Finite Group Databasebeta

← C151×#8696 #50313621

Subgroups — C151×#8696 #50313621

Order 38656.

384 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2966×C151C211yesmaximal, characteristic
2C4×#106×C151C211yesmaximal, characteristic, complemented
3#1568×C151C211yesmaximal, characteristic, complemented
4#1509×C151C212yesmaximal
5#1285×C151C212yesmaximal, complemented
6#529×C151C2211yescharacteristic
7#446×C151C411yescharacteristic, complemented
8C8×Q8×C151C411yescharacteristic, complemented
9#436×C151C411yescharacteristic, complemented
10#435×C151—21no—
11C8×D4×C151—21no—
12C8×D4×C151C411yescharacteristic, complemented
13#433×C151—21no—
14#432×C151C2212yes—
15#432×C151C2211yescharacteristic
16C2×#106×C151—21no—
17#405×C151—21no—
18C2×C4×C8×C151C2211yescharacteristic
19C4×C4⋊C4×C151C2212yes—
20#340×C151—21no—
21#335×C151—21no—
22#334×C151—21no—
23#328×C151—22no—
24#327×C151—22no—
25C2×M16×C151—21no—
26C22×C8×C151—21no—
27C22×C8×C151D411yescharacteristic
28C22×C8×C151D411yescharacteristic
29#126×C151—21no—
30#125×C151Q811yescharacteristic
31#124×C151Q811yescharacteristic
32#123×C151—21no—
33C22⋊Q8×C151D411yescharacteristic
34#121×C151D411yescharacteristic
35C4×Q8×C151C2×C411yescharacteristic
36C4×D4×C151—21no—
37C4×D4×C151C2×C411yescharacteristic
38#117×C151—21no—
39C2×C4⋊C4×C151—22no—
40C2×C42×C151—22no—
41C2×C42×C151C2311yescharacteristic
42#106×C151—24no—
43C4⋊C8×C151—21no—
44C4⋊C8×C151—21no—
45C4⋊C8×C151—22no—
46C4⋊C8×C151C2×C411yescharacteristic
47C4⋊C8×C151C2×C411yescharacteristic
48C22⋊C8×C151—21no—
49C22⋊C8×C151—21no—
50C22⋊C8×C151—21no—
51C22⋊C8×C151—22no—
52#97×C151—21no—
53#97×C151—21no—
54#97×C151—22no—
55C4×C8×C151—21no—
56C4×C8×C151C2×C411yescharacteristic
57C4×C8×C151C2×C411yescharacteristic
58C4×C8×C151D411yescharacteristic
59C4×C8×C151D411yescharacteristic
60#95×C151—22no—
61C2×Q8×C151C4⋊C411yescharacteristic
62C2×D4×C151—21no—
63C2×D4×C151C4⋊C411yescharacteristic
64C22×C4×C151—21no—
65C22×C4×C151—42no—
66C22×C4×C151C2×D411yescharacteristic
67C22×C4×C151C2×D411yescharacteristic
68C22×C4×C151#4111yescharacteristic
69M16×C151—42no—
70C2×C8×C151—22no—
71C2×C8×C151—21no—
72C2×C8×C151—21no—
73C2×C8×C151—41no—
74C2×C8×C151—42no—
75C2×C8×C151—42no—
76C2×C8×C151C22⋊C411yescharacteristic
77C2×C8×C151C22⋊C411yescharacteristic
78C2×C8×C151C22⋊C411yescharacteristic
79C2×C8×C151C22⋊C411yescharacteristic
80C4⋊C4×C151—21no—
81C4⋊C4×C151—21no—
82C4⋊C4×C151—21no—
83C4⋊C4×C151—21no—
84C4⋊C4×C151—24no—
85C4⋊C4×C151—42no—
86C4⋊C4×C151C4⋊C411yescharacteristic
87C4⋊C4×C151C4⋊C411yescharacteristic
88C22⋊C4×C151—21no—
89C22⋊C4×C151—21no—
90C22⋊C4×C151—21no—
91C22⋊C4×C151—21no—
92C22⋊C4×C151—21no—
93C42×C151—21no—
94C42×C151—82no—
95C42×C151C22×C411yescharacteristic
96C42×C151C2×D411yescharacteristic
97C42×C151C2×Q811yescharacteristic
98C42×C151#4111yescharacteristic
99C23×C151—21no—
100C23×C151#12111yescharacteristic
101Q8×C151—41no—
102D4×C151—41no—
103D4×C151—42no—
104C2×C4×C151—22no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151—41no—
113C2×C4×C151—44no—
114C2×C4×C151—82no—
115C2×C4×C151—82no—
116C2×C4×C151C2×C22⋊C411yescharacteristic
117C2×C4×C151C2×C4⋊C411yescharacteristic
118C2×C4×C151#11711yescharacteristic
119C2×C4×C151#12111yescharacteristic
120C2×C4×C151C22⋊Q811yescharacteristic
121C2×C4×C151C22⋊Q811yescharacteristic
122C8×C151—21no—
123C8×C151—21no—
124C8×C151—21no—
125C8×C151—41no—
126C8×C151—41no—
127C8×C151—82no—
128C8×C151#10412yes—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151—41no—
132C22×C151—41no—
133C22×C151—41no—
134C22×C151#38011yescharacteristic
135C22×C151#47112yes—
136C4×C151—21no—
137C4×C151—21no—
138C4×C151—21no—
139C4×C151—21no—
140C4×C151—21no—
141C4×C151—41no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—84no—
145C4×C151C2×#10411yescharacteristic
146C4×C151#42111yescharacteristic
147C2×C151—22no—
148C2×C151—81no—
149C2×C151#180611yescharacteristic
150C2×C151#181211yescharacteristic
151C2×C151#181511yescharacteristic
152#8696C15111yesmaximal, characteristic, direct product factor, Sylow
153C151#869611yescharacteristic, direct product factor, Sylow
154#2966C2×C15111yescharacteristic
155C4×#106C2×C15111yescharacteristic, complemented
156#1568C2×C15111yescharacteristic, complemented
157#1509C2×C15112yes—
158#1285C2×C15112yescomplemented
159#529C22×C15111yescharacteristic
160#446C4×C15111yescharacteristic, complemented
161C8×Q8C4×C15111yescharacteristic, complemented
162#436C4×C15111yescharacteristic, complemented
163#435—21no—
164C8×D4—21no—
165C8×D4C4×C15111yescharacteristic, complemented
166#433—21no—
167#432C22×C15112yes—
168#432C22×C15111yescharacteristic
169C2×#106—21no—
170#405—21no—
171C2×C4×C8C22×C15111yescharacteristic
172C4×C4⋊C4C22×C15112yes—
173#340—21no—
174#335—21no—
175#334—21no—
176#328—22no—
177#327—22no—
178C2×M16—21no—
179C22×C8—21no—
180C22×C8D4×C15111yescharacteristic
181C22×C8D4×C15111yescharacteristic
182#126—21no—
183#125Q8×C15111yescharacteristic
184#124Q8×C15111yescharacteristic
185#123—21no—
186C22⋊Q8D4×C15111yescharacteristic
187#121D4×C15111yescharacteristic
188C4×Q8C2×C4×C15111yescharacteristic
189C4×D4—21no—
190C4×D4C2×C4×C15111yescharacteristic
191#117—21no—
192C2×C4⋊C4—22no—
193C2×C42—22no—
194C2×C42C23×C15111yescharacteristic
195#106—24no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—22no—
199C4⋊C8C2×C4×C15111yescharacteristic
200C4⋊C8C2×C4×C15111yescharacteristic
201C22⋊C8—21no—
202C22⋊C8—21no—
203C22⋊C8—21no—
204C22⋊C8—22no—
205#97—21no—
206#97—22no—
207#97—21no—
208C4×C8—21no—
209C4×C8C2×C4×C15111yescharacteristic
210C4×C8C2×C4×C15111yescharacteristic
211C4×C8D4×C15111yescharacteristic
212C4×C8D4×C15111yescharacteristic
213#95—22no—
214C2×Q8C4⋊C4×C15111yescharacteristic
215C2×D4—21no—
216C2×D4C4⋊C4×C15111yescharacteristic
217C22×C4—21no—
218C22×C4—42no—
219C22×C4C2×D4×C15111yescharacteristic
220C22×C4C2×D4×C15111yescharacteristic
221C22×C4#41×C15111yescharacteristic
222M16—42no—
223C2×C8—22no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8C22⋊C4×C15111yescharacteristic
230C2×C8C22⋊C4×C15111yescharacteristic
231C2×C8C22⋊C4×C15111yescharacteristic
232C2×C8C22⋊C4×C15111yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4C4⋊C4×C15111yescharacteristic
240C4⋊C4C4⋊C4×C15111yescharacteristic
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—21no—
245C22⋊C4—21no—
246C42—21no—
247C42—82no—
248C42C22×C4×C15111yescharacteristic
249C42C2×D4×C15111yescharacteristic
250C42C2×Q8×C15111yescharacteristic
251C42#41×C15111yescharacteristic
252C23—21no—
253C23#121×C15111yescharacteristic
254Q8—41no—
255D4—41no—
256D4—42no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4C2×C22⋊C4×C15111yescharacteristic
270C2×C4C2×C4⋊C4×C15111yescharacteristic
271C2×C4#117×C15111yescharacteristic
272C2×C4#121×C15111yescharacteristic
273C2×C4C22⋊Q8×C15111yescharacteristic
274C2×C4C22⋊Q8×C15111yescharacteristic
275C8—21no—
276C8—21no—
277C8—21no—
278C8—41no—
279C8—41no—
280C8—82no—
281C8#104×C15112yes—
282C22—21no—
283C22—21no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22#380×C15111yescharacteristic
288C22#471×C15112yes—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—84no—
298C4C2×#104×C15111yescharacteristic
299C4#421×C15111yescharacteristic
300C2—22no—
301C2—81no—
302C2#1806×C15111yescharacteristic
303C2#1812×C15111yescharacteristic
304C2#1815×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#380
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radical#121×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#106×C151C2semidirect
3. #1568×C151C2semidirect
5. #1285×C151C2semidirect
7. #446×C151C4semidirect
8. C8×Q8×C151C4semidirect
9. #436×C151C4semidirect
12. C8×D4×C151C4semidirect
152. #8696C151direct (N × H)
153. C151#8696direct (N × H)
155. C4×#106C2×C151semidirect
156. #1568C2×C151semidirect
158. #1285C2×C151semidirect
160. #446C4×C151semidirect
161. C8×Q8C4×C151semidirect
162. #436C4×C151semidirect
165. C8×D4C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2966×C1512
C4×#106×C1512
#1568×C1512
#1509×C1512
#1285×C1512
#8696151