Finite Group Databasebeta

← C151×#19862 #50324787

Subgroups — C151×#19862 #50324787

Order 38656.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3354×C151C211yesmaximal, characteristic, complemented
2#3341×C151C211yesmaximal, characteristic, complemented
3#3341×C151C211yesmaximal, characteristic, complemented
4#3303×C151C211yesmaximal, characteristic, complemented
5#1723×C151C211yesmaximal, characteristic, complemented
6#1695×C151C211yesmaximal, characteristic, complemented
7#1683×C151C211yesmaximal, characteristic, complemented
8#1675×C151C211yesmaximal, characteristic, complemented
9#1671×C151C211yesmaximal, characteristic, complemented
10#1646×C151C211yesmaximal, characteristic, complemented
11#1635×C151C211yesmaximal, characteristic, complemented
12#1634×C151C211yesmaximal, characteristic, complemented
13#1634×C151C211yesmaximal, characteristic, complemented
14#1581×C151C211yesmaximal, characteristic, complemented
15#1580×C151C211yesmaximal, characteristic, complemented
16#555×C151C2211yescharacteristic
17#555×C151C2211yescharacteristic
18#555×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#500×C151C2211yescharacteristic
22#498×C151C2211yescharacteristic
23#494×C151C2211yescharacteristic
24#487×C151C2211yescharacteristic
25#487×C151C2211yescharacteristic
26#485×C151—21no—
27#482×C151—21no—
28#482×C151—21no—
29#482×C151—21no—
30#482×C151—21no—
31#482×C151—21no—
32#481×C151—21no—
33#476×C151C2211yescharacteristic
34#476×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#476×C151C2211yescharacteristic
37#476×C151C2211yescharacteristic
38#476×C151C2211yescharacteristic
39#474×C151C2211yescharacteristic
40#469×C151—21no—
41#466×C151—21no—
42#466×C151—21no—
43#465×C151—21no—
44#461×C151C2211yescharacteristic
45#449×C151—21no—
46C4×D8×C151C2211yescharacteristic
47C4×D8×C151C2211yescharacteristic
48#436×C151C2211yescharacteristic
49C8×D4×C151C2211yescharacteristic
50C8×D4×C151C2211yescharacteristic
51C8×D4×C151C2211yescharacteristic
52#428×C151—21no—
53#427×C151—21no—
54#427×C151—21no—
55#416×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62D4⋊C8×C151C2211yescharacteristic
63D4⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—41no—
69C2×SD16×C151—21no—
70C2×D8×C151D411yescharacteristic
71C2×D8×C151D411yescharacteristic
72C2×M16×C151—21no—
73C22×C8×C151—21no—
74C22×C8×C151—21no—
75C22×C8×C151—21no—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#124×C151—41no—
81#124×C151—41no—
82#124×C151—41no—
83#123×C151—41no—
84C22⋊Q8×C151—21no—
85#121×C151—21no—
86#121×C151—21no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92C4×D4×C151C2311yescharacteristic
93C4×D4×C151C2311yescharacteristic
94C4×D4×C151C2311yescharacteristic
95C4×D4×C151C2311yescharacteristic
96#117×C151—21no—
97#117×C151—21no—
98#117×C151—21no—
99#117×C151—21no—
100#117×C151—21no—
101#117×C151—21no—
102C2×C4⋊C4×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151D411yescharacteristic
109#107×C151D411yescharacteristic
110#106×C151—21no—
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115#106×C151—21no—
116#106×C151—21no—
117#106×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#102×C151—21no—
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×C151D411yescharacteristic
134#102×C151D411yescharacteristic
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C22⋊C8×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×C151—21no—
150C2×D4×C151—41no—
151C2×D4×C151—41no—
152C2×D4×C151—41no—
153C2×D4×C151—41no—
154C2×D4×C151C2×D411yescharacteristic
155C2×D4×C151C2×D411yescharacteristic
156C2×D4×C151C2×D411yescharacteristic
157C2×D4×C151C2×D411yescharacteristic
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—41no—
163Q16×C151—82no—
164SD16×C151—81no—
165D8×C151—22no—
166D8×C151—41no—
167M16×C151—42no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—42no—
174C2×C8×C151—42no—
175C2×C8×C151—81no—
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
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—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151C2×D411yescharacteristic
190C4⋊C4×C151C2×D411yescharacteristic
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—41no—
198C22⋊C4×C151—41no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C22⋊C4×C151—41no—
203C22⋊C4×C151—41no—
204C42×C151—41no—
205C42×C151—41no—
206C42×C151—41no—
207C42×C151C2411yescharacteristic
208C23×C151—21no—
209C23×C151—21no—
210C23×C151—21no—
211C23×C151—21no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—81no—
215Q8×C151—81no—
216Q8×C151—81no—
217D4×C151—21no—
218D4×C151—21no—
219D4×C151—21no—
220D4×C151—21no—
221D4×C151—21no—
222D4×C151—21no—
223D4×C151—21no—
224D4×C151—21no—
225D4×C151—82no—
226D4×C151—161no—
227D4×C151—161no—
228D4×C151—161no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—82no—
246C2×C4×C151C22×D411yescharacteristic
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151H(5,𝔽2)11yescharacteristic
249C8×C151—21no—
250C8×C151—21no—
251C8×C151—21no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—41no—
257C8×C151#13512yes—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—41no—
261C22×C151—41no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—41no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151D4211yescharacteristic
271C4×C151—21no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—41no—
275C4×C151—41no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151—81no—
279C4×C151—81no—
280C4×C151C2×#13511yescharacteristic
281C4×C151#57511yescharacteristic
282C4×C151#57711yescharacteristic
283C4×C151#57811yescharacteristic
284C2×C151—81no—
285C2×C151—81no—
286C2×C151—81no—
287C2×C151—81no—
288C2×C151#326711yescharacteristic
289C2×C151#328311yescharacteristic
290C2×C151#328811yescharacteristic
291#19862C15111yesmaximal, characteristic, direct product factor, Sylow
292C151#1986211yescharacteristic, direct product factor, Sylow
293#3354C2×C15111yescharacteristic, complemented
294#3341C2×C15111yescharacteristic, complemented
295#3341C2×C15111yescharacteristic, complemented
296#3303C2×C15111yescharacteristic, complemented
297#1723C2×C15111yescharacteristic, complemented
298#1695C2×C15111yescharacteristic, complemented
299#1683C2×C15111yescharacteristic, complemented
300#1675C2×C15111yescharacteristic, complemented
301#1671C2×C15111yescharacteristic, complemented
302#1646C2×C15111yescharacteristic, complemented
303#1635C2×C15111yescharacteristic, complemented
304#1634C2×C15111yescharacteristic, complemented
305#1634C2×C15111yescharacteristic, complemented
306#1581C2×C15111yescharacteristic, complemented
307#1580C2×C15111yescharacteristic, complemented
308#555C22×C15111yescharacteristic
309#555C22×C15111yescharacteristic
310#555C22×C15111yescharacteristic
311#547C22×C15111yescharacteristic
312#500C22×C15111yescharacteristic
313#500C22×C15111yescharacteristic
314#498C22×C15111yescharacteristic
315#494C22×C15111yescharacteristic
316#487C22×C15111yescharacteristic
317#487C22×C15111yescharacteristic
318#485—21no—
319#482—21no—
320#482—21no—
321#482—21no—
322#482—21no—
323#482—21no—
324#481—21no—
325#476C22×C15111yescharacteristic
326#476C22×C15111yescharacteristic
327#476C22×C15111yescharacteristic
328#476C22×C15111yescharacteristic
329#476C22×C15111yescharacteristic
330#476C22×C15111yescharacteristic
331#474C22×C15111yescharacteristic
332#469—21no—
333#466—21no—
334#466—21no—
335#465—21no—
336#461C22×C15111yescharacteristic
337#449—21no—
338C4×D8C22×C15111yescharacteristic
339C4×D8C22×C15111yescharacteristic
340#436C22×C15111yescharacteristic
341C8×D4C22×C15111yescharacteristic
342C8×D4C22×C15111yescharacteristic
343C8×D4C22×C15111yescharacteristic
344#428—21no—
345#427—21no—
346#427—21no—
347#416—21no—
348#335C22×C15111yescharacteristic
349#334C22×C15111yescharacteristic
350#333C22×C15111yescharacteristic
351#333C22×C15111yescharacteristic
352#333C22×C15111yescharacteristic
353#332C22×C15111yescharacteristic
354D4⋊C8C22×C15111yescharacteristic
355D4⋊C8C22×C15111yescharacteristic
356D4⋊C8C22×C15111yescharacteristic
357D4⋊C8C22×C15111yescharacteristic
358#322C22×C15111yescharacteristic
359C2×#41—21no—
360C2×Q16—41no—
361C2×SD16—21no—
362C2×D8D4×C15111yescharacteristic
363C2×D8D4×C15111yescharacteristic
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8C23×C15111yescharacteristic
369C4⋊Q8C23×C15111yescharacteristic
370C4⋊Q8C23×C15111yescharacteristic
371C4⋊Q8C23×C15111yescharacteristic
372#124—41no—
373#124—41no—
374#124—41no—
375#123—41no—
376C22⋊Q8—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383#121—21no—
384C4×D4C23×C15111yescharacteristic
385C4×D4C23×C15111yescharacteristic
386C4×D4C23×C15111yescharacteristic
387C4×D4C23×C15111yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394C2×C4⋊C4—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107D4×C15111yescharacteristic
401#107D4×C15111yescharacteristic
402#106—21no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410C4⋊C8C23×C15111yescharacteristic
411C4⋊C8C23×C15111yescharacteristic
412C4⋊C8C23×C15111yescharacteristic
413C4⋊C8C23×C15111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C15111yescharacteristic
426#102D4×C15111yescharacteristic
427#102D4×C15111yescharacteristic
428#102D4×C15111yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C4×C8C23×C15111yescharacteristic
434C4×C8C23×C15111yescharacteristic
435C4×C8C23×C15111yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4C2×D4×C15111yescharacteristic
447C2×D4C2×D4×C15111yescharacteristic
448C2×D4C2×D4×C15111yescharacteristic
449C2×D4C2×D4×C15111yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455Q16—82no—
456SD16—81no—
457D8—22no—
458D8—41no—
459M16—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8—81no—
468C2×C8C2×D4×C15111yescharacteristic
469C2×C8C2×D4×C15111yescharacteristic
470C2×C8C2×D4×C15111yescharacteristic
471C2×C8C2×D4×C15111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C15111yescharacteristic
482C4⋊C4C2×D4×C15111yescharacteristic
483C4⋊C4C2×D4×C15111yescharacteristic
484C4⋊C4C2×D4×C15111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42C24×C15111yescharacteristic
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508Q8—81no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4—161no—
519D4—161no—
520D4—161no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4C22×D4×C15111yescharacteristic
539C2×C4C22×D4×C15111yescharacteristic
540C2×C4H(5,𝔽2)×C15111yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8#135×C15112yes—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D42×C15111yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C2×#135×C15111yescharacteristic
573C4#575×C15111yescharacteristic
574C4#577×C15111yescharacteristic
575C4#578×C15111yescharacteristic
576C2—81no—
577C2—81no—
578C2—81no—
579C2—81no—
580C2#3267×C15111yescharacteristic
581C2#3283×C15111yescharacteristic
582C2#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. #3354×C151C2semidirect
2. #3341×C151C2semidirect
3. #3341×C151C2semidirect
4. #3303×C151C2semidirect
5. #1723×C151C2semidirect
6. #1695×C151C2semidirect
7. #1683×C151C2semidirect
8. #1675×C151C2semidirect
9. #1671×C151C2semidirect
10. #1646×C151C2semidirect
11. #1635×C151C2semidirect
12. #1634×C151C2semidirect
13. #1634×C151C2semidirect
14. #1581×C151C2semidirect
15. #1580×C151C2semidirect
291. #19862C151direct (N × H)
292. C151#19862direct (N × H)
293. #3354C2×C151semidirect
294. #3341C2×C151semidirect
295. #3341C2×C151semidirect
296. #3303C2×C151semidirect
297. #1723C2×C151semidirect
298. #1695C2×C151semidirect
299. #1683C2×C151semidirect
300. #1675C2×C151semidirect
301. #1671C2×C151semidirect
302. #1646C2×C151semidirect
303. #1635C2×C151semidirect
304. #1634C2×C151semidirect
305. #1634C2×C151semidirect
306. #1581C2×C151semidirect
307. #1580C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3354×C1512
#3341×C1512
#3303×C1512
#1723×C1512
#1695×C1512
#1683×C1512
#1675×C1512
#1671×C1512
#1646×C1512
#1635×C1512
#1634×C1512
#1581×C1512
#1580×C1512
#19862151