Finite Group Databasebeta

← C2×C32×C11×D77 #44479260

Subgroups — C2×C32×C11×D77 #44479260

Order 30492.

360 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 132 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×C11×D77C212yesmaximal, direct product factor
2C2×C32×C7×C112C211yesmaximal, characteristic, complemented
3C2×C3×C11×D77C314yesmaximal, direct product factor
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C3×C11×D77C2×C318yesdirect product factor
6C2×C3×C7×C112C2×C314yescomplemented
7C2×C32×C11×D11—71nomaximal, Hall
8C2×C11×D77C3211yescharacteristic, direct product factor, Hall
9C2×C32×C11×D7—111nomaximal
10C2×C32×D77C1111yesmaximal, characteristic, direct product factor
11C3×C7×C112C22×C314yescomplemented
12C32×C11×D11—72no—
13C2×C32×C112D711yescharacteristic, complemented
14C2×C7×C112C2×C3211yescharacteristic, complemented
15C11×D77C2×C3212yesdirect product factor
16C2×C3×C11×D11—74no—
17C2×C32×C7×C11—25no—
18C2×C32×C7×C11D1111yescharacteristic, complemented
19C2×C32×C7×C11C2×C1111yescharacteristic, complemented
20C32×D77C2×C1112yesdirect product factor
21C32×C11×D7—112no—
22C32×C112C2×D711yescharacteristic, complemented, Hall
23C2×C3×D77C3×C1114yesdirect product factor
24C2×C3×C11×D7—114no—
25C7×C112C22×C3211yescharacteristic, complemented, Hall
26C2×C3×C112C3×D714yescomplemented
27C3×C11×D11—78no—
28C32×C7×C11—25no—
29C32×C7×C11C2×D1111yescharacteristic, complemented
30C32×C7×C11C22×C1111yescharacteristic, complemented
31C2×C11×D11—71noHall
32C2×C3×C7×C11—220no—
33C2×C3×C7×C11C3×D1114yescomplemented
34C2×C3×C7×C11C2×C3×C1114yescomplemented
35C3×D77C2×C3×C1118yesdirect product factor
36C3×C11×D7—118no—
37C22×C32×C11—771no—
38C2×C32×D11—71no—
39C3×C112C2×C3×D714yescomplemented
40C2×D77C32×C1111yescharacteristic, direct product factor
41C2×C11×D7—111no—
42C2×C32×D7—111noHall
43C2×C112C32×D711yescharacteristic, complemented
44C11×D11—72no—
45C3×C7×C11—220no—
46C3×C7×C11C2×C3×D1114yescomplemented
47C3×C7×C11C22×C3×C1114yescomplemented
48C2×C32×C11—25no—
49C2×C32×C11—772no—
50C2×C32×C11C11×D711yescharacteristic, complemented
51C2×C32×C11D7711yescharacteristic, direct product factor
52C32×D11—72no—
53C2×C7×C11—25no—
54C2×C7×C11C32×D1111yescharacteristic, complemented
55C2×C7×C11C2×C32×C1111yescharacteristic, complemented
56D77C2×C32×C1112yesdirect product factor
57C11×D7—112no—
58C22×C3×C11—774no—
59C2×C3×D11—74no—
60C2×C32×C7C11×D1111yescharacteristic, complemented
61C32×D7—112no—
62C112C2×C32×D711yescharacteristic, complemented, Sylow
63C32×C11—25no—
64C32×C11C2×C11×D711yescharacteristic, complemented
65C32×C11C2×D7711yescharacteristic, direct product factor
66C2×C3×D7—114no—
67C7×C11—25no—
68C7×C11C2×C32×D1111yescharacteristic, complemented
69C7×C11C22×C32×C1111yescharacteristic, complemented
70C2×C3×C11—220no—
71C2×C3×C11—778no—
72C2×C3×C11C3×C11×D714yescomplemented
73C2×C3×C11C3×D7714yesdirect product factor
74C3×D11—78no—
75C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
76C22×C11—771no—
77C2×D11—71no—
78C2×C3×C7C3×C11×D1114yescomplemented
79C3×D7—118no—
80C22×C32—771noHall
81C3×C11—220no—
82C3×C11C2×C3×C11×D714yescomplemented
83C3×C11C2×C3×D7714yesdirect product factor
84C2×D7—111noHall
85C2×C11—25no—
86C2×C11—772no—
87C2×C11C32×C11×D711yescharacteristic, complemented
88C2×C11C32×D7711yescharacteristic, direct product factor
89D11—72no—
90C3×C7C2×C3×C11×D1114yescomplemented
91C2×C32—772no—
92C2×C32C11×D7711yescharacteristic, direct product factor
93C2×C7C32×C11×D1111yescharacteristic, complemented
94D7—112no—
95C22×C3—774no—
96C11—25no—
97C11C2×C32×D7711yescharacteristic, direct product factor
98C11C2×C32×C11×D711yescharacteristic, complemented
99C32C2×C11×D7711yescharacteristic, direct product factor, Sylow
100C7C2×C32×C11×D1111yescharacteristic, complemented, Sylow
101C2×C3—778no—
102C2×C3C3×C11×D7714yesdirect product factor
103C22—771noSylow
104C3C2×C3×C11×D7714yesdirect product factor
105C2—772no—
106C2C32×C11×D7711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C11D77
commutator, cosocle, hypocenterC7×C11C22×C32×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C32×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×D77C2direct (N × H)
2. C2×C32×C7×C112C2semidirect
3. C2×C3×C11×D77C3direct (N × H)
4. C32×C7×C112C22semidirect
5. C3×C11×D77C2×C3direct (N × H)
6. C2×C3×C7×C112C2×C3semidirect
8. C2×C11×D77C32direct (N × H)
10. C2×C32×D77C11direct (N × H)
11. C3×C7×C112C22×C3semidirect
13. C2×C32×C112D7semidirect
14. C2×C7×C112C2×C32semidirect
15. C11×D77C2×C32direct (N × H)
18. C2×C32×C7×C11D11semidirect
19. C2×C32×C7×C11C2×C11semidirect
20. C32×D77C2×C11direct (N × H)
22. C32×C112C2×D7semidirect
23. C2×C3×D77C3×C11direct (N × H)
25. C7×C112C22×C32semidirect
26. C2×C3×C112C3×D7semidirect
29. C32×C7×C11C2×D11semidirect
30. C32×C7×C11C22×C11semidirect
33. C2×C3×C7×C11C3×D11semidirect
34. C2×C3×C7×C11C2×C3×C11semidirect
35. C3×D77C2×C3×C11direct (N × H)
39. C3×C112C2×C3×D7semidirect
40. C2×D77C32×C11direct (N × H)
43. C2×C112C32×D7semidirect
46. C3×C7×C11C2×C3×D11semidirect
47. C3×C7×C11C22×C3×C11semidirect
50. C2×C32×C11C11×D7semidirect
51. C2×C32×C11D77direct (N × H)
54. C2×C7×C11C32×D11semidirect
55. C2×C7×C11C2×C32×C11semidirect
56. D77C2×C32×C11direct (N × H)
60. C2×C32×C7C11×D11semidirect
62. C112C2×C32×D7semidirect
64. C32×C11C2×C11×D7semidirect
65. C32×C11C2×D77direct (N × H)
68. C7×C11C2×C32×D11semidirect
69. C7×C11C22×C32×C11semidirect
72. C2×C3×C11C3×C11×D7semidirect
73. C2×C3×C11C3×D77direct (N × H)
75. C32×C7C2×C11×D11semidirect
78. C2×C3×C7C3×C11×D11semidirect
82. C3×C11C2×C3×C11×D7semidirect
83. C3×C11C2×C3×D77direct (N × H)
87. C2×C11C32×C11×D7semidirect
88. C2×C11C32×D77direct (N × H)
90. C3×C7C2×C3×C11×D11semidirect
92. C2×C32C11×D77direct (N × H)
93. C2×C7C32×C11×D11semidirect
97. C11C2×C32×D77direct (N × H)
98. C11C2×C32×C11×D7semidirect
99. C32C2×C11×D77direct (N × H)
100. C7C2×C32×C11×D11semidirect
102. C2×C3C3×C11×D77direct (N × H)
104. C3C2×C3×C11×D77direct (N × H)
106. C2C32×C11×D77direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D772
C2×C32×C7×C1122
C2×C3×C11×D773
C2×C32×C11×D117
C2×C32×C11×D711
C2×C32×D7711