Finite Group Databasebeta

← C151×#19395 #50324320

Subgroups — C151×#19395 #50324320

Order 38656.

628 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3231×C151C211yesmaximal, characteristic, complemented
2#3110×C151C211yesmaximal, characteristic
3#3101×C151C211yesmaximal, characteristic
4#2972×C151C211yesmaximal, characteristic
5#1683×C151C212yesmaximal, complemented
6#1679×C151C212yesmaximal, complemented
7#1673×C151C212yesmaximal, complemented
8#1671×C151C212yesmaximal, complemented
9#1572×C151C211yesmaximal, characteristic, complemented
10#1554×C151C211yesmaximal, characteristic, complemented
11#1544×C151C211yesmaximal, characteristic, complemented
12#533×C151C2211yescharacteristic
13#533×C151C2211yescharacteristic
14C2×C4×D4×C151C2211yescharacteristic
15#500×C151C2211yescharacteristic, complemented
16#498×C151C2211yescharacteristic, complemented
17#487×C151C2211yescharacteristic, complemented
18#487×C151C2211yescharacteristic, complemented
19#485×C151—22no—
20#484×C151—21no—
21#483×C151—21no—
22#479×C151—22no—
23#476×C151C2212yes—
24#474×C151C2212yes—
25#461×C151C2212yes—
26#461×C151C2212yes—
27#450×C151—21no—
28#450×C151—21no—
29#440×C151—22no—
30C4×SD16×C151—22no—
31C8×D4×C151—22no—
32C8×D4×C151C2212yes—
33C8×D4×C151C2212yes—
34#432×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38C2×C22⋊C8×C151—22no—
39#335×C151C2212yescomplemented
40#334×C151C2212yescomplemented
41#333×C151C2212yescomplemented
42#332×C151C2212yescomplemented
43#332×C151C2212yescomplemented
44#332×C151C2212yescomplemented
45C22×D4×C151D411yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—22no—
49C22×C8×C151—22no—
50C22×C8×C151—22no—
51C4⋊Q8×C151C2311yescharacteristic
52C4⋊Q8×C151C2311yescharacteristic
53C4⋊Q8×C151C2311yescharacteristic
54C4⋊Q8×C151C2311yescharacteristic
55#125×C151—21no—
56#125×C151—21no—
57C22⋊Q8×C151—21no—
58C22⋊Q8×C151—21no—
59C22⋊Q8×C151—21no—
60C22⋊Q8×C151—21no—
61C4×Q8×C151—21no—
62C4×Q8×C151—21no—
63C4×Q8×C151—21no—
64C4×Q8×C151—21no—
65C4×D4×C151—21no—
66C4×D4×C151—21no—
67C4×D4×C151D412yes—
68C4×D4×C151C2312yes—
69#117×C151—21no—
70#117×C151—21no—
71C2×C4⋊C4×C151D411yescharacteristic
72C2×C22⋊C4×C151—21no—
73C2×C42×C151C2311yescharacteristic
74#107×C151—22no—
75#107×C151—22no—
76#106×C151—22no—
77#106×C151—22no—
78C4⋊C8×C151D412yes—
79C4⋊C8×C151C2312yes—
80C4⋊C8×C151C2312yes—
81C4⋊C8×C151C2312yes—
82#103×C151—22no—
83#103×C151—22no—
84#103×C151—22no—
85#103×C151—22no—
86#102×C151—22no—
87#102×C151—22no—
88C22⋊C8×C151—21no—
89C22⋊C8×C151—21no—
90C22⋊C8×C151—21no—
91C22⋊C8×C151—22no—
92C22⋊C8×C151—22no—
93C22⋊C8×C151D412yes—
94#97×C151—21no—
95C4×C8×C151—21no—
96C4×C8×C151—21no—
97C4×C8×C151C2311yescharacteristic
98C4×C8×C151C2311yescharacteristic
99C24×C151—21no—
100C2×Q8×C151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×D4×C151—24no—
105C2×D4×C151—21no—
106C2×D4×C151C2×D412yes—
107C22×C4×C151—21no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—82no—
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151#4111yescharacteristic
114SD16×C151—44no—
115SD16×C151—44no—
116C2×C8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151—22no—
119C2×C8×C151—82no—
120C2×C8×C151—82no—
121C2×C8×C151C2×D412yes—
122C2×C8×C151C2×D412yes—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—41no—
133C4⋊C4×C151—41no—
134C4⋊C4×C151—41no—
135C4⋊C4×C151—41no—
136C4⋊C4×C151C2×D412yes—
137C22⋊C4×C151—22no—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—41no—
140C22⋊C4×C151—41no—
141C42×C151—41no—
142C42×C151—41no—
143C42×C151C2×D411yescharacteristic
144C42×C151C2×D411yescharacteristic
145C42×C151#4111yescharacteristic
146C42×C151C2411yescharacteristic
147C23×C151—24no—
148C23×C151—22no—
149C23×C151—81no—
150C23×C151—81no—
151C23×C151#12111yescharacteristic
152Q8×C151—42no—
153Q8×C151—42no—
154Q8×C151—42no—
155Q8×C151—81no—
156D4×C151—24no—
157D4×C151—22no—
158D4×C151#13514yes—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—41no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—41no—
169C2×C4×C151—82no—
170C2×C4×C151—81no—
171C2×C4×C151#12111yescharacteristic
172C2×C4×C151#12111yescharacteristic
173C2×C4×C151#12111yescharacteristic
174C2×C4×C151C22×D411yescharacteristic
175C2×C4×C151C22×D411yescharacteristic
176C2×C4×C151C2×#4111yescharacteristic
177C8×C151—22no—
178C8×C151—22no—
179C8×C151—42no—
180C8×C151—42no—
181C8×C151—42no—
182C22×C151—21no—
183C22×C151—21no—
184C22×C151—24no—
185C22×C151—21no—
186C22×C151—42no—
187C22×C151—42no—
188C22×C151—84no—
189C22×C151C2×#12111yescharacteristic
190C4×C151—21no—
191C4×C151—21no—
192C4×C151—21no—
193C4×C151—21no—
194C4×C151—42no—
195C4×C151—81no—
196C4×C151—81no—
197C4×C151—81no—
198C4×C151—81no—
199C4×C151C2×#13512yes—
200C4×C151#57712yes—
201C2×C151—41no—
202C2×C151—44no—
203C2×C151#304211yescharacteristic
204C2×C151#305011yescharacteristic
205C2×C151#306911yescharacteristic
206#19395C15111yesmaximal, characteristic, direct product factor, Sylow
207C151#1939511yescharacteristic, direct product factor, Sylow
208#3231C2×C15111yescharacteristic, complemented
209#3110C2×C15111yescharacteristic
210#3101C2×C15111yescharacteristic
211#2972C2×C15111yescharacteristic
212#1683C2×C15112yescomplemented
213#1679C2×C15112yescomplemented
214#1673C2×C15112yescomplemented
215#1671C2×C15112yescomplemented
216#1572C2×C15111yescharacteristic, complemented
217#1554C2×C15111yescharacteristic, complemented
218#1544C2×C15111yescharacteristic, complemented
219#533C22×C15111yescharacteristic
220#533C22×C15111yescharacteristic
221C2×C4×D4C22×C15111yescharacteristic
222#500C22×C15111yescharacteristic, complemented
223#498C22×C15111yescharacteristic, complemented
224#487C22×C15111yescharacteristic, complemented
225#487C22×C15111yescharacteristic, complemented
226#485—22no—
227#484—21no—
228#483—21no—
229#479—22no—
230#476C22×C15112yes—
231#474C22×C15112yes—
232#461C22×C15112yes—
233#461C22×C15112yes—
234#450—21no—
235#450—21no—
236#440—22no—
237C4×SD16—22no—
238C8×D4—22no—
239C8×D4C22×C15112yes—
240C8×D4C22×C15112yes—
241#432C22×C15111yescharacteristic
242#431C22×C15111yescharacteristic
243#431C22×C15111yescharacteristic
244#431C22×C15111yescharacteristic
245C2×C22⋊C8—22no—
246#335C22×C15112yescomplemented
247#334C22×C15112yescomplemented
248#333C22×C15112yescomplemented
249#332C22×C15112yescomplemented
250#332C22×C15112yescomplemented
251#332C22×C15112yescomplemented
252C22×D4D4×C15111yescharacteristic
253C23×C4—21no—
254C2×SD16—22no—
255C2×SD16—22no—
256C22×C8—22no—
257C22×C8—22no—
258C4⋊Q8C23×C15111yescharacteristic
259C4⋊Q8C23×C15111yescharacteristic
260C4⋊Q8C23×C15111yescharacteristic
261C4⋊Q8C23×C15111yescharacteristic
262#125—21no—
263#125—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4D4×C15112yes—
275C4×D4C23×C15112yes—
276#117—21no—
277#117—21no—
278C2×C4⋊C4D4×C15111yescharacteristic
279C2×C22⋊C4—21no—
280C2×C42C23×C15111yescharacteristic
281#107—22no—
282#107—22no—
283#106—22no—
284#106—22no—
285C4⋊C8D4×C15112yes—
286C4⋊C8C23×C15112yes—
287C4⋊C8C23×C15112yes—
288C4⋊C8C23×C15112yes—
289#103—22no—
290#103—22no—
291#103—22no—
292#103—22no—
293#102—22no—
294#102—22no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—22no—
299C22⋊C8—22no—
300C22⋊C8D4×C15112yes—
301#97—21no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8C23×C15111yescharacteristic
305C4×C8C23×C15111yescharacteristic
306C24—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×D4—24no—
312C2×D4—21no—
313C2×D4C2×D4×C15112yes—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—82no—
318C22×C4C2×D4×C15111yescharacteristic
319C22×C4C2×D4×C15111yescharacteristic
320C22×C4#41×C15111yescharacteristic
321SD16—44no—
322SD16—44no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—82no—
327C2×C8—82no—
328C2×C8C2×D4×C15112yes—
329C2×C8C2×D4×C15112yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C2×D4×C15112yes—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C42—41no—
349C42—41no—
350C42C2×D4×C15111yescharacteristic
351C42C2×D4×C15111yescharacteristic
352C42#41×C15111yescharacteristic
353C42C24×C15111yescharacteristic
354C23—24no—
355C23—22no—
356C23—81no—
357C23—81no—
358C23#121×C15111yescharacteristic
359Q8—42no—
360Q8—42no—
361Q8—42no—
362Q8—81no—
363D4—24no—
364D4—22no—
365D4#135×C15114yes—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4#121×C15111yescharacteristic
379C2×C4#121×C15111yescharacteristic
380C2×C4#121×C15111yescharacteristic
381C2×C4C22×D4×C15111yescharacteristic
382C2×C4C22×D4×C15111yescharacteristic
383C2×C4C2×#41×C15111yescharacteristic
384C8—22no—
385C8—22no—
386C8—42no—
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—24no—
392C22—21no—
393C22—42no—
394C22—42no—
395C22—84no—
396C22C2×#121×C15111yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C4C2×#135×C15112yes—
407C4#577×C15112yes—
408C2—41no—
409C2—44no—
410C2#3042×C15111yescharacteristic
411C2#3050×C15111yescharacteristic
412C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×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
1. #3231×C151C2semidirect
5. #1683×C151C2semidirect
6. #1679×C151C2semidirect
7. #1673×C151C2semidirect
8. #1671×C151C2semidirect
9. #1572×C151C2semidirect
10. #1554×C151C2semidirect
11. #1544×C151C2semidirect
15. #500×C151C22semidirect
16. #498×C151C22semidirect
17. #487×C151C22semidirect
18. #487×C151C22semidirect
39. #335×C151C22semidirect
40. #334×C151C22semidirect
41. #333×C151C22semidirect
42. #332×C151C22semidirect
43. #332×C151C22semidirect
44. #332×C151C22semidirect
206. #19395C151direct (N × H)
207. C151#19395direct (N × H)
208. #3231C2×C151semidirect
212. #1683C2×C151semidirect
213. #1679C2×C151semidirect
214. #1673C2×C151semidirect
215. #1671C2×C151semidirect
216. #1572C2×C151semidirect
217. #1554C2×C151semidirect
218. #1544C2×C151semidirect
222. #500C22×C151semidirect
223. #498C22×C151semidirect
224. #487C22×C151semidirect
225. #487C22×C151semidirect
246. #335C22×C151semidirect
247. #334C22×C151semidirect
248. #333C22×C151semidirect
249. #332C22×C151semidirect
250. #332C22×C151semidirect
251. #332C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3231×C1512
#3110×C1512
#3101×C1512
#2972×C1512
#1683×C1512
#1679×C1512
#1673×C1512
#1671×C1512
#1572×C1512
#1554×C1512
#1544×C1512
#19395151