Finite Group Databasebeta

← C25×C3×C42×C9 #72192064

Subgroups — C25×C3×C42×C9 #72192064

Order 13824.

1298580 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×C4×C9C213yesmaximal
2C24×C3×C42×C9C21124yesmaximal, direct product factor
3C25×C32×C42C311yesmaximal, characteristic
4C25×C42×C9C313yesmaximal, direct product factor
5C27×C3×C9C2211yescharacteristic
6C25×C3×C4×C9C41192yesdirect product factor
7C25×C3×C4×C9C221186yes—
8C23×C3×C42×C9C2212480yesdirect product factor
9C26×C32×C4C2×C313yes—
10C26×C4×C9C2×C319yes—
11C24×C42×C9C2×C31372yesdirect product factor
12C24×C32×C42C2×C31124yes—
13C25×C3×C42C913yesdirect product factor
14C25×C3×C42C3211yescharacteristic
15C26×C3×C9C2×C4196yes—
16C26×C3×C9C23131yes—
17C24×C3×C4×C9C2×C415952yesdirect product factor
18C24×C3×C4×C9C2311860yes—
19C22×C3×C42×C9C2319920yesdirect product factor
20C27×C32C22×C311yescharacteristic
21C25×C32×C4C3×C41192yes—
22C25×C32×C4C22×C31186yes—
23C23×C32×C42C22×C312480yes—
24C27×C9C22×C313yes—
25C25×C4×C9C3×C41576yesdirect product factor
26C25×C4×C9C22×C31558yes—
27C23×C42×C9C22×C317440yesdirect product factor
28C25×C3×C9C4211024yesdirect product factor
29C25×C3×C9C22×C411488yes—
30C25×C3×C9C241155yes—
31C23×C3×C4×C9C22×C4129760yesdirect product factor
32C23×C3×C4×C9C2413720yes—
33C2×C3×C42×C9C2417936yesdirect product factor
34C26×C3×C4C2×C919yes—
35C26×C3×C4C2×C3213yes—
36C24×C3×C42C2×C91372yesdirect product factor
37C24×C3×C42C2×C321124yes—
38C26×C32C2×C3×C4196yes—
39C26×C32C23×C3131yes—
40C24×C32×C4C2×C3×C415952yes—
41C24×C32×C4C23×C311860yes—
42C26×C9C2×C3×C41288yes—
43C26×C9C23×C3193yes—
44C22×C32×C42C23×C319920yes—
45C24×C4×C9C2×C3×C4117856yesdirect product factor
46C24×C4×C9C23×C315580yes—
47C22×C42×C9C23×C3129760yesdirect product factor
48C25×C42C3×C911yescharacteristic, direct product factor, Sylow
49C24×C3×C9C2×C4217936yesdirect product factor
50C24×C3×C9C23×C413720yes—
51C24×C3×C9C251155yes—
52C22×C3×C4×C9C23×C4129760yesdirect product factor
53C22×C3×C4×C9C2511488yes—
54C3×C42×C9C2511024yesdirect product factor
55C27×C3C22×C913yes—
56C27×C3C22×C3211yescharacteristic
57C25×C3×C4C4×C91576yesdirect product factor
58C25×C3×C4C22×C91558yes—
59C25×C3×C4C32×C41192yes—
60C25×C3×C4C22×C321186yes—
61C23×C3×C42C22×C917440yesdirect product factor
62C23×C3×C42C22×C3212480yes—
63C25×C32C3×C4211024yes—
64C25×C32C22×C3×C411488yes—
65C25×C32C24×C31155yes—
66C23×C32×C4C22×C3×C4129760yes—
67C23×C32×C4C24×C313720yes—
68C25×C9C3×C4213072yesdirect product factor
69C25×C9C22×C3×C414464yes—
70C25×C9C24×C31465yes—
71C2×C32×C42C24×C317936yes—
72C23×C4×C9C22×C3×C4189280yesdirect product factor
73C23×C4×C9C24×C3111160yes—
74C2×C42×C9C24×C3123808yesdirect product factor
75C26×C4C2×C3×C913yes—
76C24×C42C2×C3×C91124yesdirect product factor
77C23×C3×C9C22×C4219920yesdirect product factor
78C23×C3×C9C24×C411860yes—
79C23×C3×C9C26131yes—
80C2×C3×C4×C9C24×C415952yesdirect product factor
81C2×C3×C4×C9C26196yes—
82C26×C3C2×C4×C91288yes—
83C26×C3C23×C9193yes—
84C26×C3C2×C32×C4196yes—
85C26×C3C23×C32131yes—
86C24×C3×C4C2×C4×C9117856yesdirect product factor
87C24×C3×C4C23×C915580yes—
88C24×C3×C4C2×C32×C415952yes—
89C24×C3×C4C23×C3211860yes—
90C22×C3×C42C23×C9129760yesdirect product factor
91C22×C3×C42C23×C3219920yes—
92C24×C32C2×C3×C4217936yes—
93C24×C32C23×C3×C413720yes—
94C24×C32C25×C31155yes—
95C22×C32×C4C23×C3×C4129760yes—
96C22×C32×C4C25×C311488yes—
97C24×C9C2×C3×C42123808yesdirect product factor
98C24×C9C23×C3×C4111160yes—
99C24×C9C25×C31465yes—
100C32×C42C25×C311024yes—
101C22×C4×C9C23×C3×C4189280yesdirect product factor
102C22×C4×C9C25×C314464yes—
103C42×C9C25×C313072yesdirect product factor
104C27C22×C3×C911yescharacteristic
105C25×C4C3×C4×C91192yesdirect product factor
106C25×C4C22×C3×C91186yes—
107C23×C42C22×C3×C912480yesdirect product factor
108C22×C3×C9C23×C4212480yesdirect product factor
109C22×C3×C9C25×C41186yes—
110C22×C3×C9C2711yescharacteristic
111C3×C4×C9C25×C41192yesdirect product factor
112C25×C3C42×C913072yesdirect product factor
113C25×C3C22×C4×C914464yes—
114C25×C3C32×C4211024yes—
115C25×C3C24×C91465yes—
116C25×C3C22×C32×C411488yes—
117C25×C3C24×C321155yes—
118C23×C3×C4C22×C4×C9189280yesdirect product factor
119C23×C3×C4C24×C9111160yes—
120C23×C3×C4C22×C32×C4129760yes—
121C23×C3×C4C24×C3213720yes—
122C2×C3×C42C24×C9123808yesdirect product factor
123C2×C3×C42C24×C3217936yes—
124C23×C32C22×C3×C4219920yes—
125C23×C32C24×C3×C411860yes—
126C23×C32C26×C3131yes—
127C2×C32×C4C24×C3×C415952yes—
128C2×C32×C4C26×C3196yes—
129C23×C9C22×C3×C42129760yesdirect product factor
130C23×C9C24×C3×C415580yes—
131C23×C9C26×C3193yes—
132C2×C4×C9C24×C3×C4117856yesdirect product factor
133C2×C4×C9C26×C31288yes—
134C26C2×C3×C4×C9196yes—
135C26C23×C3×C9131yes—
136C24×C4C2×C3×C4×C915952yesdirect product factor
137C24×C4C23×C3×C911860yes—
138C22×C42C23×C3×C919920yesdirect product factor
139C2×C3×C9C24×C421124yesdirect product factor
140C2×C3×C9C26×C413yes—
141C24×C3C2×C42×C9123808yesdirect product factor
142C24×C3C23×C4×C9111160yes—
143C24×C3C2×C32×C4217936yes—
144C24×C3C25×C91465yes—
145C24×C3C23×C32×C413720yes—
146C24×C3C25×C321155yes—
147C22×C3×C4C23×C4×C9189280yesdirect product factor
148C22×C3×C4C25×C914464yes—
149C22×C3×C4C23×C32×C4129760yes—
150C22×C3×C4C25×C3211488yes—
151C3×C42C25×C913072yesdirect product factor
152C3×C42C25×C3211024yes—
153C22×C32C23×C3×C4212480yes—
154C22×C32C25×C3×C41186yes—
155C22×C32C27×C311yescharacteristic
156C32×C4C25×C3×C41192yes—
157C22×C9C23×C3×C4217440yesdirect product factor
158C22×C9C25×C3×C41558yes—
159C22×C9C27×C313yes—
160C4×C9C25×C3×C41576yesdirect product factor
161C25C3×C42×C911024yesdirect product factor
162C25C22×C3×C4×C911488yes—
163C25C24×C3×C91155yes—
164C23×C4C22×C3×C4×C9129760yesdirect product factor
165C23×C4C24×C3×C913720yes—
166C2×C42C24×C3×C917936yesdirect product factor
167C3×C9C25×C4211yescharacteristic, direct product factor, Sylow
168C23×C3C22×C42×C9129760yesdirect product factor
169C23×C3C24×C4×C915580yes—
170C23×C3C22×C32×C4219920yes—
171C23×C3C26×C9193yes—
172C23×C3C24×C32×C411860yes—
173C23×C3C26×C32131yes—
174C2×C3×C4C24×C4×C9117856yesdirect product factor
175C2×C3×C4C26×C91288yes—
176C2×C3×C4C24×C32×C415952yes—
177C2×C3×C4C26×C32196yes—
178C2×C32C24×C3×C421124yes—
179C2×C32C26×C3×C413yes—
180C2×C9C24×C3×C421372yesdirect product factor
181C2×C9C26×C3×C419yes—
182C24C2×C3×C42×C917936yesdirect product factor
183C24C23×C3×C4×C913720yes—
184C24C25×C3×C91155yes—
185C22×C4C23×C3×C4×C9129760yesdirect product factor
186C22×C4C25×C3×C911488yes—
187C42C25×C3×C911024yesdirect product factor
188C22×C3C23×C42×C917440yesdirect product factor
189C22×C3C25×C4×C91558yes—
190C22×C3C27×C913yes—
191C22×C3C23×C32×C4212480yes—
192C22×C3C25×C32×C41186yes—
193C22×C3C27×C3211yescharacteristic
194C3×C4C25×C4×C91576yesdirect product factor
195C3×C4C25×C32×C41192yes—
196C32C25×C3×C4211yescharacteristic
197C9C25×C3×C4213yesdirect product factor
198C23C22×C3×C42×C919920yesdirect product factor
199C23C24×C3×C4×C911860yes—
200C23C26×C3×C9131yes—
201C2×C4C24×C3×C4×C915952yesdirect product factor
202C2×C4C26×C3×C9196yes—
203C2×C3C24×C32×C421124yes—
204C2×C3C24×C42×C91372yesdirect product factor
205C2×C3C26×C4×C919yes—
206C2×C3C26×C32×C413yes—
207C22C23×C3×C42×C912480yesdirect product factor
208C22C25×C3×C4×C91186yes—
209C22C27×C3×C911yescharacteristic
210C4C25×C3×C4×C91192yesdirect product factor
211C3C25×C42×C913yesdirect product factor
212C3C25×C32×C4211yescharacteristic
213C2C24×C3×C42×C91124yesdirect product factor
214C2C26×C3×C4×C913yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C27×C32
socle, prime radicalC27×C32C22×C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C24×C3×C42×C9C2direct (N × H)
4. C25×C42×C9C3direct (N × H)
6. C25×C3×C4×C9C4direct (N × H)
8. C23×C3×C42×C9C22direct (N × H)
11. C24×C42×C9C2×C3direct (N × H)
13. C25×C3×C42C9direct (N × H)
17. C24×C3×C4×C9C2×C4direct (N × H)
19. C22×C3×C42×C9C23direct (N × H)
25. C25×C4×C9C3×C4direct (N × H)
27. C23×C42×C9C22×C3direct (N × H)
28. C25×C3×C9C42direct (N × H)
31. C23×C3×C4×C9C22×C4direct (N × H)
33. C2×C3×C42×C9C24direct (N × H)
36. C24×C3×C42C2×C9direct (N × H)
45. C24×C4×C9C2×C3×C4direct (N × H)
47. C22×C42×C9C23×C3direct (N × H)
48. C25×C42C3×C9direct (N × H)
49. C24×C3×C9C2×C42direct (N × H)
52. C22×C3×C4×C9C23×C4direct (N × H)
54. C3×C42×C9C25direct (N × H)
57. C25×C3×C4C4×C9direct (N × H)
61. C23×C3×C42C22×C9direct (N × H)
68. C25×C9C3×C42direct (N × H)
72. C23×C4×C9C22×C3×C4direct (N × H)
74. C2×C42×C9C24×C3direct (N × H)
76. C24×C42C2×C3×C9direct (N × H)
77. C23×C3×C9C22×C42direct (N × H)
80. C2×C3×C4×C9C24×C4direct (N × H)
86. C24×C3×C4C2×C4×C9direct (N × H)
90. C22×C3×C42C23×C9direct (N × H)
97. C24×C9C2×C3×C42direct (N × H)
101. C22×C4×C9C23×C3×C4direct (N × H)
103. C42×C9C25×C3direct (N × H)
105. C25×C4C3×C4×C9direct (N × H)
107. C23×C42C22×C3×C9direct (N × H)
108. C22×C3×C9C23×C42direct (N × H)
111. C3×C4×C9C25×C4direct (N × H)
112. C25×C3C42×C9direct (N × H)
118. C23×C3×C4C22×C4×C9direct (N × H)
122. C2×C3×C42C24×C9direct (N × H)
129. C23×C9C22×C3×C42direct (N × H)
132. C2×C4×C9C24×C3×C4direct (N × H)
136. C24×C4C2×C3×C4×C9direct (N × H)
138. C22×C42C23×C3×C9direct (N × H)
139. C2×C3×C9C24×C42direct (N × H)
141. C24×C3C2×C42×C9direct (N × H)
147. C22×C3×C4C23×C4×C9direct (N × H)
151. C3×C42C25×C9direct (N × H)
157. C22×C9C23×C3×C42direct (N × H)
160. C4×C9C25×C3×C4direct (N × H)
161. C25C3×C42×C9direct (N × H)
164. C23×C4C22×C3×C4×C9direct (N × H)
166. C2×C42C24×C3×C9direct (N × H)
167. C3×C9C25×C42direct (N × H)
168. C23×C3C22×C42×C9direct (N × H)
174. C2×C3×C4C24×C4×C9direct (N × H)
180. C2×C9C24×C3×C42direct (N × H)
182. C24C2×C3×C42×C9direct (N × H)
185. C22×C4C23×C3×C4×C9direct (N × H)
187. C42C25×C3×C9direct (N × H)
188. C22×C3C23×C42×C9direct (N × H)
194. C3×C4C25×C4×C9direct (N × H)
197. C9C25×C3×C42direct (N × H)
198. C23C22×C3×C42×C9direct (N × H)
201. C2×C4C24×C3×C4×C9direct (N × H)
204. C2×C3C24×C42×C9direct (N × H)
207. C22C23×C3×C42×C9direct (N × H)
210. C4C25×C3×C4×C9direct (N × H)
211. C3C25×C42×C9direct (N × H)
213. C2C24×C3×C42×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×C4×C92
C24×C3×C42×C92
C25×C32×C423
C25×C42×C93