Finite Group Databasebeta

← C25×C33×C4×C7 #72201493

Subgroups — C25×C33×C4×C7 #72201493

Order 24192.

295456 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C33×C7C211yesmaximal, characteristic
2C24×C33×C4×C7C2162yesmaximal, direct product factor
3C25×C32×C4×C7C3113yesmaximal, direct product factor
4C25×C33×C7C4132yesdirect product factor
5C25×C33×C7C22131yes—
6C23×C33×C4×C7C221620yesdirect product factor
7C26×C32×C7C2×C3113yes—
8C24×C32×C4×C7C2×C31806yesdirect product factor
9C25×C33×C4C711yesmaximal, characteristic, direct product factor, Hall
10C24×C33×C7C2×C41496yesdirect product factor
11C24×C33×C7C231155yes—
12C22×C33×C4×C7C2311240yesdirect product factor
13C25×C3×C4×C7C32113yesdirect product factor
14C25×C32×C7C3×C41416yesdirect product factor
15C25×C32×C7C22×C31403yes—
16C23×C32×C4×C7C22×C318060yesdirect product factor
17C26×C33C2×C711yescharacteristic
18C24×C33×C4C2×C7162yesdirect product factor
19C23×C33×C7C22×C411240yesdirect product factor
20C23×C33×C7C241155yes—
21C2×C33×C4×C7C241496yesdirect product factor
22C26×C3×C7C2×C32113yes—
23C24×C3×C4×C7C2×C321806yesdirect product factor
24C25×C32×C4C3×C7113yesdirect product factor
25C24×C32×C7C2×C3×C416448yesdirect product factor
26C24×C32×C7C23×C312015yes—
27C22×C32×C4×C7C23×C3116120yesdirect product factor
28C25×C4×C7C3311yescharacteristic, direct product factor, Hall
29C25×C33C4×C7132yesdirect product factor
30C25×C33C22×C7131yes—
31C23×C33×C4C22×C71620yesdirect product factor
32C22×C33×C7C23×C41620yesdirect product factor
33C22×C33×C7C25131yes—
34C33×C4×C7C25132yesdirect product factor
35C25×C3×C7C32×C41416yesdirect product factor
36C25×C3×C7C22×C321403yes—
37C23×C3×C4×C7C22×C3218060yesdirect product factor
38C26×C32C2×C3×C7113yes—
39C24×C32×C4C2×C3×C71806yesdirect product factor
40C23×C32×C7C22×C3×C4116120yesdirect product factor
41C23×C32×C7C24×C312015yes—
42C2×C32×C4×C7C24×C316448yesdirect product factor
43C26×C7C2×C3311yescharacteristic
44C24×C4×C7C2×C33162yesdirect product factor
45C24×C33C2×C4×C71496yesdirect product factor
46C24×C33C23×C71155yes—
47C22×C33×C4C23×C711240yesdirect product factor
48C25×C3×C4C32×C7113yesdirect product factor
49C2×C33×C7C24×C4162yesdirect product factor
50C2×C33×C7C2611yescharacteristic
51C24×C3×C7C2×C32×C416448yesdirect product factor
52C24×C3×C7C23×C3212015yes—
53C22×C3×C4×C7C23×C32116120yesdirect product factor
54C25×C32C3×C4×C71416yesdirect product factor
55C25×C32C22×C3×C71403yes—
56C23×C32×C4C22×C3×C718060yesdirect product factor
57C22×C32×C7C23×C3×C418060yesdirect product factor
58C22×C32×C7C25×C31403yes—
59C32×C4×C7C25×C31416yesdirect product factor
60C25×C7C33×C4132yesdirect product factor
61C25×C7C22×C33131yes—
62C23×C4×C7C22×C331620yesdirect product factor
63C23×C33C22×C4×C711240yesdirect product factor
64C23×C33C24×C71155yes—
65C2×C33×C4C24×C71496yesdirect product factor
66C26×C3C2×C32×C7113yes—
67C24×C3×C4C2×C32×C71806yesdirect product factor
68C33×C7C25×C411yescharacteristic, direct product factor, Hall
69C23×C3×C7C22×C32×C4116120yesdirect product factor
70C23×C3×C7C24×C3212015yes—
71C2×C3×C4×C7C24×C3216448yesdirect product factor
72C24×C32C2×C3×C4×C716448yesdirect product factor
73C24×C32C23×C3×C712015yes—
74C22×C32×C4C23×C3×C7116120yesdirect product factor
75C25×C4C33×C711yescharacteristic, direct product factor, Sylow
76C2×C32×C7C24×C3×C41806yesdirect product factor
77C2×C32×C7C26×C3113yes—
78C24×C7C2×C33×C41496yesdirect product factor
79C24×C7C23×C331155yes—
80C22×C4×C7C23×C3311240yesdirect product factor
81C22×C33C23×C4×C71620yesdirect product factor
82C22×C33C25×C7131yes—
83C33×C4C25×C7132yesdirect product factor
84C25×C3C32×C4×C71416yesdirect product factor
85C25×C3C22×C32×C71403yes—
86C23×C3×C4C22×C32×C718060yesdirect product factor
87C22×C3×C7C23×C32×C418060yesdirect product factor
88C22×C3×C7C25×C321403yes—
89C3×C4×C7C25×C321416yesdirect product factor
90C23×C32C22×C3×C4×C7116120yesdirect product factor
91C23×C32C24×C3×C712015yes—
92C2×C32×C4C24×C3×C716448yesdirect product factor
93C26C2×C33×C711yescharacteristic
94C24×C4C2×C33×C7162yesdirect product factor
95C32×C7C25×C3×C4113yesdirect product factor
96C23×C7C22×C33×C411240yesdirect product factor
97C23×C7C24×C331155yes—
98C2×C4×C7C24×C331496yesdirect product factor
99C2×C33C24×C4×C7162yesdirect product factor
100C2×C33C26×C711yescharacteristic
101C24×C3C2×C32×C4×C716448yesdirect product factor
102C24×C3C23×C32×C712015yes—
103C22×C3×C4C23×C32×C7116120yesdirect product factor
104C2×C3×C7C24×C32×C41806yesdirect product factor
105C2×C3×C7C26×C32113yes—
106C22×C32C23×C3×C4×C718060yesdirect product factor
107C22×C32C25×C3×C71403yes—
108C32×C4C25×C3×C71416yesdirect product factor
109C25C33×C4×C7132yesdirect product factor
110C25C22×C33×C7131yes—
111C23×C4C22×C33×C71620yesdirect product factor
112C22×C7C23×C33×C41620yesdirect product factor
113C22×C7C25×C33131yes—
114C4×C7C25×C33132yesdirect product factor
115C33C25×C4×C711yescharacteristic, direct product factor, Sylow
116C23×C3C22×C32×C4×C7116120yesdirect product factor
117C23×C3C24×C32×C712015yes—
118C2×C3×C4C24×C32×C716448yesdirect product factor
119C3×C7C25×C32×C4113yesdirect product factor
120C2×C32C24×C3×C4×C71806yesdirect product factor
121C2×C32C26×C3×C7113yes—
122C24C2×C33×C4×C71496yesdirect product factor
123C24C23×C33×C71155yes—
124C22×C4C23×C33×C711240yesdirect product factor
125C2×C7C24×C33×C4162yesdirect product factor
126C2×C7C26×C3311yescharacteristic
127C22×C3C23×C32×C4×C718060yesdirect product factor
128C22×C3C25×C32×C71403yes—
129C3×C4C25×C32×C71416yesdirect product factor
130C32C25×C3×C4×C7113yesdirect product factor
131C23C22×C33×C4×C711240yesdirect product factor
132C23C24×C33×C71155yes—
133C2×C4C24×C33×C71496yesdirect product factor
134C7C25×C33×C411yescharacteristic, direct product factor, Sylow
135C2×C3C24×C32×C4×C71806yesdirect product factor
136C2×C3C26×C32×C7113yes—
137C22C23×C33×C4×C71620yesdirect product factor
138C22C25×C33×C7131yes—
139C4C25×C33×C7132yesdirect product factor
140C3C25×C32×C4×C7113yesdirect product factor
141C2C24×C33×C4×C7162yesdirect product factor
142C2C26×C33×C711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C26×C33×C7
socle, prime radicalC26×C33×C7C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C24×C33×C4×C7C2direct (N × H)
3. C25×C32×C4×C7C3direct (N × H)
4. C25×C33×C7C4direct (N × H)
6. C23×C33×C4×C7C22direct (N × H)
8. C24×C32×C4×C7C2×C3direct (N × H)
9. C25×C33×C4C7direct (N × H)
10. C24×C33×C7C2×C4direct (N × H)
12. C22×C33×C4×C7C23direct (N × H)
13. C25×C3×C4×C7C32direct (N × H)
14. C25×C32×C7C3×C4direct (N × H)
16. C23×C32×C4×C7C22×C3direct (N × H)
18. C24×C33×C4C2×C7direct (N × H)
19. C23×C33×C7C22×C4direct (N × H)
21. C2×C33×C4×C7C24direct (N × H)
23. C24×C3×C4×C7C2×C32direct (N × H)
24. C25×C32×C4C3×C7direct (N × H)
25. C24×C32×C7C2×C3×C4direct (N × H)
27. C22×C32×C4×C7C23×C3direct (N × H)
28. C25×C4×C7C33direct (N × H)
29. C25×C33C4×C7direct (N × H)
31. C23×C33×C4C22×C7direct (N × H)
32. C22×C33×C7C23×C4direct (N × H)
34. C33×C4×C7C25direct (N × H)
35. C25×C3×C7C32×C4direct (N × H)
37. C23×C3×C4×C7C22×C32direct (N × H)
39. C24×C32×C4C2×C3×C7direct (N × H)
40. C23×C32×C7C22×C3×C4direct (N × H)
42. C2×C32×C4×C7C24×C3direct (N × H)
44. C24×C4×C7C2×C33direct (N × H)
45. C24×C33C2×C4×C7direct (N × H)
47. C22×C33×C4C23×C7direct (N × H)
48. C25×C3×C4C32×C7direct (N × H)
49. C2×C33×C7C24×C4direct (N × H)
51. C24×C3×C7C2×C32×C4direct (N × H)
53. C22×C3×C4×C7C23×C32direct (N × H)
54. C25×C32C3×C4×C7direct (N × H)
56. C23×C32×C4C22×C3×C7direct (N × H)
57. C22×C32×C7C23×C3×C4direct (N × H)
59. C32×C4×C7C25×C3direct (N × H)
60. C25×C7C33×C4direct (N × H)
62. C23×C4×C7C22×C33direct (N × H)
63. C23×C33C22×C4×C7direct (N × H)
65. C2×C33×C4C24×C7direct (N × H)
67. C24×C3×C4C2×C32×C7direct (N × H)
68. C33×C7C25×C4direct (N × H)
69. C23×C3×C7C22×C32×C4direct (N × H)
71. C2×C3×C4×C7C24×C32direct (N × H)
72. C24×C32C2×C3×C4×C7direct (N × H)
74. C22×C32×C4C23×C3×C7direct (N × H)
75. C25×C4C33×C7direct (N × H)
76. C2×C32×C7C24×C3×C4direct (N × H)
78. C24×C7C2×C33×C4direct (N × H)
80. C22×C4×C7C23×C33direct (N × H)
81. C22×C33C23×C4×C7direct (N × H)
83. C33×C4C25×C7direct (N × H)
84. C25×C3C32×C4×C7direct (N × H)
86. C23×C3×C4C22×C32×C7direct (N × H)
87. C22×C3×C7C23×C32×C4direct (N × H)
89. C3×C4×C7C25×C32direct (N × H)
90. C23×C32C22×C3×C4×C7direct (N × H)
92. C2×C32×C4C24×C3×C7direct (N × H)
94. C24×C4C2×C33×C7direct (N × H)
95. C32×C7C25×C3×C4direct (N × H)
96. C23×C7C22×C33×C4direct (N × H)
98. C2×C4×C7C24×C33direct (N × H)
99. C2×C33C24×C4×C7direct (N × H)
101. C24×C3C2×C32×C4×C7direct (N × H)
103. C22×C3×C4C23×C32×C7direct (N × H)
104. C2×C3×C7C24×C32×C4direct (N × H)
106. C22×C32C23×C3×C4×C7direct (N × H)
108. C32×C4C25×C3×C7direct (N × H)
109. C25C33×C4×C7direct (N × H)
111. C23×C4C22×C33×C7direct (N × H)
112. C22×C7C23×C33×C4direct (N × H)
114. C4×C7C25×C33direct (N × H)
115. C33C25×C4×C7direct (N × H)
116. C23×C3C22×C32×C4×C7direct (N × H)
118. C2×C3×C4C24×C32×C7direct (N × H)
119. C3×C7C25×C32×C4direct (N × H)
120. C2×C32C24×C3×C4×C7direct (N × H)
122. C24C2×C33×C4×C7direct (N × H)
124. C22×C4C23×C33×C7direct (N × H)
125. C2×C7C24×C33×C4direct (N × H)
127. C22×C3C23×C32×C4×C7direct (N × H)
129. C3×C4C25×C32×C7direct (N × H)
130. C32C25×C3×C4×C7direct (N × H)
131. C23C22×C33×C4×C7direct (N × H)
133. C2×C4C24×C33×C7direct (N × H)
134. C7C25×C33×C4direct (N × H)
135. C2×C3C24×C32×C4×C7direct (N × H)
137. C22C23×C33×C4×C7direct (N × H)
139. C4C25×C33×C7direct (N × H)
140. C3C25×C32×C4×C7direct (N × H)
141. C2C24×C33×C4×C7direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C33×C72
C24×C33×C4×C72
C25×C32×C4×C73
C25×C33×C47