Finite Group Databasebeta

← C151×#19251 #50324176

Subgroups — C151×#19251 #50324176

Order 38656.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3248×C151C211yesmaximal, characteristic
2#3233×C151C211yesmaximal, characteristic
3#3185×C151C211yesmaximal, characteristic, complemented
4#2969×C151C211yesmaximal, characteristic
5#1704×C151C211yesmaximal, characteristic, complemented
6#1700×C151C211yesmaximal, characteristic, complemented
7#1691×C151C211yesmaximal, characteristic, complemented
8#1689×C151C211yesmaximal, characteristic, complemented
9#1683×C151C211yesmaximal, characteristic, complemented
10#1679×C151C211yesmaximal, characteristic, complemented
11#1672×C151C211yesmaximal, characteristic, complemented
12#1670×C151C211yesmaximal, characteristic, complemented
13#1565×C151C211yesmaximal, characteristic, complemented
14#1544×C151C211yesmaximal, characteristic, complemented
15#1542×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#533×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#499×C151—21no—
20#498×C151C2211yescharacteristic
21#494×C151C2211yescharacteristic
22#488×C151—21no—
23#487×C151C2211yescharacteristic
24#487×C151C2211yescharacteristic
25#485×C151—21no—
26#482×C151—21no—
27#479×C151—21no—
28#477×C151C2211yescharacteristic
29#476×C151C2211yescharacteristic
30#475×C151C2211yescharacteristic
31#475×C151C2211yescharacteristic
32#474×C151C2211yescharacteristic
33#474×C151C2211yescharacteristic
34#470×C151—21no—
35#470×C151—21no—
36#467×C151—21no—
37#465×C151—21no—
38#464×C151—21no—
39#462×C151C2211yescharacteristic
40#461×C151C2211yescharacteristic
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43#441×C151—21no—
44#441×C151—21no—
45#436×C151—21no—
46#436×C151C2211yescharacteristic
47#435×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#431×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#405×C151—21no—
54C4×M16×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#332×C151C2211yescharacteristic
66#332×C151C2211yescharacteristic
67C2×Q16×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—21no—
70C2×SD16×C151—21no—
71C2×M16×C151—21no—
72C2×M16×C151D411yescharacteristic
73C2×M16×C151D411yescharacteristic
74C22×C8×C151—21no—
75C22×C8×C151—21no—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#126×C151—21no—
81#125×C151—21no—
82#125×C151—21no—
83#125×C151D411yescharacteristic
84#124×C151D411yescharacteristic
85#123×C151—21no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151D411yescharacteristic
91#121×C151D411yescharacteristic
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2311yescharacteristic
97C4×D4×C151—21no—
98C4×D4×C151C2311yescharacteristic
99#117×C151—21no—
100#117×C151—21no—
101#117×C151—21no—
102C2×C42×C151C2311yescharacteristic
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136#97×C151—21no—
137#97×C151D411yescharacteristic
138#97×C151D411yescharacteristic
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151C2×D411yescharacteristic
149C2×D4×C151—21no—
150C2×D4×C151C2×D411yescharacteristic
151C22×C4×C151—21no—
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151#4111yescharacteristic
155Q16×C151—42no—
156Q16×C151—42no—
157Q16×C151—81no—
158SD16×C151—81no—
159M16×C151—22no—
160M16×C151—41no—
161M16×C151—42no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—42no—
169C2×C8×C151—81no—
170C2×C8×C151C2×D411yescharacteristic
171C2×C8×C151C2×D411yescharacteristic
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—41no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151C2×D411yescharacteristic
191C4⋊C4×C151C2×D411yescharacteristic
192C22⋊C4×C151—21no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—41no—
198C22⋊C4×C151—41no—
199C42×C151—21no—
200C42×C151—41no—
201C42×C151—41no—
202C42×C151C2×D411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151#4111yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—21no—
207C23×C151#12111yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—41no—
211Q8×C151—41no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—81no—
217D4×C151—21no—
218D4×C151—21no—
219D4×C151—81no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151#12111yescharacteristic
235C2×C4×C151#12111yescharacteristic
236C2×C4×C151#12111yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C22×D411yescharacteristic
239C2×C4×C151C2×#4111yescharacteristic
240C8×C151—21no—
241C8×C151—21no—
242C8×C151—21no—
243C8×C151—41no—
244C8×C151—41no—
245C8×C151—41no—
246C8×C151—41no—
247C8×C151—41no—
248C8×C151—41no—
249C8×C151#13512yes—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—21no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151C2×#12111yescharacteristic
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—21no—
260C4×C151—21no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—41no—
264C4×C151—81no—
265C4×C151—81no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151C2×#13511yescharacteristic
269C4×C151#57511yescharacteristic
270C4×C151#57711yescharacteristic
271C4×C151#57811yescharacteristic
272C2×C151—41no—
273C2×C151—81no—
274C2×C151#303511yescharacteristic
275C2×C151#306311yescharacteristic
276C2×C151#306911yescharacteristic
277#19251C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#1925111yescharacteristic, direct product factor, Sylow
279#3248C2×C15111yescharacteristic
280#3233C2×C15111yescharacteristic
281#3185C2×C15111yescharacteristic, complemented
282#2969C2×C15111yescharacteristic
283#1704C2×C15111yescharacteristic, complemented
284#1700C2×C15111yescharacteristic, complemented
285#1691C2×C15111yescharacteristic, complemented
286#1689C2×C15111yescharacteristic, complemented
287#1683C2×C15111yescharacteristic, complemented
288#1679C2×C15111yescharacteristic, complemented
289#1672C2×C15111yescharacteristic, complemented
290#1670C2×C15111yescharacteristic, complemented
291#1565C2×C15111yescharacteristic, complemented
292#1544C2×C15111yescharacteristic, complemented
293#1542C2×C15111yescharacteristic, complemented
294#533C22×C15111yescharacteristic
295#533C22×C15111yescharacteristic
296#529C22×C15111yescharacteristic
297#499—21no—
298#498C22×C15111yescharacteristic
299#494C22×C15111yescharacteristic
300#488—21no—
301#487C22×C15111yescharacteristic
302#487C22×C15111yescharacteristic
303#485—21no—
304#482—21no—
305#479—21no—
306#477C22×C15111yescharacteristic
307#476C22×C15111yescharacteristic
308#475C22×C15111yescharacteristic
309#475C22×C15111yescharacteristic
310#474C22×C15111yescharacteristic
311#474C22×C15111yescharacteristic
312#470—21no—
313#470—21no—
314#467—21no—
315#465—21no—
316#464—21no—
317#462C22×C15111yescharacteristic
318#461C22×C15111yescharacteristic
319#446C22×C15111yescharacteristic
320C8×Q8C22×C15111yescharacteristic
321#441—21no—
322#441—21no—
323#436—21no—
324#436C22×C15111yescharacteristic
325#435—21no—
326C8×D4C22×C15111yescharacteristic
327#433—21no—
328#431C22×C15111yescharacteristic
329#431C22×C15111yescharacteristic
330C2×C4⋊C8C22×C15111yescharacteristic
331#405—21no—
332C4×M16C22×C15111yescharacteristic
333#335C22×C15111yescharacteristic
334#335C22×C15111yescharacteristic
335#334C22×C15111yescharacteristic
336#334C22×C15111yescharacteristic
337#333C22×C15111yescharacteristic
338#333C22×C15111yescharacteristic
339#332C22×C15111yescharacteristic
340#332C22×C15111yescharacteristic
341#332C22×C15111yescharacteristic
342#332C22×C15111yescharacteristic
343#332C22×C15111yescharacteristic
344#332C22×C15111yescharacteristic
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×SD16—21no—
349C2×M16—21no—
350C2×M16D4×C15111yescharacteristic
351C2×M16D4×C15111yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8C23×C15111yescharacteristic
355C4⋊Q8C23×C15111yescharacteristic
356C4⋊Q8C23×C15111yescharacteristic
357C4⋊Q8C23×C15111yescharacteristic
358#126—21no—
359#125—21no—
360#125—21no—
361#125D4×C15111yescharacteristic
362#124D4×C15111yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8D4×C15111yescharacteristic
369#121D4×C15111yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C15111yescharacteristic
375C4×D4—21no—
376C4×D4C23×C15111yescharacteristic
377#117—21no—
378#117—21no—
379#117—21no—
380C2×C42C23×C15111yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8C23×C15111yescharacteristic
393C4⋊C8C23×C15111yescharacteristic
394C4⋊C8C23×C15111yescharacteristic
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414#97—21no—
415#97D4×C15111yescharacteristic
416#97D4×C15111yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C15111yescharacteristic
421C4×C8C23×C15111yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C15111yescharacteristic
427C2×D4—21no—
428C2×D4C2×D4×C15111yescharacteristic
429C22×C4—21no—
430C22×C4C2×D4×C15111yescharacteristic
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4#41×C15111yescharacteristic
433Q16—42no—
434Q16—42no—
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—41no—
439M16—42no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—81no—
448C2×C8C2×D4×C15111yescharacteristic
449C2×C8C2×D4×C15111yescharacteristic
450C2×C8C2×D4×C15111yescharacteristic
451C2×C8C2×D4×C15111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C15111yescharacteristic
469C4⋊C4C2×D4×C15111yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C2×D4×C15111yescharacteristic
481C42C2×D4×C15111yescharacteristic
482C42#41×C15111yescharacteristic
483C42C24×C15111yescharacteristic
484C23—21no—
485C23#121×C15111yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4#121×C15111yescharacteristic
513C2×C4#121×C15111yescharacteristic
514C2×C4#121×C15111yescharacteristic
515C2×C4C22×D4×C15111yescharacteristic
516C2×C4C22×D4×C15111yescharacteristic
517C2×C4C2×#41×C15111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8#135×C15112yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#121×C15111yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×#135×C15111yescharacteristic
547C4#575×C15111yescharacteristic
548C4#577×C15111yescharacteristic
549C4#578×C15111yescharacteristic
550C2—41no—
551C2—81no—
552C2#3035×C15111yescharacteristic
553C2#3063×C15111yescharacteristic
554C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×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
3. #3185×C151C2semidirect
5. #1704×C151C2semidirect
6. #1700×C151C2semidirect
7. #1691×C151C2semidirect
8. #1689×C151C2semidirect
9. #1683×C151C2semidirect
10. #1679×C151C2semidirect
11. #1672×C151C2semidirect
12. #1670×C151C2semidirect
13. #1565×C151C2semidirect
14. #1544×C151C2semidirect
15. #1542×C151C2semidirect
277. #19251C151direct (N × H)
278. C151#19251direct (N × H)
281. #3185C2×C151semidirect
283. #1704C2×C151semidirect
284. #1700C2×C151semidirect
285. #1691C2×C151semidirect
286. #1689C2×C151semidirect
287. #1683C2×C151semidirect
288. #1679C2×C151semidirect
289. #1672C2×C151semidirect
290. #1670C2×C151semidirect
291. #1565C2×C151semidirect
292. #1544C2×C151semidirect
293. #1542C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3248×C1512
#3233×C1512
#3185×C1512
#2969×C1512
#1704×C1512
#1700×C1512
#1691×C1512
#1689×C1512
#1683×C1512
#1679×C1512
#1672×C1512
#1670×C1512
#1565×C1512
#1544×C1512
#1542×C1512
#19251151