Finite Group Databasebeta

← C151×#19871 #50324796

Subgroups — C151×#19871 #50324796

Order 38656.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C151C211yesmaximal, characteristic, complemented
2#3396×C151C211yesmaximal, characteristic, complemented
3#3394×C151C211yesmaximal, characteristic, complemented
4#3304×C151C211yesmaximal, characteristic, complemented
5#1721×C151C211yesmaximal, characteristic, complemented
6#1686×C151C211yesmaximal, characteristic, complemented
7#1682×C151C211yesmaximal, characteristic, complemented
8#1668×C151C211yesmaximal, characteristic, complemented
9#1667×C151C211yesmaximal, characteristic, complemented
10#1640×C151C211yesmaximal, characteristic, complemented
11#1628×C151C211yesmaximal, characteristic, complemented
12#1621×C151C211yesmaximal, characteristic, complemented
13#1620×C151C211yesmaximal, characteristic, complemented
14#1584×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16#559×C151C2211yescharacteristic
17#559×C151C2211yescharacteristic
18#556×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20#496×C151—21no—
21#495×C151—21no—
22#495×C151—21no—
23#493×C151C2211yescharacteristic
24#493×C151C2211yescharacteristic
25#493×C151C2211yescharacteristic
26#492×C151C2211yescharacteristic
27#486×C151C2211yescharacteristic
28#486×C151C2211yescharacteristic
29#482×C151—21no—
30#475×C151C2211yescharacteristic
31#465×C151—21no—
32#464×C151—21no—
33#463×C151—21no—
34#463×C151—21no—
35#463×C151—21no—
36#463×C151—21no—
37#462×C151C2211yescharacteristic
38#460×C151C2211yescharacteristic
39#460×C151C2211yescharacteristic
40#460×C151C2211yescharacteristic
41#460×C151C2211yescharacteristic
42#459×C151—21no—
43#459×C151C2211yescharacteristic
44#459×C151C2211yescharacteristic
45#452×C151—21no—
46#446×C151C2211yescharacteristic
47C8×Q8×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#442×C151—21no—
50C4×Q16×C151C2211yescharacteristic
51C4×SD16×C151—21no—
52C4×SD16×C151C2211yescharacteristic
53C4×D8×C151—21no—
54C8×D4×C151C2211yescharacteristic
55#416×C151—21no—
56#335×C151C2211yescharacteristic
57#335×C151C2211yescharacteristic
58#332×C151C2211yescharacteristic
59#331×C151C2211yescharacteristic
60#331×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151D411yescharacteristic
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151D411yescharacteristic
77C2×D8×C151—21no—
78C2×D8×C151—21no—
79C2×D8×C151—21no—
80C2×D8×C151—21no—
81C2×D8×C151—21no—
82C2×D8×C151—21no—
83C2×D8×C151—41no—
84C22×C8×C151—21no—
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151—21no—
87#127×C151C2311yescharacteristic
88#127×C151C2311yescharacteristic
89#127×C151C2311yescharacteristic
90#126×C151—41no—
91#124×C151—21no—
92#124×C151—21no—
93#124×C151—21no—
94#124×C151—21no—
95#124×C151—21no—
96#123×C151—41no—
97#123×C151—41no—
98C22⋊Q8×C151—21no—
99#121×C151—21no—
100#121×C151—41no—
101C4×Q8×C151—21no—
102C4×Q8×C151C2311yescharacteristic
103C4×Q8×C151C2311yescharacteristic
104C4×Q8×C151C2311yescharacteristic
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151C2311yescharacteristic
111#117×C151—21no—
112#107×C151D411yescharacteristic
113#106×C151—21no—
114#106×C151D411yescharacteristic
115C4⋊C8×C151—21no—
116C4⋊C8×C151—21no—
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×C151D411yescharacteristic
125#103×C151D411yescharacteristic
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×C151—21no—
135#102×C151—41no—
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138#97×C151—21no—
139C4×C8×C151—21no—
140C4×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×C151C2×D411yescharacteristic
148C2×Q8×C151C2×D411yescharacteristic
149C2×Q8×C151C2×D411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
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×C151C2×D411yescharacteristic
162C22×C4×C151—21no—
163C22×C4×C151—41no—
164C22×C4×C151—41no—
165C22×C4×C151—41no—
166Q16×C151—41no—
167Q16×C151—81no—
168SD16×C151—22no—
169SD16×C151—42no—
170SD16×C151—81no—
171SD16×C151—81no—
172SD16×C151—81no—
173SD16×C151—81no—
174SD16×C151—81no—
175D8×C151—42no—
176D8×C151—42no—
177D8×C151—81no—
178D8×C151—81no—
179D8×C151—81no—
180D8×C151—81no—
181D8×C151—82no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—81no—
188C2×C8×C151C2×D411yescharacteristic
189C2×C8×C151C2×D411yescharacteristic
190C2×C8×C151C2×D411yescharacteristic
191C2×C8×C151C2×D411yescharacteristic
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
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—41no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—41no—
209C22⋊C4×C151—41no—
210C22⋊C4×C151—41no—
211C22⋊C4×C151—41no—
212C42×C151—21no—
213C42×C151—21no—
214C42×C151—21no—
215C42×C151—41no—
216C42×C151C2411yescharacteristic
217C23×C151—21no—
218C23×C151—41no—
219C23×C151—41no—
220C23×C151—41no—
221Q8×C151—21no—
222Q8×C151—21no—
223Q8×C151—21no—
224Q8×C151—21no—
225Q8×C151—21no—
226Q8×C151—21no—
227Q8×C151—41no—
228Q8×C151—41no—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—41no—
232D4×C151—41no—
233D4×C151—41no—
234D4×C151—41no—
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—81no—
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—21no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—82no—
259C2×C4×C151—161no—
260C2×C4×C151—161no—
261C2×C4×C151C22×D411yescharacteristic
262C2×C4×C151C22×D411yescharacteristic
263C2×C4×C151H(5,𝔽2)11yescharacteristic
264C8×C151—21no—
265C8×C151—21no—
266C8×C151—21no—
267C8×C151—41no—
268C8×C151—41no—
269C8×C151—41no—
270C8×C151—41no—
271C8×C151—41no—
272C8×C151#13512yes—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151—81no—
279C22×C151—81no—
280C22×C151—81no—
281C22×C151—81no—
282C22×C151—81no—
283C22×C151—81no—
284C22×C151—81no—
285C22×C151D4211yescharacteristic
286C4×C151—21no—
287C4×C151—41no—
288C4×C151—41no—
289C4×C151—41no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—81no—
295C4×C151C2×#13511yescharacteristic
296C4×C151#57511yescharacteristic
297C4×C151#57611yescharacteristic
298C4×C151#57611yescharacteristic
299C2×C151—81no—
300C2×C151—161no—
301C2×C151—161no—
302C2×C151—161no—
303C2×C151#326811yescharacteristic
304C2×C151#328711yescharacteristic
305C2×C151#328811yescharacteristic
306#19871C15111yesmaximal, characteristic, direct product factor, Sylow
307C151#1987111yescharacteristic, direct product factor, Sylow
308#3399C2×C15111yescharacteristic, complemented
309#3396C2×C15111yescharacteristic, complemented
310#3394C2×C15111yescharacteristic, complemented
311#3304C2×C15111yescharacteristic, complemented
312#1721C2×C15111yescharacteristic, complemented
313#1686C2×C15111yescharacteristic, complemented
314#1682C2×C15111yescharacteristic, complemented
315#1668C2×C15111yescharacteristic, complemented
316#1667C2×C15111yescharacteristic, complemented
317#1640C2×C15111yescharacteristic, complemented
318#1628C2×C15111yescharacteristic, complemented
319#1621C2×C15111yescharacteristic, complemented
320#1620C2×C15111yescharacteristic, complemented
321#1584C2×C15111yescharacteristic, complemented
322SD16⋊C8C2×C15111yescharacteristic, complemented
323#559C22×C15111yescharacteristic
324#559C22×C15111yescharacteristic
325#556C22×C15111yescharacteristic
326#550C22×C15111yescharacteristic
327#496—21no—
328#495—21no—
329#495—21no—
330#493C22×C15111yescharacteristic
331#493C22×C15111yescharacteristic
332#493C22×C15111yescharacteristic
333#492C22×C15111yescharacteristic
334#486C22×C15111yescharacteristic
335#486C22×C15111yescharacteristic
336#482—21no—
337#475C22×C15111yescharacteristic
338#465—21no—
339#464—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#462C22×C15111yescharacteristic
345#460C22×C15111yescharacteristic
346#460C22×C15111yescharacteristic
347#460C22×C15111yescharacteristic
348#460C22×C15111yescharacteristic
349#459—21no—
350#459C22×C15111yescharacteristic
351#459C22×C15111yescharacteristic
352#452—21no—
353#446C22×C15111yescharacteristic
354C8×Q8C22×C15111yescharacteristic
355C8×Q8C22×C15111yescharacteristic
356#442—21no—
357C4×Q16C22×C15111yescharacteristic
358C4×SD16—21no—
359C4×SD16C22×C15111yescharacteristic
360C4×D8—21no—
361C8×D4C22×C15111yescharacteristic
362#416—21no—
363#335C22×C15111yescharacteristic
364#335C22×C15111yescharacteristic
365#332C22×C15111yescharacteristic
366#331C22×C15111yescharacteristic
367#331C22×C15111yescharacteristic
368#331C22×C15111yescharacteristic
369Q8⋊C8C22×C15111yescharacteristic
370Q8⋊C8C22×C15111yescharacteristic
371Q8⋊C8C22×C15111yescharacteristic
372D4⋊C8C22×C15111yescharacteristic
373#322C22×C15111yescharacteristic
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C15111yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C15111yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C15111yescharacteristic
393#127—21no—
394#127C23×C15111yescharacteristic
395#127C23×C15111yescharacteristic
396#127C23×C15111yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C15111yescharacteristic
410C4×Q8C23×C15111yescharacteristic
411C4×Q8C23×C15111yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C15111yescharacteristic
418#117—21no—
419#107D4×C15111yescharacteristic
420#106—21no—
421#106D4×C15111yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C15111yescharacteristic
426C4⋊C8C23×C15111yescharacteristic
427C4⋊C8C23×C15111yescharacteristic
428C4⋊C8C23×C15111yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C15111yescharacteristic
432#103D4×C15111yescharacteristic
433#103D4×C15111yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C15111yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C15111yescharacteristic
449C4×C8C23×C15111yescharacteristic
450C4×C8C23×C15111yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C15111yescharacteristic
455C2×Q8C2×D4×C15111yescharacteristic
456C2×Q8C2×D4×C15111yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C15111yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C15111yescharacteristic
496C2×C8C2×D4×C15111yescharacteristic
497C2×C8C2×D4×C15111yescharacteristic
498C2×C8C2×D4×C15111yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C15111yescharacteristic
506C4⋊C4C2×D4×C15111yescharacteristic
507C4⋊C4C2×D4×C15111yescharacteristic
508C4⋊C4C2×D4×C15111yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C15111yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C15111yescharacteristic
569C2×C4C22×D4×C15111yescharacteristic
570C2×C4H(5,𝔽2)×C15111yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C15112yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C15111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C15111yescharacteristic
603C4#575×C15111yescharacteristic
604C4#576×C15111yescharacteristic
605C4#576×C15111yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2#3268×C15111yescharacteristic
611C2#3287×C15111yescharacteristic
612C2#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. #3399×C151C2semidirect
2. #3396×C151C2semidirect
3. #3394×C151C2semidirect
4. #3304×C151C2semidirect
5. #1721×C151C2semidirect
6. #1686×C151C2semidirect
7. #1682×C151C2semidirect
8. #1668×C151C2semidirect
9. #1667×C151C2semidirect
10. #1640×C151C2semidirect
11. #1628×C151C2semidirect
12. #1621×C151C2semidirect
13. #1620×C151C2semidirect
14. #1584×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
306. #19871C151direct (N × H)
307. C151#19871direct (N × H)
308. #3399C2×C151semidirect
309. #3396C2×C151semidirect
310. #3394C2×C151semidirect
311. #3304C2×C151semidirect
312. #1721C2×C151semidirect
313. #1686C2×C151semidirect
314. #1682C2×C151semidirect
315. #1668C2×C151semidirect
316. #1667C2×C151semidirect
317. #1640C2×C151semidirect
318. #1628C2×C151semidirect
319. #1621C2×C151semidirect
320. #1620C2×C151semidirect
321. #1584C2×C151semidirect
322. SD16⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3399×C1512
#3396×C1512
#3394×C1512
#3304×C1512
#1721×C1512
#1686×C1512
#1682×C1512
#1668×C1512
#1667×C1512
#1640×C1512
#1628×C1512
#1621×C1512
#1620×C1512
#1584×C1512
SD16⋊C8×C1512
#19871151