Finite Group Databasebeta

← C151×#19776 #50324701

Subgroups — C151×#19776 #50324701

Order 38656.

630 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3334×C151C211yesmaximal, characteristic, complemented
2#3330×C151C211yesmaximal, characteristic, complemented
3#3303×C151C211yesmaximal, characteristic, complemented
4#3303×C151C211yesmaximal, characteristic, complemented
5#1718×C151C211yesmaximal, characteristic, complemented
6#1703×C151C211yesmaximal, characteristic, complemented
7#1683×C151C211yesmaximal, characteristic, complemented
8#1679×C151C211yesmaximal, characteristic, complemented
9#1673×C151C211yesmaximal, characteristic, complemented
10#1654×C151C211yesmaximal, characteristic, complemented
11#1654×C151C211yesmaximal, characteristic, complemented
12#1646×C151C211yesmaximal, characteristic, complemented
13#1635×C151C211yesmaximal, characteristic, complemented
14#1581×C151C211yesmaximal, characteristic, complemented
15#1580×C151C211yesmaximal, characteristic, complemented
16#555×C151C2211yescharacteristic
17#547×C151C2211yescharacteristic
18#547×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#498×C151C2211yescharacteristic
22#487×C151C2211yescharacteristic
23#487×C151C2211yescharacteristic
24#487×C151C2211yescharacteristic
25#487×C151C2211yescharacteristic
26#485×C151—21no—
27#485×C151—21no—
28#484×C151—21no—
29#480×C151—21no—
30#480×C151—21no—
31#476×C151C2211yescharacteristic
32#476×C151C2211yescharacteristic
33#474×C151C2211yescharacteristic
34#474×C151C2211yescharacteristic
35#474×C151C2211yescharacteristic
36#468×C151—21no—
37#466×C151—21no—
38#465×C151—21no—
39#465×C151—21no—
40#461×C151C2211yescharacteristic
41#461×C151C2211yescharacteristic
42#461×C151C2211yescharacteristic
43#449×C151—21no—
44#449×C151—21no—
45#449×C151—21no—
46C4×D8×C151C2211yescharacteristic
47C4×D8×C151C2211yescharacteristic
48#436×C151C2211yescharacteristic
49C8×D4×C151C2211yescharacteristic
50C8×D4×C151C2211yescharacteristic
51C8×D4×C151C2211yescharacteristic
52C2×#107×C151—21no—
53#417×C151—21no—
54#416×C151—21no—
55#416×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62D4⋊C8×C151C2211yescharacteristic
63D4⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×#41×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×D8×C151D411yescharacteristic
74C2×D8×C151D411yescharacteristic
75C2×M16×C151—21no—
76C22×C8×C151—21no—
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83#124×C151—41no—
84#123×C151—41no—
85#123×C151—41no—
86#123×C151—41no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151—21no—
95C4×D4×C151C2311yescharacteristic
96C4×D4×C151C2311yescharacteristic
97C4×D4×C151C2311yescharacteristic
98C4×D4×C151C2311yescharacteristic
99#117×C151—21no—
100#117×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151—21no—
109#107×C151D411yescharacteristic
110#107×C151D411yescharacteristic
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—41no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118#103×C151—21no—
119#103×C151—21no—
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—41no—
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—42no—
146#41×C151—42no—
147#41×C151—81no—
148#41×C151—81no—
149#41×C151—81no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×D4×C151—41no—
155C2×D4×C151—41no—
156C2×D4×C151—41no—
157C2×D4×C151—41no—
158C2×D4×C151C2×D411yescharacteristic
159C2×D4×C151C2×D411yescharacteristic
160C2×D4×C151C2×D411yescharacteristic
161C2×D4×C151C2×D411yescharacteristic
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—41no—
167C22×C4×C151—41no—
168C22×C4×C151—41no—
169SD16×C151—81no—
170SD16×C151—81no—
171SD16×C151—81no—
172D8×C151—22no—
173D8×C151—41no—
174M16×C151—81no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—42no—
181C2×C8×C151—81no—
182C2×C8×C151—81no—
183C2×C8×C151C2×D411yescharacteristic
184C2×C8×C151C2×D411yescharacteristic
185C2×C8×C151C2×D411yescharacteristic
186C2×C8×C151C2×D411yescharacteristic
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D411yescharacteristic
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—21no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—41no—
209C22⋊C4×C151—41no—
210C22⋊C4×C151—41no—
211C42×C151—41no—
212C42×C151C2411yescharacteristic
213C23×C151—21no—
214C23×C151—21no—
215C23×C151—21no—
216C23×C151—21no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—41no—
223Q8×C151—81no—
224D4×C151—21no—
225D4×C151—21no—
226D4×C151—21no—
227D4×C151—21no—
228D4×C151—21no—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—82no—
232D4×C151—82no—
233D4×C151—82no—
234D4×C151—161no—
235D4×C151#13512yes—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—41no—
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—41no—
251C2×C4×C151—41no—
252C2×C4×C151—82no—
253C2×C4×C151—82no—
254C2×C4×C151—82no—
255C2×C4×C151C22×D411yescharacteristic
256C2×C4×C151C22×D411yescharacteristic
257C2×C4×C151H(5,𝔽2)11yescharacteristic
258C8×C151—21no—
259C8×C151—21no—
260C8×C151—21no—
261C8×C151—21no—
262C8×C151—41no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—41no—
266C8×C151—41no—
267C22×C151—22no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151D4211yescharacteristic
280C4×C151—21no—
281C4×C151—41no—
282C4×C151—41no—
283C4×C151—41no—
284C4×C151—41no—
285C4×C151—81no—
286C4×C151—81no—
287C4×C151—81no—
288C4×C151—81no—
289C4×C151C2×#13511yescharacteristic
290C4×C151#57511yescharacteristic
291C4×C151#57611yescharacteristic
292C4×C151#57711yescharacteristic
293C2×C151—42no—
294C2×C151—81no—
295C2×C151—81no—
296C2×C151—81no—
297C2×C151#326711yescharacteristic
298C2×C151#328011yescharacteristic
299C2×C151#328911yescharacteristic
300#19776C15111yesmaximal, characteristic, direct product factor, Sylow
301C151#1977611yescharacteristic, direct product factor, Sylow
302#3334C2×C15111yescharacteristic, complemented
303#3330C2×C15111yescharacteristic, complemented
304#3303C2×C15111yescharacteristic, complemented
305#3303C2×C15111yescharacteristic, complemented
306#1718C2×C15111yescharacteristic, complemented
307#1703C2×C15111yescharacteristic, complemented
308#1683C2×C15111yescharacteristic, complemented
309#1679C2×C15111yescharacteristic, complemented
310#1673C2×C15111yescharacteristic, complemented
311#1654C2×C15111yescharacteristic, complemented
312#1654C2×C15111yescharacteristic, complemented
313#1646C2×C15111yescharacteristic, complemented
314#1635C2×C15111yescharacteristic, complemented
315#1581C2×C15111yescharacteristic, complemented
316#1580C2×C15111yescharacteristic, complemented
317#555C22×C15111yescharacteristic
318#547C22×C15111yescharacteristic
319#547C22×C15111yescharacteristic
320#547C22×C15111yescharacteristic
321#500C22×C15111yescharacteristic
322#498C22×C15111yescharacteristic
323#487C22×C15111yescharacteristic
324#487C22×C15111yescharacteristic
325#487C22×C15111yescharacteristic
326#487C22×C15111yescharacteristic
327#485—21no—
328#485—21no—
329#484—21no—
330#480—21no—
331#480—21no—
332#476C22×C15111yescharacteristic
333#476C22×C15111yescharacteristic
334#474C22×C15111yescharacteristic
335#474C22×C15111yescharacteristic
336#474C22×C15111yescharacteristic
337#468—21no—
338#466—21no—
339#465—21no—
340#465—21no—
341#461C22×C15111yescharacteristic
342#461C22×C15111yescharacteristic
343#461C22×C15111yescharacteristic
344#449—21no—
345#449—21no—
346#449—21no—
347C4×D8C22×C15111yescharacteristic
348C4×D8C22×C15111yescharacteristic
349#436C22×C15111yescharacteristic
350C8×D4C22×C15111yescharacteristic
351C8×D4C22×C15111yescharacteristic
352C8×D4C22×C15111yescharacteristic
353C2×#107—21no—
354#417—21no—
355#416—21no—
356#416—21no—
357#335C22×C15111yescharacteristic
358#334C22×C15111yescharacteristic
359#333C22×C15111yescharacteristic
360#332C22×C15111yescharacteristic
361#332C22×C15111yescharacteristic
362#332C22×C15111yescharacteristic
363D4⋊C8C22×C15111yescharacteristic
364D4⋊C8C22×C15111yescharacteristic
365D4⋊C8C22×C15111yescharacteristic
366D4⋊C8C22×C15111yescharacteristic
367#322C22×C15111yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8D4×C15111yescharacteristic
375C2×D8D4×C15111yescharacteristic
376C2×M16—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C4⋊Q8C23×C15111yescharacteristic
381C4⋊Q8C23×C15111yescharacteristic
382C4⋊Q8C23×C15111yescharacteristic
383C4⋊Q8C23×C15111yescharacteristic
384#124—41no—
385#123—41no—
386#123—41no—
387#123—41no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391#121—21no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396C4×D4C23×C15111yescharacteristic
397C4×D4C23×C15111yescharacteristic
398C4×D4C23×C15111yescharacteristic
399C4×D4C23×C15111yescharacteristic
400#117—21no—
401#117—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107D4×C15111yescharacteristic
411#107D4×C15111yescharacteristic
412#106—21no—
413#106—21no—
414#106—41no—
415C4⋊C8C23×C15111yescharacteristic
416C4⋊C8C23×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418C4⋊C8C23×C15111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—41no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102D4×C15111yescharacteristic
435#102D4×C15111yescharacteristic
436#102D4×C15111yescharacteristic
437#102D4×C15111yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C4×C8C23×C15111yescharacteristic
443C4×C8C23×C15111yescharacteristic
444C4×C8C23×C15111yescharacteristic
445#41—42no—
446#41—42no—
447#41—42no—
448#41—81no—
449#41—81no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C15111yescharacteristic
460C2×D4C2×D4×C15111yescharacteristic
461C2×D4C2×D4×C15111yescharacteristic
462C2×D4C2×D4×C15111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470SD16—81no—
471SD16—81no—
472SD16—81no—
473D8—22no—
474D8—41no—
475M16—81no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—81no—
483C2×C8—81no—
484C2×C8C2×D4×C15111yescharacteristic
485C2×C8C2×D4×C15111yescharacteristic
486C2×C8C2×D4×C15111yescharacteristic
487C2×C8C2×D4×C15111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C15111yescharacteristic
500C4⋊C4C2×D4×C15111yescharacteristic
501C4⋊C4C2×D4×C15111yescharacteristic
502C4⋊C4C2×D4×C15111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C42—41no—
513C42C24×C15111yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—82no—
533D4—82no—
534D4—82no—
535D4—161no—
536D4#135×C15112yes—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C22×D4×C15111yescharacteristic
557C2×C4C22×D4×C15111yescharacteristic
558C2×C4H(5,𝔽2)×C15111yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22D42×C15111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4C2×#135×C15111yescharacteristic
591C4#575×C15111yescharacteristic
592C4#576×C15111yescharacteristic
593C4#577×C15111yescharacteristic
594C2—42no—
595C2—81no—
596C2—81no—
597C2—81no—
598C2#3267×C15111yescharacteristic
599C2#3280×C15111yescharacteristic
600C2#3289×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. #3334×C151C2semidirect
2. #3330×C151C2semidirect
3. #3303×C151C2semidirect
4. #3303×C151C2semidirect
5. #1718×C151C2semidirect
6. #1703×C151C2semidirect
7. #1683×C151C2semidirect
8. #1679×C151C2semidirect
9. #1673×C151C2semidirect
10. #1654×C151C2semidirect
11. #1654×C151C2semidirect
12. #1646×C151C2semidirect
13. #1635×C151C2semidirect
14. #1581×C151C2semidirect
15. #1580×C151C2semidirect
300. #19776C151direct (N × H)
301. C151#19776direct (N × H)
302. #3334C2×C151semidirect
303. #3330C2×C151semidirect
304. #3303C2×C151semidirect
305. #3303C2×C151semidirect
306. #1718C2×C151semidirect
307. #1703C2×C151semidirect
308. #1683C2×C151semidirect
309. #1679C2×C151semidirect
310. #1673C2×C151semidirect
311. #1654C2×C151semidirect
312. #1654C2×C151semidirect
313. #1646C2×C151semidirect
314. #1635C2×C151semidirect
315. #1581C2×C151semidirect
316. #1580C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3334×C1512
#3330×C1512
#3303×C1512
#1718×C1512
#1703×C1512
#1683×C1512
#1679×C1512
#1673×C1512
#1654×C1512
#1646×C1512
#1635×C1512
#1581×C1512
#1580×C1512
#19776151