Finite Group Databasebeta

← C32×D11×D91 #49114897

Subgroups — C32×D11×D91 #49114897

Order 36036.

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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×C13×D11C211yesmaximal, characteristic, complemented
2C32×C11×D91C211yesmaximal, characteristic, complemented
3C32×D1001C211yesmaximal, characteristic, complemented
4C3×D11×D91C314yesmaximal, direct product factor
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C3×D1001C2×C314yescomplemented
7C3×C11×D91C2×C314yescomplemented
8C3×C7×C13×D11C2×C314yescomplemented
9C32×D11×D13—71nomaximal, Hall
10D11×D91C3211yescharacteristic, direct product factor, Hall
11C2×C32×D91—111nomaximal, Hall
12C3×C7×C11×C13C22×C314yescomplemented
13C32×D7×D11—131nomaximal, Hall
14C32×D143—71no—
15C32×C13×D11D711yescharacteristic, complemented
16C32×C11×D13—71no—
17D1001C2×C3211yescharacteristic, complemented
18C11×D91C2×C3211yescharacteristic, complemented
19C7×C13×D11C2×C3211yescharacteristic, complemented
20C3×D11×D13—74no—
21C2×C32×C7×C13—111no—
22C32×D91—111no—
23C32×D91D1111yescharacteristic, direct product factor
24C32×D77—131no—
25C32×C11×D7—131no—
26C32×C7×D11D1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28C2×C3×D91—114no—
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C3×D7×D11—134no—
31C3×D143—74no—
32C3×C13×D11C3×D714yescomplemented
33C3×C11×D13—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—71noHall
37C2×C3×C7×C13—114no—
38C3×D91—114no—
39C3×D91C3×D1114yesdirect product factor
40C2×C32×D13—771noHall
41C3×D77—134no—
42C3×C11×D7—134no—
43C3×C7×D11C3×D1314yescomplemented
44C3×C11×C13C2×C3×D714yescomplemented
45C2×C32×D11—911noHall
46C2×D91—111noHall
47D7×D11—131noHall
48D143—71no—
49C11×D13—71no—
50C13×D11C32×D711yescharacteristic, complemented
51C3×C7×C13C2×C3×D1114yescomplemented
52C2×C32×D7—1431noHall
53C2×C32×C13—111no—
54C32×D13—71no—
55C32×D13—771no—
56C3×C7×C11C2×C3×D1314yescomplemented
57C2×C32×C11—911no—
58C32×D11—911no—
59C32×D11D9111yescharacteristic, direct product factor
60C2×C7×C13—111no—
61D91—111no—
62D91C32×D1111yescharacteristic, direct product factor
63C2×C3×D13—774no—
64D77—131no—
65C7×D11C32×D1311yescharacteristic, complemented
66C11×D7—131no—
67C11×C13C2×C32×D711yescharacteristic, complemented, Hall
68C2×C3×D11—914no—
69C2×C32×C7—111no—
70C32×D7—131no—
71C32×D7—1431no—
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×D9111yescharacteristic, complemented, Hall
74C7×C13C2×C32×D1111yescharacteristic, complemented, Hall
75C2×C3×D7—1434no—
76C2×C3×C13—114no—
77C3×D13—74no—
78C3×D13—774no—
79C7×C11C2×C32×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—914no—
81C3×D11—914no—
82C3×D11C3×D9114yesdirect product factor
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—771noHall
85C2×D11—911noHall
86C2×C3×C7—114no—
87C3×D7—134no—
88C3×D7—1434no—
89C3×C13C3×D7×D1114yescomplemented
90C22×C32—10011noHall
91C3×C11C2×C3×D9114yescomplemented
92C2×D7—1431noHall
93C2×C13—111no—
94D13—71no—
95D13—771no—
96C2×C11—911no—
97D11—911no—
98D11C32×D9111yescharacteristic, direct product factor
99C3×C7C3×D11×D1314yescomplemented
100C2×C32—111no—
101C2×C32—911no—
102C2×C32—10011no—
103C2×C7—111no—
104D7—131no—
105D7—1431no—
106C13C32×D7×D1111yescharacteristic, complemented, Sylow
107C22×C3—10014no—
108C11C2×C32×D9111yescharacteristic, complemented, Sylow
109C32D11×D9111yescharacteristic, direct product factor, Sylow
110C7C32×D11×D1311yescharacteristic, complemented, Sylow
111C2×C3—114no—
112C2×C3—914no—
113C2×C3—10014no—
114C22—10011noSylow
115C3C3×D11×D9114yesdirect product factor
116C2—111no—
117C2—911no—
118C2—10011no—
subgroupG/H
center, hypercenterC32D11×D91
commutator, cosocle, hypocenterC7×C11×C13C22×C32
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C7×C11×C13
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D11C2semidirect
2. C32×C11×D91C2semidirect
3. C32×D1001C2semidirect
4. C3×D11×D91C3direct (N × H)
5. C32×C7×C11×C13C22semidirect
6. C3×D1001C2×C3semidirect
7. C3×C11×D91C2×C3semidirect
8. C3×C7×C13×D11C2×C3semidirect
10. D11×D91C32direct (N × H)
12. C3×C7×C11×C13C22×C3semidirect
15. C32×C13×D11D7semidirect
17. D1001C2×C32semidirect
18. C11×D91C2×C32semidirect
19. C7×C13×D11C2×C32semidirect
23. C32×D91D11direct (N × H)
26. C32×C7×D11D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C22×C32semidirect
32. C3×C13×D11C3×D7semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×D91C3×D11direct (N × H)
43. C3×C7×D11C3×D13semidirect
44. C3×C11×C13C2×C3×D7semidirect
50. C13×D11C32×D7semidirect
51. C3×C7×C13C2×C3×D11semidirect
56. C3×C7×C11C2×C3×D13semidirect
59. C32×D11D91direct (N × H)
62. D91C32×D11direct (N × H)
65. C7×D11C32×D13semidirect
67. C11×C13C2×C32×D7semidirect
72. C32×C13D7×D11semidirect
73. C32×C11C2×D91semidirect
74. C7×C13C2×C32×D11semidirect
79. C7×C11C2×C32×D13semidirect
82. C3×D11C3×D91direct (N × H)
83. C32×C7D11×D13semidirect
89. C3×C13C3×D7×D11semidirect
91. C3×C11C2×C3×D91semidirect
98. D11C32×D91direct (N × H)
99. C3×C7C3×D11×D13semidirect
106. C13C32×D7×D11semidirect
108. C11C2×C32×D91semidirect
109. C32D11×D91direct (N × H)
110. C7C32×D11×D13semidirect
115. C3C3×D11×D91direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C13×D112
C32×C11×D912
C32×D10012
C3×D11×D913
C32×D11×D137
C2×C32×D9111
C32×D7×D1113