Finite Group Databasebeta

← C32×C11×D7×D11 #44479182

Subgroups — C32×C11×D7×D11 #44479182

Order 30492.

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

normal subgroups only

This group has 360 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×D11C211yesmaximal, characteristic, complemented
2C32×C112×D7C211yesmaximal, characteristic, complemented
3C32×C11×D77C211yesmaximal, characteristic, complemented
4C3×C11×D7×D11C314yesmaximal, direct product factor
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C3×C11×D77C2×C314yescomplemented
7C3×C112×D7C2×C314yescomplemented
8C3×C7×C11×D11C2×C314yescomplemented
9C2×C32×C11×D11—71nomaximal, Hall
10C11×D7×D11C3211yescharacteristic, direct product factor, Hall
11C2×C32×C11×D7—111nomaximal
12C32×D7×D11C1111yesmaximal, characteristic, direct product factor
13C3×C7×C112C22×C314yescomplemented
14C32×C11×D11—71no—
15C32×C11×D11D711yescharacteristic, direct product factor
16C2×C32×C112—71no—
17C11×D77C2×C3211yescharacteristic, complemented
18C112×D7C2×C3211yescharacteristic, complemented
19C7×C11×D11C2×C3211yescharacteristic, complemented
20C2×C3×C11×D11—74no—
21C2×C32×C7×C11—111no—
22C32×D77C2×C1111yescharacteristic, complemented
23C32×C11×D7—25no—
24C32×C11×D7—111no—
25C32×C11×D7D1111yescharacteristic, direct product factor
26C32×C11×D7C2×C1111yescharacteristic, complemented
27C32×C7×D11C2×C1111yescharacteristic, complemented
28C32×C112C2×D711yescharacteristic, complemented, Hall
29C2×C3×C11×D7—114no—
30C3×D7×D11C3×C1114yesdirect product factor
31C7×C112C22×C3211yescharacteristic, complemented, Hall
32C2×C3×C112—74no—
33C3×C11×D11—74no—
34C3×C11×D11C3×D714yesdirect product factor
35C32×C7×C11—25no—
36C32×C7×C11C2×D1111yescharacteristic, complemented
37C32×C7×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—71noHall
39C2×C3×C7×C11—114no—
40C3×D77C2×C3×C1114yescomplemented
41C3×C11×D7—220no—
42C3×C11×D7—114no—
43C3×C11×D7C3×D1114yesdirect product factor
44C3×C11×D7C2×C3×C1114yescomplemented
45C3×C7×D11C2×C3×C1114yescomplemented
46C22×C32×C11—771no—
47C2×C32×D11—71no—
48C3×C112C2×C3×D714yescomplemented
49C2×C11×D7—111no—
50D7×D11C32×C1111yescharacteristic, direct product factor
51C2×C32×D7—111noHall
52C2×C112—71no—
53C11×D11—71no—
54C11×D11C32×D711yescharacteristic, direct product factor
55C3×C7×C11—220no—
56C3×C7×C11C2×C3×D1114yescomplemented
57C3×C7×C11C22×C3×C1114yescomplemented
58C2×C32×C11—71no—
59C2×C32×C11—71no—
60C2×C32×C11—111no—
61C2×C32×C11—145no—
62C2×C32×C11—771no—
63C32×D11—71no—
64C32×D11C11×D711yescharacteristic, direct product factor
65C2×C7×C11—111no—
66D77C2×C32×C1111yescharacteristic, complemented
67C7×D11C2×C32×C1111yescharacteristic, complemented
68C11×D7—25no—
69C11×D7—111no—
70C11×D7C32×D1111yescharacteristic, direct product factor
71C11×D7C2×C32×C1111yescharacteristic, complemented
72C22×C3×C11—774no—
73C2×C3×D11—74no—
74C2×C32×C7—111no—
75C32×D7—111no—
76C32×D7C11×D1111yescharacteristic, direct product factor
77C112C2×C32×D711yescharacteristic, complemented, Sylow
78C32×C11—25no—
79C32×C11D7×D1111yescharacteristic, direct product factor
80C32×C11C2×C11×D711yescharacteristic, complemented
81C2×C3×D7—114no—
82C7×C11—25no—
83C7×C11C2×C32×D1111yescharacteristic, complemented
84C7×C11C22×C32×C1111yescharacteristic, complemented
85C2×C3×C11—74no—
86C2×C3×C11—74no—
87C2×C3×C11—114no—
88C2×C3×C11—1420no—
89C2×C3×C11—774no—
90C3×D11—74no—
91C3×D11C3×C11×D714yesdirect product factor
92C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—771no—
94C2×D11—71no—
95C2×C3×C7—114no—
96C3×D7—114no—
97C3×D7C3×C11×D1114yesdirect product factor
98C22×C32—771noHall
99C3×C11—220no—
100C3×C11C3×D7×D1114yesdirect product factor
101C3×C11C2×C3×C11×D714yescomplemented
102C2×D7—111noHall
103C2×C11—71no—
104C2×C11—71no—
105C2×C11—111no—
106C2×C11—145no—
107C2×C11—771no—
108D11—71no—
109D11C32×C11×D711yescharacteristic, direct product factor
110C3×C7C2×C3×C11×D1114yescomplemented
111C2×C32—71no—
112C2×C32—111no—
113C2×C32—771no—
114C2×C7—111no—
115D7—111no—
116D7C32×C11×D1111yescharacteristic, direct product factor
117C22×C3—774no—
118C11—25no—
119C11C32×D7×D1111yescharacteristic, direct product factor
120C11C2×C32×C11×D711yescharacteristic, complemented
121C32C11×D7×D1111yescharacteristic, direct product factor, Sylow
122C7C2×C32×C11×D1111yescharacteristic, complemented, Sylow
123C2×C3—74no—
124C2×C3—114no—
125C2×C3—774no—
126C22—771noSylow
127C3C3×C11×D7×D1114yesdirect product factor
128C2—71no—
129C2—111no—
130C2—771no—
subgroupG/H
center, hypercenterC32×C11D7×D11
commutator, cosocle, hypocenterC7×C11C22×C32×C11
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C7×C11
UCSC1 ◁ C32×C11

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D11C2semidirect
2. C32×C112×D7C2semidirect
3. C32×C11×D77C2semidirect
4. C3×C11×D7×D11C3direct (N × H)
5. C32×C7×C112C22semidirect
6. C3×C11×D77C2×C3semidirect
7. C3×C112×D7C2×C3semidirect
8. C3×C7×C11×D11C2×C3semidirect
10. C11×D7×D11C32direct (N × H)
12. C32×D7×D11C11direct (N × H)
13. C3×C7×C112C22×C3semidirect
15. C32×C11×D11D7direct (N × H)
17. C11×D77C2×C32semidirect
18. C112×D7C2×C32semidirect
19. C7×C11×D11C2×C32semidirect
22. C32×D77C2×C11semidirect
25. C32×C11×D7D11direct (N × H)
26. C32×C11×D7C2×C11semidirect
27. C32×C7×D11C2×C11semidirect
28. C32×C112C2×D7semidirect
30. C3×D7×D11C3×C11direct (N × H)
31. C7×C112C22×C32semidirect
34. C3×C11×D11C3×D7direct (N × H)
36. C32×C7×C11C2×D11semidirect
37. C32×C7×C11C22×C11semidirect
40. C3×D77C2×C3×C11semidirect
43. C3×C11×D7C3×D11direct (N × H)
44. C3×C11×D7C2×C3×C11semidirect
45. C3×C7×D11C2×C3×C11semidirect
48. C3×C112C2×C3×D7semidirect
50. D7×D11C32×C11direct (N × H)
54. C11×D11C32×D7direct (N × H)
56. C3×C7×C11C2×C3×D11semidirect
57. C3×C7×C11C22×C3×C11semidirect
64. C32×D11C11×D7direct (N × H)
66. D77C2×C32×C11semidirect
67. C7×D11C2×C32×C11semidirect
70. C11×D7C32×D11direct (N × H)
71. C11×D7C2×C32×C11semidirect
76. C32×D7C11×D11direct (N × H)
77. C112C2×C32×D7semidirect
79. C32×C11D7×D11direct (N × H)
80. C32×C11C2×C11×D7semidirect
83. C7×C11C2×C32×D11semidirect
84. C7×C11C22×C32×C11semidirect
91. C3×D11C3×C11×D7direct (N × H)
92. C32×C7C2×C11×D11semidirect
97. C3×D7C3×C11×D11direct (N × H)
100. C3×C11C3×D7×D11direct (N × H)
101. C3×C11C2×C3×C11×D7semidirect
109. D11C32×C11×D7direct (N × H)
110. C3×C7C2×C3×C11×D11semidirect
116. D7C32×C11×D11direct (N × H)
119. C11C32×D7×D11direct (N × H)
120. C11C2×C32×C11×D7semidirect
121. C32C11×D7×D11direct (N × H)
122. C7C2×C32×C11×D11semidirect
127. C3C3×C11×D7×D11direct (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×D112
C32×C112×D72
C32×C11×D772
C3×C11×D7×D113
C2×C32×C11×D117
C2×C32×C11×D711
C32×D7×D1111