Finite Group Databasebeta

← C151×#8730 #50313655

Subgroups — C151×#8730 #50313655

Order 38656.

522 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#117×C151C211yesmaximal, characteristic
2#1458×C151C212yesmaximal
3#1276×C151C212yesmaximal, complemented
4#1274×C151C212yesmaximal, complemented
5C2×#117×C151C411yescharacteristic
6C2×#117×C151C2211yescharacteristic
7C22×C42×C151C411yescharacteristic
8#431×C151C2214yes—
9C4×C4⋊C4×C151—22no—
10C4×C22⋊C4×C151—22no—
11#376×C151C411yescharacteristic
12#376×C151C2211yescharacteristic
13C43×C151C411yescharacteristic
14C43×C151C2211yescharacteristic
15#324×C151—22no—
16#323×C151—22no—
17C23×C4×C151—21no—
18C23×C4×C151C2×C411yescharacteristic
19#117×C151—22no—
20#117×C151—22no—
21#117×C151—22no—
22#117×C151—22no—
23C2×C4⋊C4×C151—21no—
24C2×C4⋊C4×C151D412yes—
25C2×C22⋊C4×C151—21no—
26C2×C22⋊C4×C151D412yes—
27C2×C42×C151—21no—
28C2×C42×C151—22no—
29C2×C42×C151—22no—
30C2×C42×C151—22no—
31C2×C42×C151C814yescomplemented
32C2×C42×C151C2×C411yescharacteristic
33C2×C42×C151C2×C411yescharacteristic
34C2×C42×C151C2×C411yescharacteristic
35C2×C42×C151C2×C411yescharacteristic
36C2×C42×C151C2×C411yescharacteristic
37C2×C42×C151C2311yescharacteristic
38C4⋊C8×C151—24no—
39C22⋊C8×C151—24no—
40C4×C8×C151—24no—
41#95×C151—22no—
42#95×C151—22no—
43C24×C151C22⋊C411yescharacteristic
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151—21no—
47C22×C4×C151—21no—
48C22×C4×C151—21no—
49C22×C4×C151—24no—
50C22×C4×C151—21no—
51C22×C4×C151—21no—
52C22×C4×C151—21no—
53C22×C4×C151—44no—
54C22×C4×C151C22⋊C411yescharacteristic
55C22×C4×C151C22⋊C412yes—
56C22×C4×C151C2×C812yes—
57C22×C4×C151M1612yes—
58C22×C4×C151C22×C411yescharacteristic
59C22×C4×C151C2×D412yes—
60C2×C8×C151—44no—
61C4⋊C4×C151—24no—
62C4⋊C4×C151—24no—
63C22⋊C4×C151—24no—
64C22⋊C4×C151—24no—
65C42×C151—24no—
66C42×C151—21no—
67C42×C151—21no—
68C42×C151—21no—
69C42×C151—21no—
70C42×C151—21no—
71C42×C151—21no—
72C42×C151—44no—
73C42×C151—44no—
74C42×C151C2×C812yes—
75C42×C151C2×C812yes—
76C42×C151M1612yes—
77C42×C151M1612yes—
78C42×C151#4112yes—
79C42×C151#4112yes—
80C23×C151—21no—
81C23×C151—21no—
82C23×C151—42no—
83C23×C151C22⋊C812yes—
84C23×C151C2×C22⋊C411yescharacteristic
85C2×C4×C151—24no—
86C2×C4×C151—21no—
87C2×C4×C151—22no—
88C2×C4×C151—21no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—42no—
98C2×C4×C151—48no—
99C2×C4×C151—42no—
100C2×C4×C151—42no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151C22⋊C812yes—
104C2×C4×C151#11711yescharacteristic
105C2×C4×C151#11711yescharacteristic
106C2×C4×C151#12314yes—
107C2×C4×C151C22×C811yescharacteristic
108C2×C4×C151C2×M1611yescharacteristic
109C2×C4×C151C2×M1611yescharacteristic
110C2×C4×C151C2×M1611yescharacteristic
111C8×C151—84no—
112C22×C151—22no—
113C22×C151—22no—
114C22×C151—42no—
115C22×C151—42no—
116C22×C151—42no—
117C22×C151#38111yescharacteristic
118C22×C151C2×C22⋊C811yescharacteristic
119C22×C151#40711yescharacteristic
120C4×C151—24no—
121C4×C151—22no—
122C4×C151—24no—
123C4×C151—42no—
124C4×C151—42no—
125C4×C151—42no—
126C4×C151—42no—
127C4×C151#43111yescharacteristic
128C4×C151#43111yescharacteristic
129C4×C151#43211yescharacteristic
130C4×C151#43211yescharacteristic
131C2×C151—21no—
132C2×C151—21no—
133C2×C151—42no—
134C2×C151#181711yescharacteristic
135C2×C151#182712yes—
136#8730C15111yesmaximal, characteristic, direct product factor, Sylow
137C151#873011yescharacteristic, direct product factor, Sylow
138C4×#117C2×C15111yescharacteristic
139#1458C2×C15112yes—
140#1276C2×C15112yescomplemented
141#1274C2×C15112yescomplemented
142C2×#117C4×C15111yescharacteristic
143C2×#117C22×C15111yescharacteristic
144C22×C42C4×C15111yescharacteristic
145#431C22×C15114yes—
146C4×C4⋊C4—22no—
147C4×C22⋊C4—22no—
148#376C4×C15111yescharacteristic
149#376C22×C15111yescharacteristic
150C43C4×C15111yescharacteristic
151C43C22×C15111yescharacteristic
152#324—22no—
153#323—22no—
154C23×C4—21no—
155C23×C4C2×C4×C15111yescharacteristic
156#117—22no—
157#117—22no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4D4×C15112yes—
162C2×C22⋊C4—21no—
163C2×C22⋊C4D4×C15112yes—
164C2×C42—21no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42C8×C15114yescomplemented
169C2×C42C2×C4×C15111yescharacteristic
170C2×C42C2×C4×C15111yescharacteristic
171C2×C42C2×C4×C15111yescharacteristic
172C2×C42C2×C4×C15111yescharacteristic
173C2×C42C2×C4×C15111yescharacteristic
174C2×C42C23×C15111yescharacteristic
175C4⋊C8—24no—
176C22⋊C8—24no—
177C4×C8—24no—
178#95—22no—
179#95—22no—
180C24C22⋊C4×C15111yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—24no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—44no—
191C22×C4C22⋊C4×C15111yescharacteristic
192C22×C4C22⋊C4×C15112yes—
193C22×C4C2×C8×C15112yes—
194C22×C4M16×C15112yes—
195C22×C4C22×C4×C15111yescharacteristic
196C22×C4C2×D4×C15112yes—
197C2×C8—44no—
198C4⋊C4—24no—
199C4⋊C4—24no—
200C22⋊C4—24no—
201C22⋊C4—24no—
202C42—24no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—44no—
210C42—44no—
211C42C2×C8×C15112yes—
212C42C2×C8×C15112yes—
213C42M16×C15112yes—
214C42M16×C15112yes—
215C42#41×C15112yes—
216C42#41×C15112yes—
217C23—21no—
218C23—21no—
219C23—42no—
220C23C22⋊C8×C15112yes—
221C23C2×C22⋊C4×C15111yescharacteristic
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—48no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4C22⋊C8×C15112yes—
241C2×C4#117×C15111yescharacteristic
242C2×C4#117×C15111yescharacteristic
243C2×C4#123×C15114yes—
244C2×C4C22×C8×C15111yescharacteristic
245C2×C4C2×M16×C15111yescharacteristic
246C2×C4C2×M16×C15111yescharacteristic
247C2×C4C2×M16×C15111yescharacteristic
248C8—84no—
249C22—22no—
250C22—22no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22#381×C15111yescharacteristic
255C22C2×C22⋊C8×C15111yescharacteristic
256C22#407×C15111yescharacteristic
257C4—24no—
258C4—24no—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—42no—
263C4—42no—
264C4#431×C15111yescharacteristic
265C4#431×C15111yescharacteristic
266C4#432×C15111yescharacteristic
267C4#432×C15111yescharacteristic
268C2—21no—
269C2—21no—
270C2—42no—
271C2#1817×C15111yescharacteristic
272C2#1827×C15112yes—
subgroupG/H
centerC2×C4×C151#117
commutatorC2×C4C22×C8×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#381
prime radicalC24×C151C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1276×C151C2semidirect
4. #1274×C151C2semidirect
31. C2×C42×C151C8semidirect
136. #8730C151direct (N × H)
137. C151#8730direct (N × H)
140. #1276C2×C151semidirect
141. #1274C2×C151semidirect
168. C2×C42C8×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#117×C1512
#1458×C1512
#1276×C1512
#1274×C1512
#8730151