Finite Group Databasebeta

← C151×#19947 #50324872

Subgroups — C151×#19947 #50324872

Order 38656.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C151C211yesmaximal, characteristic, complemented
2#3394×C151C211yesmaximal, characteristic, complemented
3#3353×C151C211yesmaximal, characteristic, complemented
4#3284×C151C211yesmaximal, characteristic, complemented
5#1706×C151C211yesmaximal, characteristic, complemented
6#1694×C151C211yesmaximal, characteristic, complemented
7#1687×C151C211yesmaximal, characteristic, complemented
8#1666×C151C211yesmaximal, characteristic, complemented
9#1665×C151C211yesmaximal, characteristic, complemented
10#1641×C151C211yesmaximal, characteristic, complemented
11#1640×C151C211yesmaximal, characteristic, complemented
12#1628×C151C211yesmaximal, characteristic, complemented
13#1625×C151C211yesmaximal, characteristic, complemented
14#1590×C151C211yesmaximal, characteristic, complemented
15C8×SD16×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151—21no—
17#559×C151C2211yescharacteristic
18#556×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20#547×C151C2211yescharacteristic
21#500×C151C2211yescharacteristic
22#496×C151—21no—
23#495×C151—21no—
24#493×C151C2211yescharacteristic
25#492×C151C2211yescharacteristic
26#492×C151C2211yescharacteristic
27#486×C151C2211yescharacteristic
28#486×C151C2211yescharacteristic
29#484×C151—21no—
30#482×C151—21no—
31#475×C151C2211yescharacteristic
32#474×C151C2211yescharacteristic
33#468×C151—21no—
34#465×C151—21no—
35#464×C151—21no—
36#463×C151—21no—
37#463×C151—21no—
38#462×C151C2211yescharacteristic
39#462×C151C2211yescharacteristic
40#460×C151C2211yescharacteristic
41#459×C151—21no—
42#459×C151C2211yescharacteristic
43#459×C151C2211yescharacteristic
44#459×C151C2211yescharacteristic
45#452×C151—21no—
46#449×C151—21no—
47#446×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#442×C151—21no—
50C4×SD16×C151—21no—
51C4×SD16×C151C2211yescharacteristic
52C4×SD16×C151C2211yescharacteristic
53#436×C151C2211yescharacteristic
54C8×D4×C151C2211yescharacteristic
55#428×C151—21no—
56#334×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#332×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#331×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69#135×C151—44no—
70C2×Q16×C151—21no—
71C2×Q16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C2×SD16×C151D411yescharacteristic
78C2×SD16×C151D411yescharacteristic
79C2×D8×C151—21no—
80C2×D8×C151—21no—
81C2×D8×C151—21no—
82C2×D8×C151—21no—
83C2×D8×C151—21no—
84C2×M16×C151—21no—
85C22×C8×C151—21no—
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88#127×C151—21no—
89#127×C151C2311yescharacteristic
90#127×C151C2311yescharacteristic
91#126×C151—41no—
92#124×C151—21no—
93#124×C151—21no—
94#124×C151—21no—
95#123×C151—41no—
96#123×C151—41no—
97C22⋊Q8×C151—21no—
98C22⋊Q8×C151—21no—
99#121×C151—21no—
100#121×C151—21no—
101#121×C151—41no—
102C4×Q8×C151—21no—
103C4×Q8×C151C2311yescharacteristic
104C4×Q8×C151C2311yescharacteristic
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151C2311yescharacteristic
109C4×D4×C151C2311yescharacteristic
110#117×C151—21no—
111C2×C4⋊C4×C151—21no—
112#107×C151—21no—
113#107×C151—21no—
114#107×C151—21no—
115#106×C151—21no—
116#106×C151D411yescharacteristic
117#106×C151D411yescharacteristic
118C4⋊C8×C151—21no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151D411yescharacteristic
128#103×C151D411yescharacteristic
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—41no—
135#102×C151—41no—
136#102×C151D411yescharacteristic
137#102×C151D411yescharacteristic
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140#97×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C4×C8×C151C2311yescharacteristic
145#41×C151—42no—
146#41×C151—42no—
147#41×C151—81no—
148#41×C151—81no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151C2×D411yescharacteristic
152C2×Q8×C151C2×D411yescharacteristic
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—41no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151C2×D411yescharacteristic
163C2×D4×C151C2×D411yescharacteristic
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—41no—
167C22×C4×C151—41no—
168C22×C4×C151—41no—
169Q16×C151—42no—
170Q16×C151—81no—
171SD16×C151—22no—
172SD16×C151—22no—
173SD16×C151—42no—
174SD16×C151—42no—
175SD16×C151—81no—
176SD16×C151—81no—
177SD16×C151—81no—
178D8×C151—42no—
179D8×C151—42no—
180D8×C151—81no—
181D8×C151—81no—
182D8×C151—81no—
183M16×C151—42no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—42no—
190C2×C8×C151C2×D411yescharacteristic
191C2×C8×C151C2×D411yescharacteristic
192C2×C8×C151C2×D411yescharacteristic
193C2×C8×C151C2×D411yescharacteristic
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—41no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D411yescharacteristic
204C4⋊C4×C151C2×D411yescharacteristic
205C4⋊C4×C151C2×D411yescharacteristic
206C22⋊C4×C151—21no—
207C22⋊C4×C151—21no—
208C22⋊C4×C151—41no—
209C22⋊C4×C151—41no—
210C22⋊C4×C151—41no—
211C22⋊C4×C151—41no—
212C22⋊C4×C151—41no—
213C22⋊C4×C151—41no—
214C22⋊C4×C151—41no—
215C42×C151—21no—
216C42×C151—21no—
217C42×C151—41no—
218C42×C151C2411yescharacteristic
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—41no—
222C23×C151—41no—
223Q8×C151—21no—
224Q8×C151—21no—
225Q8×C151—21no—
226Q8×C151—21no—
227Q8×C151—41no—
228Q8×C151—41no—
229Q8×C151—41no—
230Q8×C151—41no—
231D4×C151—21no—
232D4×C151—21no—
233D4×C151—21no—
234D4×C151—21no—
235D4×C151—41no—
236D4×C151—41no—
237D4×C151—41no—
238D4×C151—41no—
239D4×C151—41no—
240D4×C151—41no—
241D4×C151—41no—
242D4×C151—41no—
243D4×C151—81no—
244D4×C151—81no—
245D4×C151—82no—
246D4×C151—82no—
247D4×C151—161no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—82no—
261C2×C4×C151—82no—
262C2×C4×C151—161no—
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151H(5,𝔽2)11yescharacteristic
266C8×C151—21no—
267C8×C151—21no—
268C8×C151—41no—
269C8×C151—41no—
270C8×C151—41no—
271C8×C151—41no—
272C8×C151—41no—
273C8×C151#13512yescomplemented
274C8×C151AGL(1,ℤ/8)12yes—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—81no—
282C22×C151—81no—
283C22×C151—81no—
284C22×C151—81no—
285C22×C151—81no—
286C22×C151—81no—
287C22×C151D4211yescharacteristic
288C4×C151—21no—
289C4×C151—41no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—81no—
296C4×C151—81no—
297C4×C151C2×#13511yescharacteristic
298C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C151#57611yescharacteristic
300C4×C151#57711yescharacteristic
301C2×C151—81no—
302C2×C151—81no—
303C2×C151—161no—
304C2×C151—161no—
305C2×C151#327411yescharacteristic
306C2×C151#328411yescharacteristic
307C2×C151#329011yescharacteristic
308#19947C15111yesmaximal, characteristic, direct product factor, Sylow
309C151#1994711yescharacteristic, direct product factor, Sylow
310#3399C2×C15111yescharacteristic, complemented
311#3394C2×C15111yescharacteristic, complemented
312#3353C2×C15111yescharacteristic, complemented
313#3284C2×C15111yescharacteristic, complemented
314#1706C2×C15111yescharacteristic, complemented
315#1694C2×C15111yescharacteristic, complemented
316#1687C2×C15111yescharacteristic, complemented
317#1666C2×C15111yescharacteristic, complemented
318#1665C2×C15111yescharacteristic, complemented
319#1641C2×C15111yescharacteristic, complemented
320#1640C2×C15111yescharacteristic, complemented
321#1628C2×C15111yescharacteristic, complemented
322#1625C2×C15111yescharacteristic, complemented
323#1590C2×C15111yescharacteristic, complemented
324C8×SD16C2×C15111yescharacteristic, complemented
325C2×#135—21no—
326#559C22×C15111yescharacteristic
327#556C22×C15111yescharacteristic
328#550C22×C15111yescharacteristic
329#547C22×C15111yescharacteristic
330#500C22×C15111yescharacteristic
331#496—21no—
332#495—21no—
333#493C22×C15111yescharacteristic
334#492C22×C15111yescharacteristic
335#492C22×C15111yescharacteristic
336#486C22×C15111yescharacteristic
337#486C22×C15111yescharacteristic
338#484—21no—
339#482—21no—
340#475C22×C15111yescharacteristic
341#474C22×C15111yescharacteristic
342#468—21no—
343#465—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462C22×C15111yescharacteristic
348#462C22×C15111yescharacteristic
349#460C22×C15111yescharacteristic
350#459—21no—
351#459C22×C15111yescharacteristic
352#459C22×C15111yescharacteristic
353#459C22×C15111yescharacteristic
354#452—21no—
355#449—21no—
356#446C22×C15111yescharacteristic
357C8×Q8C22×C15111yescharacteristic
358#442—21no—
359C4×SD16—21no—
360C4×SD16C22×C15111yescharacteristic
361C4×SD16C22×C15111yescharacteristic
362#436C22×C15111yescharacteristic
363C8×D4C22×C15111yescharacteristic
364#428—21no—
365#334C22×C15111yescharacteristic
366#334C22×C15111yescharacteristic
367#332C22×C15111yescharacteristic
368#332C22×C15111yescharacteristic
369#331C22×C15111yescharacteristic
370#331C22×C15111yescharacteristic
371Q8⋊C8C22×C15111yescharacteristic
372Q8⋊C8C22×C15111yescharacteristic
373D4⋊C8C22×C15111yescharacteristic
374D4⋊C8C22×C15111yescharacteristic
375C82C22×C15111yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16D4×C15111yescharacteristic
387C2×SD16D4×C15111yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×M16—21no—
394C22×C8—21no—
395C4⋊Q8C23×C15111yescharacteristic
396C4⋊Q8C23×C15111yescharacteristic
397#127—21no—
398#127C23×C15111yescharacteristic
399#127C23×C15111yescharacteristic
400#126—41no—
401#124—21no—
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8—21no—
412C4×Q8C23×C15111yescharacteristic
413C4×Q8C23×C15111yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C15111yescharacteristic
418C4×D4C23×C15111yescharacteristic
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106D4×C15111yescharacteristic
426#106D4×C15111yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C15111yescharacteristic
430C4⋊C8C23×C15111yescharacteristic
431C4⋊C8C23×C15111yescharacteristic
432C4⋊C8C23×C15111yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C15111yescharacteristic
437#103D4×C15111yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102—41no—
445#102D4×C15111yescharacteristic
446#102D4×C15111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C15111yescharacteristic
452C4×C8C23×C15111yescharacteristic
453C4×C8C23×C15111yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C15111yescharacteristic
461C2×Q8C2×D4×C15111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C15111yescharacteristic
472C2×D4C2×D4×C15111yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C15111yescharacteristic
500C2×C8C2×D4×C15111yescharacteristic
501C2×C8C2×D4×C15111yescharacteristic
502C2×C8C2×D4×C15111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C15111yescharacteristic
512C4⋊C4C2×D4×C15111yescharacteristic
513C4⋊C4C2×D4×C15111yescharacteristic
514C4⋊C4C2×D4×C15111yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C15111yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C15111yescharacteristic
573C2×C4C22×D4×C15111yescharacteristic
574C2×C4H(5,𝔽2)×C15111yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8#135×C15112yescomplemented
583C8AGL(1,ℤ/8)×C15112yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C15111yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C15111yescharacteristic
607C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
608C4#576×C15111yescharacteristic
609C4#577×C15111yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2#3274×C15111yescharacteristic
615C2#3284×C15111yescharacteristic
616C2#3290×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. #3399×C151C2semidirect
2. #3394×C151C2semidirect
3. #3353×C151C2semidirect
4. #3284×C151C2semidirect
5. #1706×C151C2semidirect
6. #1694×C151C2semidirect
7. #1687×C151C2semidirect
8. #1666×C151C2semidirect
9. #1665×C151C2semidirect
10. #1641×C151C2semidirect
11. #1640×C151C2semidirect
12. #1628×C151C2semidirect
13. #1625×C151C2semidirect
14. #1590×C151C2semidirect
15. C8×SD16×C151C2semidirect
273. C8×C151#135semidirect
308. #19947C151direct (N × H)
309. C151#19947direct (N × H)
310. #3399C2×C151semidirect
311. #3394C2×C151semidirect
312. #3353C2×C151semidirect
313. #3284C2×C151semidirect
314. #1706C2×C151semidirect
315. #1694C2×C151semidirect
316. #1687C2×C151semidirect
317. #1666C2×C151semidirect
318. #1665C2×C151semidirect
319. #1641C2×C151semidirect
320. #1640C2×C151semidirect
321. #1628C2×C151semidirect
322. #1625C2×C151semidirect
323. #1590C2×C151semidirect
324. C8×SD16C2×C151semidirect
582. C8#135×C151semidirect

Maximal subgroups

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

subgroupindex
#3399×C1512
#3394×C1512
#3353×C1512
#3284×C1512
#1706×C1512
#1694×C1512
#1687×C1512
#1666×C1512
#1665×C1512
#1641×C1512
#1640×C1512
#1628×C1512
#1625×C1512
#1590×C1512
C8×SD16×C1512
#19947151