Finite Group Databasebeta

← C151×#19854 #50324779

Subgroups — C151×#19854 #50324779

Order 38656.

612 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3397×C151C211yesmaximal, characteristic, complemented
2#3341×C151C211yesmaximal, characteristic, complemented
3#3340×C151C211yesmaximal, characteristic, complemented
4#3305×C151C211yesmaximal, characteristic, complemented
5#1714×C151C211yesmaximal, characteristic, complemented
6#1696×C151C211yesmaximal, characteristic, complemented
7#1677×C151C211yesmaximal, characteristic, complemented
8#1671×C151C211yesmaximal, characteristic, complemented
9#1665×C151C211yesmaximal, characteristic, complemented
10#1646×C151C211yesmaximal, characteristic, complemented
11#1638×C151C211yesmaximal, characteristic, complemented
12#1631×C151C211yesmaximal, characteristic, complemented
13#1624×C151C211yesmaximal, characteristic, complemented
14#1582×C151C211yesmaximal, characteristic, complemented
15#1580×C151C211yesmaximal, characteristic, complemented
16#556×C151C2211yescharacteristic
17#555×C151C2211yescharacteristic
18#555×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#498×C151C2211yescharacteristic
22#496×C151—21no—
23#492×C151C2211yescharacteristic
24#492×C151C2211yescharacteristic
25#487×C151C2211yescharacteristic
26#486×C151C2211yescharacteristic
27#485×C151—21no—
28#482×C151—21no—
29#482×C151—21no—
30#482×C151—21no—
31#482×C151—21no—
32#477×C151C2211yescharacteristic
33#477×C151C2211yescharacteristic
34#476×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#474×C151C2211yescharacteristic
37#466×C151—21no—
38#466×C151—21no—
39#465×C151—21no—
40#463×C151—21no—
41#461×C151C2211yescharacteristic
42#460×C151—21no—
43#459×C151C2211yescharacteristic
44#459×C151C2211yescharacteristic
45#449×C151—21no—
46#446×C151C2211yescharacteristic
47#440×C151—21no—
48C4×SD16×C151C2211yescharacteristic
49C4×D8×C151C2211yescharacteristic
50C8×D4×C151C2211yescharacteristic
51C8×D4×C151C2211yescharacteristic
52C8×D4×C151C2211yescharacteristic
53#427×C151—21no—
54#427×C151—21no—
55#416×C151—21no—
56#334×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63D4⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×SD16×C151—21no—
69C2×SD16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—41no—
72C2×SD16×C151D411yescharacteristic
73C2×D8×C151—21no—
74C2×D8×C151—21no—
75C2×D8×C151D411yescharacteristic
76C22×C8×C151—21no—
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82#127×C151—21no—
83#127×C151C2311yescharacteristic
84#126×C151—41no—
85#124×C151—21no—
86#124×C151—41no—
87#124×C151—41no—
88C22⋊Q8×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151—41no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2311yescharacteristic
97C4×D4×C151—21no—
98C4×D4×C151C2311yescharacteristic
99C4×D4×C151C2311yescharacteristic
100C4×D4×C151C2311yescharacteristic
101#117×C151—21no—
102#117×C151—21no—
103#117×C151—21no—
104#117×C151—21no—
105#117×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151—21no—
109#107×C151—21no—
110#107×C151—21no—
111#107×C151D411yescharacteristic
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115#106×C151—21no—
116#106×C151D411yescharacteristic
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—41no—
126#103×C151D411yescharacteristic
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151D411yescharacteristic
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140#97×C151—21no—
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—42no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151C2×D411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—41no—
154C2×D4×C151—41no—
155C2×D4×C151—41no—
156C2×D4×C151—41no—
157C2×D4×C151C2×D411yescharacteristic
158C2×D4×C151C2×D411yescharacteristic
159C2×D4×C151C2×D411yescharacteristic
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—41no—
164SD16×C151—41no—
165SD16×C151—42no—
166SD16×C151—81no—
167SD16×C151—81no—
168SD16×C151—82no—
169D8×C151—22no—
170D8×C151—81no—
171D8×C151—81no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—42no—
178C2×C8×C151—42no—
179C2×C8×C151—81no—
180C2×C8×C151C2×D411yescharacteristic
181C2×C8×C151C2×D411yescharacteristic
182C2×C8×C151C2×D411yescharacteristic
183C2×C8×C151C2×D411yescharacteristic
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D411yescharacteristic
194C4⋊C4×C151C2×D411yescharacteristic
195C4⋊C4×C151C2×D411yescharacteristic
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C22⋊C4×C151—41no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C42×C151—21no—
207C42×C151—41no—
208C42×C151—41no—
209C42×C151—41no—
210C42×C151C2411yescharacteristic
211C23×C151—21no—
212C23×C151—21no—
213C23×C151—21no—
214C23×C151—41no—
215Q8×C151—21no—
216Q8×C151—21no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—81no—
220Q8×C151—81no—
221D4×C151—21no—
222D4×C151—21no—
223D4×C151—21no—
224D4×C151—21no—
225D4×C151—21no—
226D4×C151—21no—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—81no—
232D4×C151—82no—
233D4×C151—161no—
234D4×C151—161no—
235D4×C151—161no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—82no—
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C2×C4×C151H(5,𝔽2)11yescharacteristic
254C8×C151—21no—
255C8×C151—21no—
256C8×C151—21no—
257C8×C151—41no—
258C8×C151—41no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151#13512yes—
263C22×C151—41no—
264C22×C151—41no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—81no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151D4211yescharacteristic
276C4×C151—21no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—41no—
280C4×C151—41no—
281C4×C151—41no—
282C4×C151—81no—
283C4×C151—81no—
284C4×C151—81no—
285C4×C151C2×#13511yescharacteristic
286C4×C151#57511yescharacteristic
287C4×C151#57711yescharacteristic
288C4×C151#57711yescharacteristic
289C2×C151—81no—
290C2×C151—81no—
291C2×C151—81no—
292C2×C151—161no—
293C2×C151#326711yescharacteristic
294C2×C151#328411yescharacteristic
295C2×C151#328811yescharacteristic
296#19854C15111yesmaximal, characteristic, direct product factor, Sylow
297C151#1985411yescharacteristic, direct product factor, Sylow
298#3397C2×C15111yescharacteristic, complemented
299#3341C2×C15111yescharacteristic, complemented
300#3340C2×C15111yescharacteristic, complemented
301#3305C2×C15111yescharacteristic, complemented
302#1714C2×C15111yescharacteristic, complemented
303#1696C2×C15111yescharacteristic, complemented
304#1677C2×C15111yescharacteristic, complemented
305#1671C2×C15111yescharacteristic, complemented
306#1665C2×C15111yescharacteristic, complemented
307#1646C2×C15111yescharacteristic, complemented
308#1638C2×C15111yescharacteristic, complemented
309#1631C2×C15111yescharacteristic, complemented
310#1624C2×C15111yescharacteristic, complemented
311#1582C2×C15111yescharacteristic, complemented
312#1580C2×C15111yescharacteristic, complemented
313#556C22×C15111yescharacteristic
314#555C22×C15111yescharacteristic
315#555C22×C15111yescharacteristic
316#550C22×C15111yescharacteristic
317#500C22×C15111yescharacteristic
318#498C22×C15111yescharacteristic
319#496—21no—
320#492C22×C15111yescharacteristic
321#492C22×C15111yescharacteristic
322#487C22×C15111yescharacteristic
323#486C22×C15111yescharacteristic
324#485—21no—
325#482—21no—
326#482—21no—
327#482—21no—
328#482—21no—
329#477C22×C15111yescharacteristic
330#477C22×C15111yescharacteristic
331#476C22×C15111yescharacteristic
332#476C22×C15111yescharacteristic
333#474C22×C15111yescharacteristic
334#466—21no—
335#466—21no—
336#465—21no—
337#463—21no—
338#461C22×C15111yescharacteristic
339#460—21no—
340#459C22×C15111yescharacteristic
341#459C22×C15111yescharacteristic
342#449—21no—
343#446C22×C15111yescharacteristic
344#440—21no—
345C4×SD16C22×C15111yescharacteristic
346C4×D8C22×C15111yescharacteristic
347C8×D4C22×C15111yescharacteristic
348C8×D4C22×C15111yescharacteristic
349C8×D4C22×C15111yescharacteristic
350#427—21no—
351#427—21no—
352#416—21no—
353#334C22×C15111yescharacteristic
354#334C22×C15111yescharacteristic
355#333C22×C15111yescharacteristic
356#333C22×C15111yescharacteristic
357#332C22×C15111yescharacteristic
358#331C22×C15111yescharacteristic
359Q8⋊C8C22×C15111yescharacteristic
360D4⋊C8C22×C15111yescharacteristic
361D4⋊C8C22×C15111yescharacteristic
362D4⋊C8C22×C15111yescharacteristic
363#322C22×C15111yescharacteristic
364C2×#41—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—41no—
369C2×SD16D4×C15111yescharacteristic
370C2×D8—21no—
371C2×D8—21no—
372C2×D8D4×C15111yescharacteristic
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8C23×C15111yescharacteristic
377C4⋊Q8C23×C15111yescharacteristic
378C4⋊Q8C23×C15111yescharacteristic
379#127—21no—
380#127C23×C15111yescharacteristic
381#126—41no—
382#124—21no—
383#124—41no—
384#124—41no—
385C22⋊Q8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8C23×C15111yescharacteristic
394C4×D4—21no—
395C4×D4C23×C15111yescharacteristic
396C4×D4C23×C15111yescharacteristic
397C4×D4C23×C15111yescharacteristic
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107D4×C15111yescharacteristic
409#106—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106D4×C15111yescharacteristic
414C4⋊C8—21no—
415C4⋊C8C23×C15111yescharacteristic
416C4⋊C8C23×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418C4⋊C8C23×C15111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C15111yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102D4×C15111yescharacteristic
432#102D4×C15111yescharacteristic
433#102D4×C15111yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97—21no—
438C4×C8C23×C15111yescharacteristic
439C4×C8C23×C15111yescharacteristic
440C4×C8C23×C15111yescharacteristic
441#41—42no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C15111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C15111yescharacteristic
455C2×D4C2×D4×C15111yescharacteristic
456C2×D4C2×D4×C15111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461SD16—41no—
462SD16—42no—
463SD16—81no—
464SD16—81no—
465SD16—82no—
466D8—22no—
467D8—81no—
468D8—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—42no—
476C2×C8—81no—
477C2×C8C2×D4×C15111yescharacteristic
478C2×C8C2×D4×C15111yescharacteristic
479C2×C8C2×D4×C15111yescharacteristic
480C2×C8C2×D4×C15111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C15111yescharacteristic
490C4⋊C4C2×D4×C15111yescharacteristic
491C4⋊C4C2×D4×C15111yescharacteristic
492C4⋊C4C2×D4×C15111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—41no—
505C42—41no—
506C42—41no—
507C42C24×C15111yescharacteristic
508C23—21no—
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531D4—161no—
532D4—161no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4C22×D4×C15111yescharacteristic
549C2×C4C22×D4×C15111yescharacteristic
550C2×C4H(5,𝔽2)×C15111yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8#135×C15112yes—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D42×C15111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4C2×#135×C15111yescharacteristic
583C4#575×C15111yescharacteristic
584C4#577×C15111yescharacteristic
585C4#577×C15111yescharacteristic
586C2—81no—
587C2—81no—
588C2—81no—
589C2—161no—
590C2#3267×C15111yescharacteristic
591C2#3284×C15111yescharacteristic
592C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3397×C151C2semidirect
2. #3341×C151C2semidirect
3. #3340×C151C2semidirect
4. #3305×C151C2semidirect
5. #1714×C151C2semidirect
6. #1696×C151C2semidirect
7. #1677×C151C2semidirect
8. #1671×C151C2semidirect
9. #1665×C151C2semidirect
10. #1646×C151C2semidirect
11. #1638×C151C2semidirect
12. #1631×C151C2semidirect
13. #1624×C151C2semidirect
14. #1582×C151C2semidirect
15. #1580×C151C2semidirect
296. #19854C151direct (N × H)
297. C151#19854direct (N × H)
298. #3397C2×C151semidirect
299. #3341C2×C151semidirect
300. #3340C2×C151semidirect
301. #3305C2×C151semidirect
302. #1714C2×C151semidirect
303. #1696C2×C151semidirect
304. #1677C2×C151semidirect
305. #1671C2×C151semidirect
306. #1665C2×C151semidirect
307. #1646C2×C151semidirect
308. #1638C2×C151semidirect
309. #1631C2×C151semidirect
310. #1624C2×C151semidirect
311. #1582C2×C151semidirect
312. #1580C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3397×C1512
#3341×C1512
#3340×C1512
#3305×C1512
#1714×C1512
#1696×C1512
#1677×C1512
#1671×C1512
#1665×C1512
#1646×C1512
#1638×C1512
#1631×C1512
#1624×C1512
#1582×C1512
#1580×C1512
#19854151