Finite Group Databasebeta

← C151×#9323 #50314248

Subgroups — C151×#9323 #50314248

Order 38656.

612 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3110×C151C211yesmaximal, characteristic
2#2275×C151C211yesmaximal, characteristic
3#1986×C151C211yesmaximal, characteristic, complemented
4#1506×C151C211yesmaximal, characteristic, complemented
5#1490×C151C211yesmaximal, characteristic
6#1300×C151C211yesmaximal, characteristic, complemented
7#1285×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9C2×C4×D4×C151—21no—
10C2×C4×D4×C151C2211yescharacteristic
11#484×C151—21no—
12#474×C151C412yescomplemented
13#461×C151C412yescomplemented
14#450×C151—21no—
15#440×C151—22no—
16#432×C151C2211yescharacteristic
17#432×C151C2211yescharacteristic
18C4×M16×C151C2211yescharacteristic
19C4×C4⋊C4×C151—21no—
20C4×C4⋊C4×C151C2211yescharacteristic
21C4×C22⋊C4×C151—22no—
22C4×C22⋊C4×C151—21no—
23#376×C151C2211yescharacteristic
24C2×#95×C151—21no—
25#339×C151—22no—
26#328×C151—21no—
27#328×C151—21no—
28D4⋊C8×C151—22no—
29C22×D4×C151D411yescharacteristic
30C23×C4×C151—22no—
31C23×C4×C151—21no—
32C2×SD16×C151—22no—
33C2×M16×C151—21no—
34C4⋊Q8×C151C2×C411yescharacteristic, complemented
35C4⋊Q8×C151C2×C411yescharacteristic, complemented
36#125×C151—21no—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151—21no—
39C4×Q8×C151—21no—
40C4×Q8×C151—21no—
41C4×D4×C151—28no—
42C4×D4×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151C2×C412yes—
45C4×D4×C151D412yes—
46#117×C151—21no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151D411yescharacteristic
49C2×C22⋊C4×C151—22no—
50C2×C22⋊C4×C151—21no—
51C2×C42×C151—21no—
52C2×C42×C151—22no—
53C2×C42×C151D412yes—
54C2×C42×C151C2311yescharacteristic
55#107×C151—22no—
56C4⋊C8×C151—21no—
57C4⋊C8×C151C2×C412yescomplemented
58#103×C151—22no—
59#102×C151—22no—
60C22⋊C8×C151—21no—
61C22⋊C8×C151—21no—
62#97×C151—21no—
63#97×C151—21no—
64#97×C151—21no—
65C4×C8×C151—21no—
66#95×C151—22no—
67#95×C151—21no—
68#95×C151—21no—
69#95×C151D411yescharacteristic
70#95×C151D411yescharacteristic
71C24×C151—21no—
72C2×Q8×C151—21no—
73C2×Q8×C151—21no—
74C2×D4×C151—24no—
75C2×D4×C151—21no—
76C2×D4×C151C22⋊C412yes—
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—22no—
80C22×C4×C151—21no—
81C22×C4×C151—28no—
82C22×C4×C151—22no—
83C22×C4×C151—22no—
84C22×C4×C151—82no—
85C22×C4×C151—82no—
86C22×C4×C151—82no—
87C22×C4×C151C2×D411yescharacteristic
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90SD16×C151—44no—
91M16×C151—22no—
92M16×C151—41no—
93C2×C8×C151—22no—
94C2×C8×C151—41no—
95C2×C8×C151—41no—
96C4⋊C4×C151—24no—
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—41no—
103C4⋊C4×C151—41no—
104C4⋊C4×C151C22⋊C412yes—
105C22⋊C4×C151—28no—
106C22⋊C4×C151—22no—
107C22⋊C4×C151—22no—
108C22⋊C4×C151—41no—
109C42×C151—24no—
110C42×C151—42no—
111C42×C151—41no—
112C42×C151—82no—
113C42×C151C22×C411yescharacteristic
114C42×C151C2×D411yescharacteristic
115C42×C151#4111yescharacteristic
116C42×C151#4111yescharacteristic
117C23×C151—24no—
118C23×C151—22no—
119C23×C151—42no—
120C23×C151—41no—
121C23×C151—41no—
122C23×C151#12011yescharacteristic
123Q8×C151—42no—
124Q8×C151—81no—
125D4×C151—24no—
126D4×C151—22no—
127D4×C151#10414yes—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—22no—
131C2×C4×C151—22no—
132C2×C4×C151—22no—
133C2×C4×C151—24no—
134C2×C4×C151—22no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—42no—
138C2×C4×C151—42no—
139C2×C4×C151—41no—
140C2×C4×C151—42no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—82no—
146C2×C4×C151—82no—
147C2×C4×C151—88no—
148C2×C4×C151C2×C22⋊C411yescharacteristic
149C2×C4×C151C4×D411yescharacteristic
150C2×C4×C151C4×D411yescharacteristic
151C2×C4×C151#12111yescharacteristic
152C2×C4×C151#12111yescharacteristic
153C2×C4×C151#12311yescharacteristic
154C8×C151—42no—
155C8×C151—42no—
156C8×C151—81no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—24no—
160C22×C151—44no—
161C22×C151—44no—
162C22×C151—42no—
163C22×C151—42no—
164C22×C151#38611yescharacteristic
165C22×C151#45511yescharacteristic
166C22×C151#45611yescharacteristic
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—42no—
173C4×C151—44no—
174C4×C151—42no—
175C4×C151—42no—
176C4×C151—81no—
177C4×C151—81no—
178C4×C151C2×#10412yes—
179C2×C151—21no—
180C2×C151—21no—
181C2×C151—44no—
182C2×C151#188211yescharacteristic
183C2×C151#189611yescharacteristic
184C2×C151#190411yescharacteristic
185#9323C15111yesmaximal, characteristic, direct product factor, Sylow
186C151#932311yescharacteristic, direct product factor, Sylow
187#3110C2×C15111yescharacteristic
188#2275C2×C15111yescharacteristic
189#1986C2×C15111yescharacteristic, complemented
190#1506C2×C15111yescharacteristic, complemented
191#1490C2×C15111yescharacteristic
192#1300C2×C15111yescharacteristic, complemented
193#1285C2×C15111yescharacteristic, complemented
194#533C22×C15111yescharacteristic
195C2×C4×D4—21no—
196C2×C4×D4C22×C15111yescharacteristic
197#484—21no—
198#474C4×C15112yescomplemented
199#461C4×C15112yescomplemented
200#450—21no—
201#440—22no—
202#432C22×C15111yescharacteristic
203#432C22×C15111yescharacteristic
204C4×M16C22×C15111yescharacteristic
205C4×C4⋊C4—21no—
206C4×C4⋊C4C22×C15111yescharacteristic
207C4×C22⋊C4—22no—
208C4×C22⋊C4—21no—
209#376C22×C15111yescharacteristic
210C2×#95—21no—
211#339—22no—
212#328—21no—
213#328—21no—
214D4⋊C8—22no—
215C22×D4D4×C15111yescharacteristic
216C23×C4—22no—
217C23×C4—21no—
218C2×SD16—22no—
219C2×M16—21no—
220C4⋊Q8C2×C4×C15111yescharacteristic, complemented
221C4⋊Q8C2×C4×C15111yescharacteristic, complemented
222#125—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×D4—28no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4C2×C4×C15112yes—
231C4×D4D4×C15112yes—
232#117—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C15111yescharacteristic
235C2×C22⋊C4—22no—
236C2×C22⋊C4—21no—
237C2×C42—21no—
238C2×C42—22no—
239C2×C42D4×C15112yes—
240C2×C42C23×C15111yescharacteristic
241#107—22no—
242C4⋊C8—21no—
243C4⋊C8C2×C4×C15112yescomplemented
244#103—22no—
245#102—22no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248#97—21no—
249#97—21no—
250#97—21no—
251C4×C8—21no—
252#95—22no—
253#95—21no—
254#95—21no—
255#95D4×C15111yescharacteristic
256#95D4×C15111yescharacteristic
257C24—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×D4—24no—
261C2×D4—21no—
262C2×D4C22⋊C4×C15112yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—28no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—82no—
271C22×C4—82no—
272C22×C4—82no—
273C22×C4C2×D4×C15111yescharacteristic
274C22×C4C2×D4×C15111yescharacteristic
275C22×C4C2×D4×C15111yescharacteristic
276SD16—44no—
277M16—22no—
278M16—41no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C4⋊C4—24no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C22⋊C4×C15112yes—
291C22⋊C4—28no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C42—24no—
296C42—42no—
297C42—41no—
298C42—82no—
299C42C22×C4×C15111yescharacteristic
300C42C2×D4×C15111yescharacteristic
301C42#41×C15111yescharacteristic
302C42#41×C15111yescharacteristic
303C23—24no—
304C23—22no—
305C23—42no—
306C23—41no—
307C23—41no—
308C23#120×C15111yescharacteristic
309Q8—42no—
310Q8—81no—
311D4—24no—
312D4—22no—
313D4#104×C15114yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—88no—
334C2×C4C2×C22⋊C4×C15111yescharacteristic
335C2×C4C4×D4×C15111yescharacteristic
336C2×C4C4×D4×C15111yescharacteristic
337C2×C4#121×C15111yescharacteristic
338C2×C4#121×C15111yescharacteristic
339C2×C4#123×C15111yescharacteristic
340C8—42no—
341C8—42no—
342C8—81no—
343C22—21no—
344C22—21no—
345C22—24no—
346C22—44no—
347C22—44no—
348C22—42no—
349C22—42no—
350C22#386×C15111yescharacteristic
351C22#455×C15111yescharacteristic
352C22#456×C15111yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—44no—
360C4—42no—
361C4—42no—
362C4—81no—
363C4—81no—
364C4C2×#104×C15112yes—
365C2—21no—
366C2—21no—
367C2—44no—
368C2#1882×C15111yescharacteristic
369C2#1896×C15111yescharacteristic
370C2#1904×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×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
3. #1986×C151C2semidirect
4. #1506×C151C2semidirect
6. #1300×C151C2semidirect
7. #1285×C151C2semidirect
12. #474×C151C4semidirect
13. #461×C151C4semidirect
34. C4⋊Q8×C151C2×C4semidirect
35. C4⋊Q8×C151C2×C4semidirect
57. C4⋊C8×C151C2×C4semidirect
185. #9323C151direct (N × H)
186. C151#9323direct (N × H)
189. #1986C2×C151semidirect
190. #1506C2×C151semidirect
192. #1300C2×C151semidirect
193. #1285C2×C151semidirect
198. #474C4×C151semidirect
199. #461C4×C151semidirect
220. C4⋊Q8C2×C4×C151semidirect
221. C4⋊Q8C2×C4×C151semidirect
243. C4⋊C8C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3110×C1512
#2275×C1512
#1986×C1512
#1506×C1512
#1490×C1512
#1300×C1512
#1285×C1512
#9323151