Finite Group Databasebeta

← C32×D13×D77 #49114895

Subgroups — C32×D13×D77 #49114895

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×C11×D13C211yesmaximal, characteristic, complemented
2C32×C13×D77C211yesmaximal, characteristic, complemented
3C32×D1001C211yesmaximal, characteristic, complemented
4C3×D13×D77C314yesmaximal, direct product factor
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C3×D1001C2×C314yescomplemented
7C3×C13×D77C2×C314yescomplemented
8C3×C7×C11×D13C2×C314yescomplemented
9C32×D11×D13—71nomaximal, Hall
10D13×D77C3211yescharacteristic, direct product factor, Hall
11C32×D7×D13—111nomaximal, Hall
12C3×C7×C11×C13C22×C314yescomplemented
13C2×C32×D77—131nomaximal, Hall
14C32×D143—71no—
15C32×C13×D11—71no—
16C32×C11×D13D711yescharacteristic, complemented
17D1001C2×C3211yescharacteristic, complemented
18C13×D77C2×C3211yescharacteristic, complemented
19C7×C11×D13C2×C3211yescharacteristic, complemented
20C3×D11×D13—74no—
21C32×D91—111no—
22C32×C13×D7—111no—
23C32×C7×D13D1111yescharacteristic, complemented
24C2×C32×C7×C11—131no—
25C32×D77—131no—
26C32×D77D1311yescharacteristic, direct product factor
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28C3×D7×D13—114no—
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C2×C3×D77—134no—
31C3×D143—74no—
32C3×C13×D11—74no—
33C3×C11×D13C3×D714yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—71noHall
37C3×D91—114no—
38C3×C13×D7—114no—
39C3×C7×D13C3×D1114yescomplemented
40C2×C32×D13—771noHall
41C2×C3×C7×C11—134no—
42C3×D77—134no—
43C3×D77C3×D1314yesdirect product factor
44C3×C11×C13C2×C3×D714yescomplemented
45C2×C32×D11—911noHall
46D7×D13—111noHall
47C2×D77—131noHall
48D143—71no—
49C11×D13C32×D711yescharacteristic, complemented
50C13×D11—71no—
51C3×C7×C13C2×C3×D1114yescomplemented
52C2×C32×D7—1431noHall
53C2×C32×C13—771no—
54C32×D13—771no—
55C32×D13D7711yescharacteristic, direct product factor
56C3×C7×C11C2×C3×D1314yescomplemented
57C2×C32×C11—131no—
58C32×D11—71no—
59C32×D11—911no—
60D91—111no—
61C7×D13C32×D1111yescharacteristic, complemented
62C13×D7—111no—
63C2×C3×D13—774no—
64C2×C7×C11—131no—
65D77—131no—
66D77C32×D1311yescharacteristic, direct product factor
67C11×C13C2×C32×D711yescharacteristic, complemented, Hall
68C2×C3×D11—914no—
69C2×C32×C7—131no—
70C32×D7—111no—
71C32×D7—1431no—
72C32×C13C2×D7711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C32×D1111yescharacteristic, complemented, Hall
75C2×C3×D7—1434no—
76C2×C3×C13—774no—
77C3×D13—774no—
78C3×D13C3×D7714yesdirect product factor
79C7×C11C2×C32×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—134no—
81C3×D11—74no—
82C3×D11—914no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—771noHall
85C2×D11—911noHall
86C2×C3×C7—134no—
87C3×D7—114no—
88C3×D7—1434no—
89C3×C13C2×C3×D7714yescomplemented
90C22×C32—10011noHall
91C3×C11C3×D7×D1314yescomplemented
92C2×D7—1431noHall
93C2×C13—771no—
94D13—771no—
95D13C32×D7711yescharacteristic, direct product factor
96C2×C11—131no—
97D11—71no—
98D11—911no—
99C3×C7C3×D11×D1314yescomplemented
100C2×C32—131no—
101C2×C32—771no—
102C2×C32—10011no—
103C2×C7—131no—
104D7—111no—
105D7—1431no—
106C13C2×C32×D7711yescharacteristic, complemented, Sylow
107C22×C3—10014no—
108C11C32×D7×D1311yescharacteristic, complemented, Sylow
109C32D13×D7711yescharacteristic, direct product factor, Sylow
110C7C32×D11×D1311yescharacteristic, complemented, Sylow
111C2×C3—134no—
112C2×C3—774no—
113C2×C3—10014no—
114C22—10011noSylow
115C3C3×D13×D7714yesdirect product factor
116C2—131no—
117C2—771no—
118C2—10011no—
subgroupG/H
center, hypercenterC32D13×D77
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×C11×D13C2semidirect
2. C32×C13×D77C2semidirect
3. C32×D1001C2semidirect
4. C3×D13×D77C3direct (N × H)
5. C32×C7×C11×C13C22semidirect
6. C3×D1001C2×C3semidirect
7. C3×C13×D77C2×C3semidirect
8. C3×C7×C11×D13C2×C3semidirect
10. D13×D77C32direct (N × H)
12. C3×C7×C11×C13C22×C3semidirect
16. C32×C11×D13D7semidirect
17. D1001C2×C32semidirect
18. C13×D77C2×C32semidirect
19. C7×C11×D13C2×C32semidirect
23. C32×C7×D13D11semidirect
26. C32×D77D13direct (N × H)
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C22×C32semidirect
33. C3×C11×D13C3×D7semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C7×D13C3×D11semidirect
43. C3×D77C3×D13direct (N × H)
44. C3×C11×C13C2×C3×D7semidirect
49. C11×D13C32×D7semidirect
51. C3×C7×C13C2×C3×D11semidirect
55. C32×D13D77direct (N × H)
56. C3×C7×C11C2×C3×D13semidirect
61. C7×D13C32×D11semidirect
66. D77C32×D13direct (N × H)
67. C11×C13C2×C32×D7semidirect
72. C32×C13C2×D77semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C32×D11semidirect
78. C3×D13C3×D77direct (N × H)
79. C7×C11C2×C32×D13semidirect
83. C32×C7D11×D13semidirect
89. C3×C13C2×C3×D77semidirect
91. C3×C11C3×D7×D13semidirect
95. D13C32×D77direct (N × H)
99. C3×C7C3×D11×D13semidirect
106. C13C2×C32×D77semidirect
108. C11C32×D7×D13semidirect
109. C32D13×D77direct (N × H)
110. C7C32×D11×D13semidirect
115. C3C3×D13×D77direct (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×C13×D772
C32×D10012
C3×D13×D773
C32×D11×D137
C32×D7×D1311
C2×C32×D7713