Finite Group Databasebeta

← C24×C33×C4×C13 #72199883

Subgroups — C24×C33×C4×C13 #72199883

Order 22464.

38136 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×C33×C13C211yesmaximal, characteristic
2C23×C33×C4×C13C2130yesmaximal, direct product factor
3C24×C32×C4×C13C3113yesmaximal, direct product factor
4C24×C33×C13C4116yesdirect product factor
5C24×C33×C13C22115yes—
6C22×C33×C4×C13C221140yesdirect product factor
7C25×C32×C13C2×C3113yes—
8C23×C32×C4×C13C2×C31390yesdirect product factor
9C23×C33×C13C2×C41120yesdirect product factor
10C23×C33×C13C23135yes—
11C2×C33×C4×C13C231120yesdirect product factor
12C24×C3×C4×C13C32113yesdirect product factor
13C24×C32×C13C3×C41208yesdirect product factor
14C24×C32×C13C22×C31195yes—
15C22×C32×C4×C13C22×C311820yesdirect product factor
16C24×C33×C4C1311yesmaximal, characteristic, direct product factor, Hall
17C22×C33×C13C22×C41140yesdirect product factor
18C22×C33×C13C24115yes—
19C33×C4×C13C24116yesdirect product factor
20C25×C3×C13C2×C32113yes—
21C23×C3×C4×C13C2×C321390yesdirect product factor
22C23×C32×C13C2×C3×C411560yesdirect product factor
23C23×C32×C13C23×C31455yes—
24C2×C32×C4×C13C23×C311560yesdirect product factor
25C25×C33C2×C1311yescharacteristic
26C23×C33×C4C2×C13130yesdirect product factor
27C24×C4×C13C3311yescharacteristic, direct product factor, Hall
28C2×C33×C13C23×C4130yesdirect product factor
29C2×C33×C13C2511yescharacteristic
30C24×C3×C13C32×C41208yesdirect product factor
31C24×C3×C13C22×C321195yes—
32C22×C3×C4×C13C22×C3211820yesdirect product factor
33C24×C32×C4C3×C13113yesdirect product factor
34C22×C32×C13C22×C3×C411820yesdirect product factor
35C22×C32×C13C24×C31195yes—
36C32×C4×C13C24×C31208yesdirect product factor
37C24×C33C4×C13116yesdirect product factor
38C24×C33C22×C13115yes—
39C22×C33×C4C22×C131140yesdirect product factor
40C25×C13C2×C3311yescharacteristic
41C23×C4×C13C2×C33130yesdirect product factor
42C33×C13C24×C411yescharacteristic, direct product factor, Hall
43C23×C3×C13C2×C32×C411560yesdirect product factor
44C23×C3×C13C23×C321455yes—
45C2×C3×C4×C13C23×C3211560yesdirect product factor
46C25×C32C2×C3×C13113yes—
47C23×C32×C4C2×C3×C131390yesdirect product factor
48C2×C32×C13C23×C3×C41390yesdirect product factor
49C2×C32×C13C25×C3113yes—
50C23×C33C2×C4×C131120yesdirect product factor
51C23×C33C23×C13135yes—
52C2×C33×C4C23×C131120yesdirect product factor
53C24×C13C33×C4116yesdirect product factor
54C24×C13C22×C33115yes—
55C22×C4×C13C22×C331140yesdirect product factor
56C24×C3×C4C32×C13113yesdirect product factor
57C22×C3×C13C22×C32×C411820yesdirect product factor
58C22×C3×C13C24×C321195yes—
59C3×C4×C13C24×C321208yesdirect product factor
60C24×C32C3×C4×C131208yesdirect product factor
61C24×C32C22×C3×C131195yes—
62C22×C32×C4C22×C3×C1311820yesdirect product factor
63C32×C13C24×C3×C4113yesdirect product factor
64C22×C33C22×C4×C131140yesdirect product factor
65C22×C33C24×C13115yes—
66C33×C4C24×C13116yesdirect product factor
67C23×C13C2×C33×C41120yesdirect product factor
68C23×C13C23×C33135yes—
69C2×C4×C13C23×C331120yesdirect product factor
70C25×C3C2×C32×C13113yes—
71C23×C3×C4C2×C32×C131390yesdirect product factor
72C2×C3×C13C23×C32×C41390yesdirect product factor
73C2×C3×C13C25×C32113yes—
74C23×C32C2×C3×C4×C1311560yesdirect product factor
75C23×C32C23×C3×C131455yes—
76C2×C32×C4C23×C3×C1311560yesdirect product factor
77C24×C4C33×C1311yescharacteristic, direct product factor, Sylow
78C2×C33C23×C4×C13130yesdirect product factor
79C2×C33C25×C1311yescharacteristic
80C22×C13C22×C33×C41140yesdirect product factor
81C22×C13C24×C33115yes—
82C4×C13C24×C33116yesdirect product factor
83C24×C3C32×C4×C131208yesdirect product factor
84C24×C3C22×C32×C131195yes—
85C22×C3×C4C22×C32×C1311820yesdirect product factor
86C3×C13C24×C32×C4113yesdirect product factor
87C22×C32C22×C3×C4×C1311820yesdirect product factor
88C22×C32C24×C3×C131195yes—
89C32×C4C24×C3×C131208yesdirect product factor
90C25C2×C33×C1311yescharacteristic
91C23×C4C2×C33×C13130yesdirect product factor
92C33C24×C4×C1311yescharacteristic, direct product factor, Sylow
93C2×C13C23×C33×C4130yesdirect product factor
94C2×C13C25×C3311yescharacteristic
95C23×C3C2×C32×C4×C1311560yesdirect product factor
96C23×C3C23×C32×C131455yes—
97C2×C3×C4C23×C32×C1311560yesdirect product factor
98C2×C32C23×C3×C4×C131390yesdirect product factor
99C2×C32C25×C3×C13113yes—
100C24C33×C4×C13116yesdirect product factor
101C24C22×C33×C13115yes—
102C22×C4C22×C33×C131140yesdirect product factor
103C13C24×C33×C411yescharacteristic, direct product factor, Sylow
104C22×C3C22×C32×C4×C1311820yesdirect product factor
105C22×C3C24×C32×C131195yes—
106C3×C4C24×C32×C131208yesdirect product factor
107C32C24×C3×C4×C13113yesdirect product factor
108C23C2×C33×C4×C131120yesdirect product factor
109C23C23×C33×C13135yes—
110C2×C4C23×C33×C131120yesdirect product factor
111C2×C3C23×C32×C4×C131390yesdirect product factor
112C2×C3C25×C32×C13113yes—
113C22C22×C33×C4×C131140yesdirect product factor
114C22C24×C33×C13115yes—
115C4C24×C33×C13116yesdirect product factor
116C3C24×C32×C4×C13113yesdirect product factor
117C2C23×C33×C4×C13130yesdirect product factor
118C2C25×C33×C1311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C33×C13
socle, prime radicalC25×C33×C13C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C33×C4×C13C2direct (N × H)
3. C24×C32×C4×C13C3direct (N × H)
4. C24×C33×C13C4direct (N × H)
6. C22×C33×C4×C13C22direct (N × H)
8. C23×C32×C4×C13C2×C3direct (N × H)
9. C23×C33×C13C2×C4direct (N × H)
11. C2×C33×C4×C13C23direct (N × H)
12. C24×C3×C4×C13C32direct (N × H)
13. C24×C32×C13C3×C4direct (N × H)
15. C22×C32×C4×C13C22×C3direct (N × H)
16. C24×C33×C4C13direct (N × H)
17. C22×C33×C13C22×C4direct (N × H)
19. C33×C4×C13C24direct (N × H)
21. C23×C3×C4×C13C2×C32direct (N × H)
22. C23×C32×C13C2×C3×C4direct (N × H)
24. C2×C32×C4×C13C23×C3direct (N × H)
26. C23×C33×C4C2×C13direct (N × H)
27. C24×C4×C13C33direct (N × H)
28. C2×C33×C13C23×C4direct (N × H)
30. C24×C3×C13C32×C4direct (N × H)
32. C22×C3×C4×C13C22×C32direct (N × H)
33. C24×C32×C4C3×C13direct (N × H)
34. C22×C32×C13C22×C3×C4direct (N × H)
36. C32×C4×C13C24×C3direct (N × H)
37. C24×C33C4×C13direct (N × H)
39. C22×C33×C4C22×C13direct (N × H)
41. C23×C4×C13C2×C33direct (N × H)
42. C33×C13C24×C4direct (N × H)
43. C23×C3×C13C2×C32×C4direct (N × H)
45. C2×C3×C4×C13C23×C32direct (N × H)
47. C23×C32×C4C2×C3×C13direct (N × H)
48. C2×C32×C13C23×C3×C4direct (N × H)
50. C23×C33C2×C4×C13direct (N × H)
52. C2×C33×C4C23×C13direct (N × H)
53. C24×C13C33×C4direct (N × H)
55. C22×C4×C13C22×C33direct (N × H)
56. C24×C3×C4C32×C13direct (N × H)
57. C22×C3×C13C22×C32×C4direct (N × H)
59. C3×C4×C13C24×C32direct (N × H)
60. C24×C32C3×C4×C13direct (N × H)
62. C22×C32×C4C22×C3×C13direct (N × H)
63. C32×C13C24×C3×C4direct (N × H)
64. C22×C33C22×C4×C13direct (N × H)
66. C33×C4C24×C13direct (N × H)
67. C23×C13C2×C33×C4direct (N × H)
69. C2×C4×C13C23×C33direct (N × H)
71. C23×C3×C4C2×C32×C13direct (N × H)
72. C2×C3×C13C23×C32×C4direct (N × H)
74. C23×C32C2×C3×C4×C13direct (N × H)
76. C2×C32×C4C23×C3×C13direct (N × H)
77. C24×C4C33×C13direct (N × H)
78. C2×C33C23×C4×C13direct (N × H)
80. C22×C13C22×C33×C4direct (N × H)
82. C4×C13C24×C33direct (N × H)
83. C24×C3C32×C4×C13direct (N × H)
85. C22×C3×C4C22×C32×C13direct (N × H)
86. C3×C13C24×C32×C4direct (N × H)
87. C22×C32C22×C3×C4×C13direct (N × H)
89. C32×C4C24×C3×C13direct (N × H)
91. C23×C4C2×C33×C13direct (N × H)
92. C33C24×C4×C13direct (N × H)
93. C2×C13C23×C33×C4direct (N × H)
95. C23×C3C2×C32×C4×C13direct (N × H)
97. C2×C3×C4C23×C32×C13direct (N × H)
98. C2×C32C23×C3×C4×C13direct (N × H)
100. C24C33×C4×C13direct (N × H)
102. C22×C4C22×C33×C13direct (N × H)
103. C13C24×C33×C4direct (N × H)
104. C22×C3C22×C32×C4×C13direct (N × H)
106. C3×C4C24×C32×C13direct (N × H)
107. C32C24×C3×C4×C13direct (N × H)
108. C23C2×C33×C4×C13direct (N × H)
110. C2×C4C23×C33×C13direct (N × H)
111. C2×C3C23×C32×C4×C13direct (N × H)
113. C22C22×C33×C4×C13direct (N × H)
115. C4C24×C33×C13direct (N × H)
116. C3C24×C32×C4×C13direct (N × H)
117. C2C23×C33×C4×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C33×C132
C23×C33×C4×C132
C24×C32×C4×C133
C24×C33×C413