×D7—131noHall
48C2×C11×C13—71no—
49C11×D13—71no—
50C11×D13C32×D711yescharacteristic, direct product factor
51C3×C7×C13C22×C3×C1114yescomplemented
52C2×C32×D7—131noHall
53C2×C32×C13—71no—
54C32×D13—71no—
55C32×D13C11×D711yescharacteristic, direct product factor
56C3×C7×C11C2×C3×D1314yescomplemented
57C2×C32×C11—71no—
58C2×C32×C11—131no—
59C2×C32×C11—911no—
60D91C2×C32×C1111yescharacteristic, complemented
61C7×D13C2×C32×C1111yescharacteristic, complemented
62C13×D7C2×C32×C1111yescharacteristic, complemented
63C2×C3×D13—74no—
64C2×C7×C11—131no—
65C11×D7—131no—
66C11×D7C32×D1311yescharacteristic, direct product factor
67C11×C13C2×C32×D711yescharacteristic, complemented, Hall
68C22×C3×C11—914no—
69C2×C32×C7—131no—
70C32×D7—131no—
71C32×D7C11×D1311yescharacteristic, direct product factor
72C32×C13C2×C11×D711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, direct product factor, Hall
74C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
75C2×C3×D7—134no—
76C2×C3×C13—74no—
77C3×D13—74no—
78C3×D13C3×C11×D714yesdirect product factor
79C7×C11C2×C32×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—74no—
81C2×C3×C11—134no—
82C2×C3×C11—914no—
83C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—71noHall
85C22×C11—911noHall
86C2×C3×C7—134no—
87C3×D7—134no—
88C3×D7C3×C11×D1314yesdirect product factor
89C3×C13C2×C3×C11×D714yescomplemented
90C22×C32—911noHall
91C3×C11C3×D7×D1314yesdirect product factor
92C2×D7—131noHall
93C2×C13—71no—
94D13—71no—
95D13C32×C11×D711yescharacteristic, direct product factor
96C2×C11—71no—
97C2×C11—131no—
98C2×C11—911no—
99C3×C7C2×C3×C11×D1314yescomplemented
100C2×C32—71no—
101C2×C32—131no—
102C2×C32—911no—
103C2×C7—131no—
104D7—131no—
105D7C32×C11×D1311yescharacteristic, direct product factor
106C13C2×C32×C11×D711yescharacteristic, complemented, Sylow
107C22×C3—914no—
108C11C32×D7×D1311yescharacteristic, direct product factor, Sylow
109C32C11×D7×D1311yescharacteristic, direct product factor, Sylow
110C7C2×C32×C11×D1311yescharacteristic, complemented, Sylow
111C2×C3—74no—
112C2×C3—134no—
113C2×C3—914no—
114C22—911noSylow
115C3C3×C11×D7×D1314yesdirect product factor
116C2—71no—
117C2—131no—
118C2—911no—
subgroupG/H
center, hypercenterC32×C11D7×D13
commutator, cosocle, hypocenterC7×C13C22×C32×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C7×C13
UCSC1 ◁ C32×C11

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D13C2semidirect
2. C32×C11×C13×D7C2semidirect
3. C32×C11×D91C2semidirect
4. C3×C11×D7×D13C3direct (N × H)
5. C32×C7×C11×C13C22semidirect
6. C3×C11×D91C2×C3semidirect
7. C3×C11×C13×D7C2×C3semidirect
8. C3×C7×C11×D13C2×C3semidirect
10. C11×D7×D13C32direct (N × H)
11. C32×D7×D13C11direct (N × H)
12. C3×C7×C11×C13C22×C3semidirect
15. C32×C11×D13D7direct (N × H)
17. C11×D91C2×C32semidirect
18. C11×C13×D7C2×C32semidirect
19. C7×C11×D13C2×C32semidirect
21. C32×D91C2×C11semidirect
22. C32×C13×D7C2×C11semidirect
23. C32×C7×D13C2×C11semidirect
26. C32×C11×D7D13direct (N × H)
27. C32×C11×C13C2×D7semidirect
28. C3×D7×D13C3×C11direct (N × H)
29. C7×C11×C13C22×C32semidirect
33. C3×C11×D13C3×D7direct (N × H)
34. C32×C7×C13C22×C11semidirect
35. C32×C7×C11C2×D13semidirect
37. C3×D91C2×C3×C11semidirect
38. C3×C13×D7C2×C3×C11semidirect
39. C3×C7×D13C2×C3×C11semidirect
43. C3×C11×D7C3×D13direct (N × H)
44. C3×C11×C13C2×C3×D7semidirect
46. D7×D13C32×C11direct (N × H)
50. C11×D13C32×D7direct (N × H)
51. C3×C7×C13C22×C3×C11semidirect
55. C32×D13C11×D7direct (N × H)
56. C3×C7×C11C2×C3×D13semidirect
60. D91C2×C32×C11semidirect
61. C7×D13C2×C32×C11semidirect
62. C13×D7C2×C32×C11semidirect
66. C11×D7C32×D13direct (N × H)
67. C11×C13C2×C32×D7semidirect
71. C32×D7C11×D13direct (N × H)
72. C32×C13C2×C11×D7semidirect
73. C32×C11D7×D13direct (N × H)
74. C7×C13C22×C32×C11semidirect
78. C3×D13C3×C11×D7direct (N × H)
79. C7×C11C2×C32×D13semidirect
83. C32×C7C2×C11×D13semidirect
88. C3×D7C3×C11×D13direct (N × H)
89. C3×C13C2×C3×C11×D7semidirect
91. C3×C11C3×D7×D13direct (N × H)
95. D13C32×C11×D7direct (N × H)
99. C3×C7C2×C3×C11×D13semidirect
105. D7C32×C11×D13direct (N × H)
106. C13C2×C32×C11×D7semidirect
108. C11C32×D7×D13direct (N × H)
109. C32C11×D7×D13direct (N × H)
110. C7C2×C32×C11×D13semidirect
115. C3C3×C11×D7×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C32×C11×C13×D72
C32×C11×D912
C3×C11×D7×D133
C2×C32×C11×D137
C32×D7×D1311
C2×C32×C11×D713