Finite Group Databasebeta

← C24×C4×C5×C7×C11 #72201964

Subgroups — C24×C4×C5×C7×C11 #72201964

Order 24640.

5448 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C5×C7×C11C211yesmaximal, characteristic
2C23×C4×C5×C7×C11C2130yesmaximal, direct product factor
3C24×C5×C7×C11C4116yesdirect product factor
4C24×C5×C7×C11C22115yes—
5C22×C4×C5×C7×C11C221140yesdirect product factor
6C24×C4×C7×C11C511yesmaximal, characteristic, direct product factor, Hall
7C24×C4×C5×C11C711yesmaximal, characteristic, direct product factor, Hall
8C23×C5×C7×C11C2×C41120yesdirect product factor
9C23×C5×C7×C11C23135yes—
10C2×C4×C5×C7×C11C231120yesdirect product factor
11C25×C7×C11C2×C511yescharacteristic
12C23×C4×C7×C11C2×C5130yesdirect product factor
13C24×C4×C5×C7C1111yesmaximal, characteristic, direct product factor, Hall
14C25×C5×C11C2×C711yescharacteristic
15C23×C4×C5×C11C2×C7130yesdirect product factor
16C22×C5×C7×C11C22×C41140yesdirect product factor
17C22×C5×C7×C11C24115yes—
18C4×C5×C7×C11C24116yesdirect product factor
19C24×C7×C11C4×C5116yesdirect product factor
20C24×C7×C11C22×C5115yes—
21C22×C4×C7×C11C22×C51140yesdirect product factor
22C25×C5×C7C2×C1111yescharacteristic
23C23×C4×C5×C7C2×C11130yesdirect product factor
24C24×C5×C11C4×C7116yesdirect product factor
25C24×C5×C11C22×C7115yes—
26C22×C4×C5×C11C22×C71140yesdirect product factor
27C2×C5×C7×C11C23×C4130yesdirect product factor
28C2×C5×C7×C11C2511yescharacteristic
29C24×C4×C11C5×C711yescharacteristic, direct product factor, Hall
30C23×C7×C11C2×C4×C51120yesdirect product factor
31C23×C7×C11C23×C5135yes—
32C2×C4×C7×C11C23×C51120yesdirect product factor
33C24×C5×C7C4×C11116yesdirect product factor
34C24×C5×C7C22×C11115yes—
35C22×C4×C5×C7C22×C111140yesdirect product factor
36C24×C4×C7C5×C1111yescharacteristic, direct product factor, Hall
37C23×C5×C11C2×C4×C71120yesdirect product factor
38C23×C5×C11C23×C7135yes—
39C2×C4×C5×C11C23×C71120yesdirect product factor
40C5×C7×C11C24×C411yescharacteristic, direct product factor, Hall
41C25×C11C2×C5×C711yescharacteristic
42C23×C4×C11C2×C5×C7130yesdirect product factor
43C24×C4×C5C7×C1111yescharacteristic, direct product factor, Hall
44C22×C7×C11C22×C4×C51140yesdirect product factor
45C22×C7×C11C24×C5115yes—
46C4×C7×C11C24×C5116yesdirect product factor
47C23×C5×C7C2×C4×C111120yesdirect product factor
48C23×C5×C7C23×C11135yes—
49C2×C4×C5×C7C23×C111120yesdirect product factor
50C25×C7C2×C5×C1111yescharacteristic
51C23×C4×C7C2×C5×C11130yesdirect product factor
52C22×C5×C11C22×C4×C71140yesdirect product factor
53C22×C5×C11C24×C7115yes—
54C4×C5×C11C24×C7116yesdirect product factor
55C24×C11C4×C5×C7116yesdirect product factor
56C24×C11C22×C5×C7115yes—
57C22×C4×C11C22×C5×C71140yesdirect product factor
58C25×C5C2×C7×C1111yescharacteristic
59C23×C4×C5C2×C7×C11130yesdirect product factor
60C2×C7×C11C23×C4×C5130yesdirect product factor
61C2×C7×C11C25×C511yescharacteristic
62C22×C5×C7C22×C4×C111140yesdirect product factor
63C22×C5×C7C24×C11115yes—
64C4×C5×C7C24×C11116yesdirect product factor
65C24×C7C4×C5×C11116yesdirect product factor
66C24×C7C22×C5×C11115yes—
67C22×C4×C7C22×C5×C111140yesdirect product factor
68C2×C5×C11C23×C4×C7130yesdirect product factor
69C2×C5×C11C25×C711yescharacteristic
70C23×C11C2×C4×C5×C71120yesdirect product factor
71C23×C11C23×C5×C7135yes—
72C2×C4×C11C23×C5×C71120yesdirect product factor
73C24×C5C4×C7×C11116yesdirect product factor
74C24×C5C22×C7×C11115yes—
75C22×C4×C5C22×C7×C111140yesdirect product factor
76C7×C11C24×C4×C511yescharacteristic, direct product factor, Hall
77C2×C5×C7C23×C4×C11130yesdirect product factor
78C2×C5×C7C25×C1111yescharacteristic
79C24×C4C5×C7×C1111yescharacteristic, direct product factor, Sylow
80C23×C7C2×C4×C5×C111120yesdirect product factor
81C23×C7C23×C5×C11135yes—
82C2×C4×C7C23×C5×C111120yesdirect product factor
83C5×C11C24×C4×C711yescharacteristic, direct product factor, Hall
84C22×C11C22×C4×C5×C71140yesdirect product factor
85C22×C11C24×C5×C7115yes—
86C4×C11C24×C5×C7116yesdirect product factor
87C23×C5C2×C4×C7×C111120yesdirect product factor
88C23×C5C23×C7×C11135yes—
89C2×C4×C5C23×C7×C111120yesdirect product factor
90C5×C7C24×C4×C1111yescharacteristic, direct product factor, Hall
91C25C2×C5×C7×C1111yescharacteristic
92C23×C4C2×C5×C7×C11130yesdirect product factor
93C22×C7C22×C4×C5×C111140yesdirect product factor
94C22×C7C24×C5×C11115yes—
95C4×C7C24×C5×C11116yesdirect product factor
96C2×C11C23×C4×C5×C7130yesdirect product factor
97C2×C11C25×C5×C711yescharacteristic
98C22×C5C22×C4×C7×C111140yesdirect product factor
99C22×C5C24×C7×C11115yes—
100C4×C5C24×C7×C11116yesdirect product factor
101C24C4×C5×C7×C11116yesdirect product factor
102C24C22×C5×C7×C11115yes—
103C22×C4C22×C5×C7×C111140yesdirect product factor
104C2×C7C23×C4×C5×C11130yesdirect product factor
105C2×C7C25×C5×C1111yescharacteristic
106C11C24×C4×C5×C711yescharacteristic, direct product factor, Sylow
107C2×C5C23×C4×C7×C11130yesdirect product factor
108C2×C5C25×C7×C1111yescharacteristic
109C23C2×C4×C5×C7×C111120yesdirect product factor
110C23C23×C5×C7×C11135yes—
111C2×C4C23×C5×C7×C111120yesdirect product factor
112C7C24×C4×C5×C1111yescharacteristic, direct product factor, Sylow
113C5C24×C4×C7×C1111yescharacteristic, direct product factor, Sylow
114C22C22×C4×C5×C7×C111140yesdirect product factor
115C22C24×C5×C7×C11115yes—
116C4C24×C5×C7×C11116yesdirect product factor
117C2C23×C4×C5×C7×C11130yesdirect product factor
118C2C25×C5×C7×C1111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C5×C7×C11
socle, prime radicalC25×C5×C7×C11C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4×C5×C7×C11C2direct (N × H)
3. C24×C5×C7×C11C4direct (N × H)
5. C22×C4×C5×C7×C11C22direct (N × H)
6. C24×C4×C7×C11C5direct (N × H)
7. C24×C4×C5×C11C7direct (N × H)
8. C23×C5×C7×C11C2×C4direct (N × H)
10. C2×C4×C5×C7×C11C23direct (N × H)
12. C23×C4×C7×C11C2×C5direct (N × H)
13. C24×C4×C5×C7C11direct (N × H)
15. C23×C4×C5×C11C2×C7direct (N × H)
16. C22×C5×C7×C11C22×C4direct (N × H)
18. C4×C5×C7×C11C24direct (N × H)
19. C24×C7×C11C4×C5direct (N × H)
21. C22×C4×C7×C11C22×C5direct (N × H)
23. C23×C4×C5×C7C2×C11direct (N × H)
24. C24×C5×C11C4×C7direct (N × H)
26. C22×C4×C5×C11C22×C7direct (N × H)
27. C2×C5×C7×C11C23×C4direct (N × H)
29. C24×C4×C11C5×C7direct (N × H)
30. C23×C7×C11C2×C4×C5direct (N × H)
32. C2×C4×C7×C11C23×C5direct (N × H)
33. C24×C5×C7C4×C11direct (N × H)
35. C22×C4×C5×C7C22×C11direct (N × H)
36. C24×C4×C7C5×C11direct (N × H)
37. C23×C5×C11C2×C4×C7direct (N × H)
39. C2×C4×C5×C11C23×C7direct (N × H)
40. C5×C7×C11C24×C4direct (N × H)
42. C23×C4×C11C2×C5×C7direct (N × H)
43. C24×C4×C5C7×C11direct (N × H)
44. C22×C7×C11C22×C4×C5direct (N × H)
46. C4×C7×C11C24×C5direct (N × H)
47. C23×C5×C7C2×C4×C11direct (N × H)
49. C2×C4×C5×C7C23×C11direct (N × H)
51. C23×C4×C7C2×C5×C11direct (N × H)
52. C22×C5×C11C22×C4×C7direct (N × H)
54. C4×C5×C11C24×C7direct (N × H)
55. C24×C11C4×C5×C7direct (N × H)
57. C22×C4×C11C22×C5×C7direct (N × H)
59. C23×C4×C5C2×C7×C11direct (N × H)
60. C2×C7×C11C23×C4×C5direct (N × H)
62. C22×C5×C7C22×C4×C11direct (N × H)
64. C4×C5×C7C24×C11direct (N × H)
65. C24×C7C4×C5×C11direct (N × H)
67. C22×C4×C7C22×C5×C11direct (N × H)
68. C2×C5×C11C23×C4×C7direct (N × H)
70. C23×C11C2×C4×C5×C7direct (N × H)
72. C2×C4×C11C23×C5×C7direct (N × H)
73. C24×C5C4×C7×C11direct (N × H)
75. C22×C4×C5C22×C7×C11direct (N × H)
76. C7×C11C24×C4×C5direct (N × H)
77. C2×C5×C7C23×C4×C11direct (N × H)
79. C24×C4C5×C7×C11direct (N × H)
80. C23×C7C2×C4×C5×C11direct (N × H)
82. C2×C4×C7C23×C5×C11direct (N × H)
83. C5×C11C24×C4×C7direct (N × H)
84. C22×C11C22×C4×C5×C7direct (N × H)
86. C4×C11C24×C5×C7direct (N × H)
87. C23×C5C2×C4×C7×C11direct (N × H)
89. C2×C4×C5C23×C7×C11direct (N × H)
90. C5×C7C24×C4×C11direct (N × H)
92. C23×C4C2×C5×C7×C11direct (N × H)
93. C22×C7C22×C4×C5×C11direct (N × H)
95. C4×C7C24×C5×C11direct (N × H)
96. C2×C11C23×C4×C5×C7direct (N × H)
98. C22×C5C22×C4×C7×C11direct (N × H)
100. C4×C5C24×C7×C11direct (N × H)
101. C24C4×C5×C7×C11direct (N × H)
103. C22×C4C22×C5×C7×C11direct (N × H)
104. C2×C7C23×C4×C5×C11direct (N × H)
106. C11C24×C4×C5×C7direct (N × H)
107. C2×C5C23×C4×C7×C11direct (N × H)
109. C23C2×C4×C5×C7×C11direct (N × H)
111. C2×C4C23×C5×C7×C11direct (N × H)
112. C7C24×C4×C5×C11direct (N × H)
113. C5C24×C4×C7×C11direct (N × H)
114. C22C22×C4×C5×C7×C11direct (N × H)
116. C4C24×C5×C7×C11direct (N × H)
117. C2C23×C4×C5×C7×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C5×C7×C112
C23×C4×C5×C7×C112
C24×C4×C7×C115
C24×C4×C5×C117
C24×C4×C5×C711