Finite Group Databasebeta

← C151×#8697 #50313622

Subgroups — C151×#8697 #50313622

Order 38656.

384 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2966×C151C211yesmaximal, characteristic
2C4×#107×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×#107×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#107×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—41no—
104D4×C151—41no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—44no—
116C2×C4×C151—82no—
117C2×C4×C151—82no—
118C2×C4×C151C2×C22⋊C411yescharacteristic
119C2×C4×C151C2×C4⋊C411yescharacteristic
120C2×C4×C151#11711yescharacteristic
121C2×C4×C151#12111yescharacteristic
122C2×C4×C151C22⋊Q811yescharacteristic
123C2×C4×C151C22⋊Q811yescharacteristic
124C8×C151—21no—
125C8×C151—21no—
126C8×C151—21no—
127C8×C151—41no—
128C8×C151—41no—
129C8×C151—82no—
130C8×C151#10412yes—
131C22×C151—21no—
132C22×C151—21no—
133C22×C151—41no—
134C22×C151—41no—
135C22×C151—41no—
136C22×C151#38011yescharacteristic
137C22×C151#47211yescharacteristic
138C22×C151#47311yescharacteristic
139C4×C151—21no—
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—41no—
145C4×C151—41no—
146C4×C151—41no—
147C4×C151—84no—
148C4×C151C2×#10411yescharacteristic
149C4×C151#42111yescharacteristic
150C2×C151—21no—
151C2×C151—21no—
152C2×C151—81no—
153C2×C151#180611yescharacteristic
154C2×C151#181211yescharacteristic
155C2×C151#181611yescharacteristic
156#8697C15111yesmaximal, characteristic, direct product factor, Sylow
157C151#869711yescharacteristic, direct product factor, Sylow
158#2966C2×C15111yescharacteristic
159C4×#107C2×C15111yescharacteristic, complemented
160#1568C2×C15111yescharacteristic, complemented
161#1509C2×C15112yes—
162#1285C2×C15112yescomplemented
163#529C22×C15111yescharacteristic
164#446C4×C15111yescharacteristic, complemented
165C8×Q8C4×C15111yescharacteristic, complemented
166#436C4×C15111yescharacteristic, complemented
167#435—21no—
168C8×D4—21no—
169C8×D4C4×C15111yescharacteristic, complemented
170#433—21no—
171#432C22×C15112yes—
172#432C22×C15111yescharacteristic
173C2×#107—21no—
174#405—21no—
175C2×C4×C8C22×C15111yescharacteristic
176C4×C4⋊C4C22×C15112yes—
177#340—21no—
178#335—21no—
179#334—21no—
180#328—22no—
181#327—22no—
182C2×M16—21no—
183C22×C8—21no—
184C22×C8D4×C15111yescharacteristic
185C22×C8D4×C15111yescharacteristic
186#126—21no—
187#125Q8×C15111yescharacteristic
188#124Q8×C15111yescharacteristic
189#123—21no—
190C22⋊Q8D4×C15111yescharacteristic
191#121D4×C15111yescharacteristic
192C4×Q8C2×C4×C15111yescharacteristic
193C4×D4—21no—
194C4×D4C2×C4×C15111yescharacteristic
195#117—21no—
196C2×C4⋊C4—22no—
197C2×C42—22no—
198C2×C42C23×C15111yescharacteristic
199#107—24no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—22no—
203C4⋊C8C2×C4×C15111yescharacteristic
204C4⋊C8C2×C4×C15111yescharacteristic
205C22⋊C8—21no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208C22⋊C8—22no—
209#97—21no—
210#97—22no—
211#97—21no—
212C4×C8—21no—
213C4×C8C2×C4×C15111yescharacteristic
214C4×C8C2×C4×C15111yescharacteristic
215C4×C8D4×C15111yescharacteristic
216C4×C8D4×C15111yescharacteristic
217#95—22no—
218C2×Q8C4⋊C4×C15111yescharacteristic
219C2×D4—21no—
220C2×D4C4⋊C4×C15111yescharacteristic
221C22×C4—21no—
222C22×C4—42no—
223C22×C4C2×D4×C15111yescharacteristic
224C22×C4C2×D4×C15111yescharacteristic
225C22×C4#41×C15111yescharacteristic
226M16—42no—
227C2×C8—22no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8C22⋊C4×C15111yescharacteristic
234C2×C8C22⋊C4×C15111yescharacteristic
235C2×C8C22⋊C4×C15111yescharacteristic
236C2×C8C22⋊C4×C15111yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—24no—
242C4⋊C4—42no—
243C4⋊C4C4⋊C4×C15111yescharacteristic
244C4⋊C4C4⋊C4×C15111yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—21no—
249C22⋊C4—21no—
250C42—21no—
251C42—82no—
252C42C22×C4×C15111yescharacteristic
253C42C2×D4×C15111yescharacteristic
254C42C2×Q8×C15111yescharacteristic
255C42#41×C15111yescharacteristic
256C23—21no—
257C23#121×C15111yescharacteristic
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—41no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4C2×C22⋊C4×C15111yescharacteristic
276C2×C4C2×C4⋊C4×C15111yescharacteristic
277C2×C4#117×C15111yescharacteristic
278C2×C4#121×C15111yescharacteristic
279C2×C4C22⋊Q8×C15111yescharacteristic
280C2×C4C22⋊Q8×C15111yescharacteristic
281C8—21no—
282C8—21no—
283C8—21no—
284C8—41no—
285C8—41no—
286C8—82no—
287C8#104×C15112yes—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22#380×C15111yescharacteristic
294C22#472×C15111yescharacteristic
295C22#473×C15111yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—84no—
305C4C2×#104×C15111yescharacteristic
306C4#421×C15111yescharacteristic
307C2—21no—
308C2—21no—
309C2—81no—
310C2#1806×C15111yescharacteristic
311C2#1812×C15111yescharacteristic
312C2#1816×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×#107×C151C2semidirect
3. #1568×C151C2semidirect
5. #1285×C151C2semidirect
7. #446×C151C4semidirect
8. C8×Q8×C151C4semidirect
9. #436×C151C4semidirect
12. C8×D4×C151C4semidirect
156. #8697C151direct (N × H)
157. C151#8697direct (N × H)
159. C4×#107C2×C151semidirect
160. #1568C2×C151semidirect
162. #1285C2×C151semidirect
164. #446C4×C151semidirect
165. C8×Q8C4×C151semidirect
166. #436C4×C151semidirect
169. 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×#107×C1512
#1568×C1512
#1509×C1512
#1285×C1512
#8697151