Finite Group Databasebeta

← C25×C3×C4×C7×C9 #72201494

Subgroups — C25×C3×C4×C7×C9 #72201494

Order 24192.

105520 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C3×C7×C9C211yesmaximal, characteristic
2C24×C3×C4×C7×C9C2162yesmaximal, direct product factor
3C25×C32×C4×C7C311yesmaximal, characteristic
4C25×C4×C7×C9C313yesmaximal, direct product factor
5C25×C3×C7×C9C4132yesdirect product factor
6C25×C3×C7×C9C22131yes—
7C23×C3×C4×C7×C9C221620yesdirect product factor
8C26×C32×C7C2×C311yescharacteristic
9C26×C7×C9C2×C313yes—
10C24×C32×C4×C7C2×C3162yes—
11C24×C4×C7×C9C2×C31186yesdirect product factor
12C25×C3×C4×C9C711yesmaximal, characteristic, direct product factor, Hall
13C24×C3×C7×C9C2×C41496yesdirect product factor
14C24×C3×C7×C9C231155yes—
15C22×C3×C4×C7×C9C2311240yesdirect product factor
16C25×C3×C4×C7C913yesdirect product factor
17C25×C3×C4×C7C3211yescharacteristic
18C25×C32×C7C3×C4132yes—
19C25×C32×C7C22×C3131yes—
20C25×C7×C9C3×C4196yesdirect product factor
21C25×C7×C9C22×C3193yes—
22C23×C32×C4×C7C22×C31620yes—
23C23×C4×C7×C9C22×C311860yesdirect product factor
24C26×C3×C9C2×C711yescharacteristic
25C24×C3×C4×C9C2×C7162yesdirect product factor
26C23×C3×C7×C9C22×C411240yesdirect product factor
27C23×C3×C7×C9C241155yes—
28C2×C3×C4×C7×C9C241496yesdirect product factor
29C26×C3×C7C2×C913yes—
30C26×C3×C7C2×C3211yescharacteristic
31C24×C3×C4×C7C2×C91186yesdirect product factor
32C24×C3×C4×C7C2×C32162yes—
33C25×C32×C4C3×C711yescharacteristic
34C25×C4×C9C3×C713yesdirect product factor
35C24×C32×C7C2×C3×C41496yes—
36C24×C32×C7C23×C31155yes—
37C22×C32×C4×C7C23×C311240yes—
38C24×C7×C9C2×C3×C411488yesdirect product factor
39C24×C7×C9C23×C31465yes—
40C22×C4×C7×C9C23×C313720yesdirect product factor
41C25×C4×C7C3×C911yescharacteristic, direct product factor, Hall
42C25×C3×C9C4×C7132yesdirect product factor
43C25×C3×C9C22×C7131yes—
44C23×C3×C4×C9C22×C71620yesdirect product factor
45C22×C3×C7×C9C23×C41620yesdirect product factor
46C22×C3×C7×C9C25131yes—
47C3×C4×C7×C9C25132yesdirect product factor
48C25×C3×C7C4×C9196yesdirect product factor
49C25×C3×C7C22×C9193yes—
50C25×C3×C7C32×C4132yes—
51C25×C3×C7C22×C32131yes—
52C23×C3×C4×C7C22×C911860yesdirect product factor
53C23×C3×C4×C7C22×C321620yes—
54C26×C32C2×C3×C711yescharacteristic
55C24×C32×C4C2×C3×C7162yes—
56C26×C9C2×C3×C713yes—
57C24×C4×C9C2×C3×C71186yesdirect product factor
58C23×C32×C7C22×C3×C411240yes—
59C23×C32×C7C24×C31155yes—
60C2×C32×C4×C7C24×C31496yes—
61C23×C7×C9C22×C3×C413720yesdirect product factor
62C23×C7×C9C24×C31465yes—
63C2×C4×C7×C9C24×C311488yesdirect product factor
64C26×C7C2×C3×C911yescharacteristic
65C24×C4×C7C2×C3×C9162yesdirect product factor
66C24×C3×C9C2×C4×C71496yesdirect product factor
67C24×C3×C9C23×C71155yes—
68C22×C3×C4×C9C23×C711240yesdirect product factor
69C25×C3×C4C7×C913yesdirect product factor
70C25×C3×C4C32×C711yescharacteristic
71C2×C3×C7×C9C24×C4162yesdirect product factor
72C2×C3×C7×C9C2611yescharacteristic
73C24×C3×C7C2×C4×C911488yesdirect product factor
74C24×C3×C7C23×C91465yes—
75C24×C3×C7C2×C32×C41496yes—
76C24×C3×C7C23×C321155yes—
77C22×C3×C4×C7C23×C913720yesdirect product factor
78C22×C3×C4×C7C23×C3211240yes—
79C25×C32C3×C4×C7132yes—
80C25×C32C22×C3×C7131yes—
81C23×C32×C4C22×C3×C71620yes—
82C25×C9C3×C4×C7196yesdirect product factor
83C25×C9C22×C3×C7193yes—
84C23×C4×C9C22×C3×C711860yesdirect product factor
85C22×C32×C7C23×C3×C41620yes—
86C22×C32×C7C25×C3131yes—
87C32×C4×C7C25×C3132yes—
88C22×C7×C9C23×C3×C411860yesdirect product factor
89C22×C7×C9C25×C3193yes—
90C4×C7×C9C25×C3196yesdirect product factor
91C25×C7C3×C4×C9132yesdirect product factor
92C25×C7C22×C3×C9131yes—
93C23×C4×C7C22×C3×C91620yesdirect product factor
94C23×C3×C9C22×C4×C711240yesdirect product factor
95C23×C3×C9C24×C71155yes—
96C2×C3×C4×C9C24×C71496yesdirect product factor
97C26×C3C2×C7×C913yes—
98C26×C3C2×C32×C711yescharacteristic
99C24×C3×C4C2×C7×C91186yesdirect product factor
100C24×C3×C4C2×C32×C7162yes—
101C3×C7×C9C25×C411yescharacteristic, direct product factor, Hall
102C23×C3×C7C22×C4×C913720yesdirect product factor
103C23×C3×C7C24×C91465yes—
104C23×C3×C7C22×C32×C411240yes—
105C23×C3×C7C24×C321155yes—
106C2×C3×C4×C7C24×C911488yesdirect product factor
107C2×C3×C4×C7C24×C321496yes—
108C24×C32C2×C3×C4×C71496yes—
109C24×C32C23×C3×C71155yes—
110C22×C32×C4C23×C3×C711240yes—
111C24×C9C2×C3×C4×C711488yesdirect product factor
112C24×C9C23×C3×C71465yes—
113C22×C4×C9C23×C3×C713720yesdirect product factor
114C25×C4C3×C7×C911yescharacteristic, direct product factor, Sylow
115C2×C32×C7C24×C3×C4162yes—
116C2×C32×C7C26×C311yescharacteristic
117C2×C7×C9C24×C3×C41186yesdirect product factor
118C2×C7×C9C26×C313yes—
119C24×C7C2×C3×C4×C91496yesdirect product factor
120C24×C7C23×C3×C91155yes—
121C22×C4×C7C23×C3×C911240yesdirect product factor
122C22×C3×C9C23×C4×C71620yesdirect product factor
123C22×C3×C9C25×C7131yes—
124C3×C4×C9C25×C7132yesdirect product factor
125C25×C3C4×C7×C9196yesdirect product factor
126C25×C3C22×C7×C9193yes—
127C25×C3C32×C4×C7132yes—
128C25×C3C22×C32×C7131yes—
129C23×C3×C4C22×C7×C911860yesdirect product factor
130C23×C3×C4C22×C32×C71620yes—
131C22×C3×C7C23×C4×C911860yesdirect product factor
132C22×C3×C7C25×C9193yes—
133C22×C3×C7C23×C32×C41620yes—
134C22×C3×C7C25×C32131yes—
135C3×C4×C7C25×C9196yesdirect product factor
136C3×C4×C7C25×C32132yes—
137C23×C32C22×C3×C4×C711240yes—
138C23×C32C24×C3×C71155yes—
139C2×C32×C4C24×C3×C71496yes—
140C23×C9C22×C3×C4×C713720yesdirect product factor
141C23×C9C24×C3×C71465yes—
142C2×C4×C9C24×C3×C711488yesdirect product factor
143C26C2×C3×C7×C911yescharacteristic
144C24×C4C2×C3×C7×C9162yesdirect product factor
145C32×C7C25×C3×C411yescharacteristic
146C7×C9C25×C3×C413yesdirect product factor
147C23×C7C22×C3×C4×C911240yesdirect product factor
148C23×C7C24×C3×C91155yes—
149C2×C4×C7C24×C3×C91496yesdirect product factor
150C2×C3×C9C24×C4×C7162yesdirect product factor
151C2×C3×C9C26×C711yescharacteristic
152C24×C3C2×C4×C7×C911488yesdirect product factor
153C24×C3C23×C7×C91465yes—
154C24×C3C2×C32×C4×C71496yes—
155C24×C3C23×C32×C71155yes—
156C22×C3×C4C23×C7×C913720yesdirect product factor
157C22×C3×C4C23×C32×C711240yes—
158C2×C3×C7C24×C4×C91186yesdirect product factor
159C2×C3×C7C26×C913yes—
160C2×C3×C7C24×C32×C4162yes—
161C2×C3×C7C26×C3211yescharacteristic
162C22×C32C23×C3×C4×C71620yes—
163C22×C32C25×C3×C7131yes—
164C32×C4C25×C3×C7132yes—
165C22×C9C23×C3×C4×C711860yesdirect product factor
166C22×C9C25×C3×C7193yes—
167C4×C9C25×C3×C7196yesdirect product factor
168C25C3×C4×C7×C9132yesdirect product factor
169C25C22×C3×C7×C9131yes—
170C23×C4C22×C3×C7×C91620yesdirect product factor
171C22×C7C23×C3×C4×C91620yesdirect product factor
172C22×C7C25×C3×C9131yes—
173C4×C7C25×C3×C9132yesdirect product factor
174C3×C9C25×C4×C711yescharacteristic, direct product factor, Sylow
175C23×C3C22×C4×C7×C913720yesdirect product factor
176C23×C3C24×C7×C91465yes—
177C23×C3C22×C32×C4×C711240yes—
178C23×C3C24×C32×C71155yes—
179C2×C3×C4C24×C7×C911488yesdirect product factor
180C2×C3×C4C24×C32×C71496yes—
181C3×C7C25×C4×C913yesdirect product factor
182C3×C7C25×C32×C411yescharacteristic
183C2×C32C24×C3×C4×C7162yes—
184C2×C32C26×C3×C711yescharacteristic
185C2×C9C24×C3×C4×C71186yesdirect product factor
186C2×C9C26×C3×C713yes—
187C24C2×C3×C4×C7×C91496yesdirect product factor
188C24C23×C3×C7×C91155yes—
189C22×C4C23×C3×C7×C911240yesdirect product factor
190C2×C7C24×C3×C4×C9162yesdirect product factor
191C2×C7C26×C3×C911yescharacteristic
192C22×C3C23×C4×C7×C911860yesdirect product factor
193C22×C3C23×C32×C4×C71620yes—
194C22×C3C25×C7×C9193yes—
195C22×C3C25×C32×C7131yes—
196C3×C4C25×C7×C9196yesdirect product factor
197C3×C4C25×C32×C7132yes—
198C32C25×C3×C4×C711yescharacteristic
199C9C25×C3×C4×C713yesdirect product factor
200C23C22×C3×C4×C7×C911240yesdirect product factor
201C23C24×C3×C7×C91155yes—
202C2×C4C24×C3×C7×C91496yesdirect product factor
203C7C25×C3×C4×C911yescharacteristic, direct product factor, Sylow
204C2×C3C24×C4×C7×C91186yesdirect product factor
205C2×C3C24×C32×C4×C7162yes—
206C2×C3C26×C7×C913yes—
207C2×C3C26×C32×C711yescharacteristic
208C22C23×C3×C4×C7×C91620yesdirect product factor
209C22C25×C3×C7×C9131yes—
210C4C25×C3×C7×C9132yesdirect product factor
211C3C25×C4×C7×C913yesdirect product factor
212C3C25×C32×C4×C711yescharacteristic
213C2C24×C3×C4×C7×C9162yesdirect product factor
214C2C26×C3×C7×C911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C26×C32×C7
socle, prime radicalC26×C32×C7C2×C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C24×C3×C4×C7×C9C2direct (N × H)
4. C25×C4×C7×C9C3direct (N × H)
5. C25×C3×C7×C9C4direct (N × H)
7. C23×C3×C4×C7×C9C22direct (N × H)
11. C24×C4×C7×C9C2×C3direct (N × H)
12. C25×C3×C4×C9C7direct (N × H)
13. C24×C3×C7×C9C2×C4direct (N × H)
15. C22×C3×C4×C7×C9C23direct (N × H)
16. C25×C3×C4×C7C9direct (N × H)
20. C25×C7×C9C3×C4direct (N × H)
23. C23×C4×C7×C9C22×C3direct (N × H)
25. C24×C3×C4×C9C2×C7direct (N × H)
26. C23×C3×C7×C9C22×C4direct (N × H)
28. C2×C3×C4×C7×C9C24direct (N × H)
31. C24×C3×C4×C7C2×C9direct (N × H)
34. C25×C4×C9C3×C7direct (N × H)
38. C24×C7×C9C2×C3×C4direct (N × H)
40. C22×C4×C7×C9C23×C3direct (N × H)
41. C25×C4×C7C3×C9direct (N × H)
42. C25×C3×C9C4×C7direct (N × H)
44. C23×C3×C4×C9C22×C7direct (N × H)
45. C22×C3×C7×C9C23×C4direct (N × H)
47. C3×C4×C7×C9C25direct (N × H)
48. C25×C3×C7C4×C9direct (N × H)
52. C23×C3×C4×C7C22×C9direct (N × H)
57. C24×C4×C9C2×C3×C7direct (N × H)
61. C23×C7×C9C22×C3×C4direct (N × H)
63. C2×C4×C7×C9C24×C3direct (N × H)
65. C24×C4×C7C2×C3×C9direct (N × H)
66. C24×C3×C9C2×C4×C7direct (N × H)
68. C22×C3×C4×C9C23×C7direct (N × H)
69. C25×C3×C4C7×C9direct (N × H)
71. C2×C3×C7×C9C24×C4direct (N × H)
73. C24×C3×C7C2×C4×C9direct (N × H)
77. C22×C3×C4×C7C23×C9direct (N × H)
82. C25×C9C3×C4×C7direct (N × H)
84. C23×C4×C9C22×C3×C7direct (N × H)
88. C22×C7×C9C23×C3×C4direct (N × H)
90. C4×C7×C9C25×C3direct (N × H)
91. C25×C7C3×C4×C9direct (N × H)
93. C23×C4×C7C22×C3×C9direct (N × H)
94. C23×C3×C9C22×C4×C7direct (N × H)
96. C2×C3×C4×C9C24×C7direct (N × H)
99. C24×C3×C4C2×C7×C9direct (N × H)
101. C3×C7×C9C25×C4direct (N × H)
102. C23×C3×C7C22×C4×C9direct (N × H)
106. C2×C3×C4×C7C24×C9direct (N × H)
111. C24×C9C2×C3×C4×C7direct (N × H)
113. C22×C4×C9C23×C3×C7direct (N × H)
114. C25×C4C3×C7×C9direct (N × H)
117. C2×C7×C9C24×C3×C4direct (N × H)
119. C24×C7C2×C3×C4×C9direct (N × H)
121. C22×C4×C7C23×C3×C9direct (N × H)
122. C22×C3×C9C23×C4×C7direct (N × H)
124. C3×C4×C9C25×C7direct (N × H)
125. C25×C3C4×C7×C9direct (N × H)
129. C23×C3×C4C22×C7×C9direct (N × H)
131. C22×C3×C7C23×C4×C9direct (N × H)
135. C3×C4×C7C25×C9direct (N × H)
140. C23×C9C22×C3×C4×C7direct (N × H)
142. C2×C4×C9C24×C3×C7direct (N × H)
144. C24×C4C2×C3×C7×C9direct (N × H)
146. C7×C9C25×C3×C4direct (N × H)
147. C23×C7C22×C3×C4×C9direct (N × H)
149. C2×C4×C7C24×C3×C9direct (N × H)
150. C2×C3×C9C24×C4×C7direct (N × H)
152. C24×C3C2×C4×C7×C9direct (N × H)
156. C22×C3×C4C23×C7×C9direct (N × H)
158. C2×C3×C7C24×C4×C9direct (N × H)
165. C22×C9C23×C3×C4×C7direct (N × H)
167. C4×C9C25×C3×C7direct (N × H)
168. C25C3×C4×C7×C9direct (N × H)
170. C23×C4C22×C3×C7×C9direct (N × H)
171. C22×C7C23×C3×C4×C9direct (N × H)
173. C4×C7C25×C3×C9direct (N × H)
174. C3×C9C25×C4×C7direct (N × H)
175. C23×C3C22×C4×C7×C9direct (N × H)
179. C2×C3×C4C24×C7×C9direct (N × H)
181. C3×C7C25×C4×C9direct (N × H)
185. C2×C9C24×C3×C4×C7direct (N × H)
187. C24C2×C3×C4×C7×C9direct (N × H)
189. C22×C4C23×C3×C7×C9direct (N × H)
190. C2×C7C24×C3×C4×C9direct (N × H)
192. C22×C3C23×C4×C7×C9direct (N × H)
196. C3×C4C25×C7×C9direct (N × H)
199. C9C25×C3×C4×C7direct (N × H)
200. C23C22×C3×C4×C7×C9direct (N × H)
202. C2×C4C24×C3×C7×C9direct (N × H)
203. C7C25×C3×C4×C9direct (N × H)
204. C2×C3C24×C4×C7×C9direct (N × H)
208. C22C23×C3×C4×C7×C9direct (N × H)
210. C4C25×C3×C7×C9direct (N × H)
211. C3C25×C4×C7×C9direct (N × H)
213. C2C24×C3×C4×C7×C9direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C3×C7×C92
C24×C3×C4×C7×C92
C25×C32×C4×C73
C25×C4×C7×C93
C25×C3×C4×C97