Finite Group Databasebeta

← C151×#19827 #50324752

Subgroups — C151×#19827 #50324752

Order 38656.

668 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#3362×C151C211yesmaximal, characteristic, complemented
2#3362×C151C211yesmaximal, characteristic, complemented
3#3332×C151C211yesmaximal, characteristic, complemented
4#3284×C151C211yesmaximal, characteristic, complemented
5#1717×C151C211yesmaximal, characteristic, complemented
6#1697×C151C211yesmaximal, characteristic, complemented
7#1682×C151C211yesmaximal, characteristic, complemented
8#1677×C151C211yesmaximal, characteristic, complemented
9#1666×C151C211yesmaximal, characteristic, complemented
10#1645×C151C211yesmaximal, characteristic, complemented
11#1635×C151C211yesmaximal, characteristic, complemented
12#1621×C151C211yesmaximal, characteristic, complemented
13#1621×C151C211yesmaximal, characteristic, complemented
14#1583×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151—21no—
17Q82×C151C2211yescharacteristic
18#550×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20#547×C151C2211yescharacteristic
21#493×C151C2211yescharacteristic
22#492×C151C2211yescharacteristic
23#487×C151C2211yescharacteristic
24#486×C151—21no—
25#486×C151—21no—
26#486×C151C2211yescharacteristic
27#486×C151C2211yescharacteristic
28#486×C151C2211yescharacteristic
29#481×C151—21no—
30#476×C151—21no—
31#476×C151—21no—
32#476×C151C2211yescharacteristic
33#476×C151C2211yescharacteristic
34#475×C151C2211yescharacteristic
35#469×C151—21no—
36#465×C151—21no—
37#462×C151C2211yescharacteristic
38#460×C151—21no—
39#460×C151—21no—
40#460×C151C2211yescharacteristic
41#460×C151C2211yescharacteristic
42#459×C151C2211yescharacteristic
43#459×C151C2211yescharacteristic
44#452×C151—21no—
45#449×C151—21no—
46#449×C151—21no—
47C8×Q8×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49C4×SD16×C151—21no—
50C4×SD16×C151—21no—
51C4×SD16×C151C2211yescharacteristic
52C4×SD16×C151C2211yescharacteristic
53#436×C151C2211yescharacteristic
54C8×D4×C151C2211yescharacteristic
55#417×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#331×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×#41×C151—21no—
70#135×C151—44no—
71C2×Q16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151D411yescharacteristic
77C2×SD16×C151D411yescharacteristic
78C2×D8×C151—21no—
79C2×D8×C151—21no—
80C2×D8×C151—41no—
81C2×M16×C151—21no—
82C22×C8×C151—21no—
83C4⋊Q8×C151—21no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—41no—
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88#127×C151—21no—
89#127×C151—21no—
90#127×C151C2311yescharacteristic
91#127×C151C2311yescharacteristic
92#123×C151—41no—
93C22⋊Q8×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97#121×C151—41no—
98#121×C151—41no—
99C4×Q8×C151—21no—
100C4×Q8×C151—21no—
101C4×Q8×C151C2311yescharacteristic
102C4×Q8×C151C2311yescharacteristic
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151C2311yescharacteristic
106C4×D4×C151C2311yescharacteristic
107C2×C4⋊C4×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111#106×C151D411yescharacteristic
112#106×C151D411yescharacteristic
113C4⋊C8×C151—21no—
114C4⋊C8×C151—21no—
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—41no—
122#103×C151D411yescharacteristic
123#103×C151D411yescharacteristic
124#102×C151—21no—
125#102×C151—21no—
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×C151—21no—
134#102×C151—21no—
135#102×C151—21no—
136#102×C151D411yescharacteristic
137#102×C151D411yescharacteristic
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C4×C8×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—42no—
148#41×C151—81no—
149#41×C151—81no—
150#41×C151—81no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—41no—
154C2×Q8×C151C2×D411yescharacteristic
155C2×Q8×C151C2×D411yescharacteristic
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—41no—
163C2×D4×C151—41no—
164C2×D4×C151—41no—
165C2×D4×C151—41no—
166C2×D4×C151—41no—
167C2×D4×C151C2×D411yescharacteristic
168C2×D4×C151C2×D411yescharacteristic
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—41no—
172C22×C4×C151—41no—
173C22×C4×C151—41no—
174Q16×C151—42no—
175SD16×C151—22no—
176SD16×C151—22no—
177SD16×C151—42no—
178SD16×C151—42no—
179SD16×C151—42no—
180SD16×C151—81no—
181D8×C151—42no—
182D8×C151—81no—
183D8×C151—82no—
184M16×C151—81no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—42no—
191C2×C8×C151C2×D411yescharacteristic
192C2×C8×C151C2×D411yescharacteristic
193C2×C8×C151C2×D411yescharacteristic
194C2×C8×C151C2×D411yescharacteristic
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151C2×D411yescharacteristic
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D411yescharacteristic
207C4⋊C4×C151C2×D411yescharacteristic
208C22⋊C4×C151—21no—
209C22⋊C4×C151—21no—
210C22⋊C4×C151—41no—
211C22⋊C4×C151—41no—
212C22⋊C4×C151—41no—
213C42×C151—21no—
214C42×C151—21no—
215C42×C151—41no—
216C42×C151C2411yescharacteristic
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—41no—
220C23×C151—41no—
221Q8×C151—21no—
222Q8×C151—21no—
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151—81no—
226Q8×C151—161no—
227Q8×C151#13512yescomplemented
228Q8×C151AGL(1,ℤ/8)12yes—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—21no—
232D4×C151—21no—
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—82no—
242D4×C151—82no—
243D4×C151—81no—
244D4×C151—81no—
245D4×C151—82no—
246D4×C151—161no—
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—82no—
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151H(5,𝔽2)11yescharacteristic
266C8×C151—21no—
267C8×C151—21no—
268C8×C151—21no—
269C8×C151—21no—
270C8×C151—41no—
271C8×C151—41no—
272C8×C151—41no—
273C8×C151—41no—
274C8×C151—41no—
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—22no—
289C4×C151—22no—
290C4×C151—21no—
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#57711yescharacteristic
300C4×C151#57711yescharacteristic
301C2×C151—81no—
302C2×C151—81no—
303C2×C151—161no—
304C2×C151—161no—
305C2×C151#326511yescharacteristic
306C2×C151#328211yescharacteristic
307C2×C151#328811yescharacteristic
308#19827C15111yesmaximal, characteristic, direct product factor, Sylow
309C151#1982711yescharacteristic, direct product factor, Sylow
310#3362C2×C15111yescharacteristic, complemented
311#3362C2×C15111yescharacteristic, complemented
312#3332C2×C15111yescharacteristic, complemented
313#3284C2×C15111yescharacteristic, complemented
314#1717C2×C15111yescharacteristic, complemented
315#1697C2×C15111yescharacteristic, complemented
316#1682C2×C15111yescharacteristic, complemented
317#1677C2×C15111yescharacteristic, complemented
318#1666C2×C15111yescharacteristic, complemented
319#1645C2×C15111yescharacteristic, complemented
320#1635C2×C15111yescharacteristic, complemented
321#1621C2×C15111yescharacteristic, complemented
322#1621C2×C15111yescharacteristic, complemented
323#1583C2×C15111yescharacteristic, complemented
324SD16⋊C8C2×C15111yescharacteristic, complemented
325C2×#135—21no—
326Q82C22×C15111yescharacteristic
327#550C22×C15111yescharacteristic
328#550C22×C15111yescharacteristic
329#547C22×C15111yescharacteristic
330#493C22×C15111yescharacteristic
331#492C22×C15111yescharacteristic
332#487C22×C15111yescharacteristic
333#486—21no—
334#486—21no—
335#486C22×C15111yescharacteristic
336#486C22×C15111yescharacteristic
337#486C22×C15111yescharacteristic
338#481—21no—
339#476—21no—
340#476—21no—
341#476C22×C15111yescharacteristic
342#476C22×C15111yescharacteristic
343#475C22×C15111yescharacteristic
344#469—21no—
345#465—21no—
346#462C22×C15111yescharacteristic
347#460—21no—
348#460—21no—
349#460C22×C15111yescharacteristic
350#460C22×C15111yescharacteristic
351#459C22×C15111yescharacteristic
352#459C22×C15111yescharacteristic
353#452—21no—
354#449—21no—
355#449—21no—
356C8×Q8C22×C15111yescharacteristic
357C8×Q8C22×C15111yescharacteristic
358C4×SD16—21no—
359C4×SD16—21no—
360C4×SD16C22×C15111yescharacteristic
361C4×SD16C22×C15111yescharacteristic
362#436C22×C15111yescharacteristic
363C8×D4C22×C15111yescharacteristic
364#417—21no—
365#335C22×C15111yescharacteristic
366#334C22×C15111yescharacteristic
367#333C22×C15111yescharacteristic
368#332C22×C15111yescharacteristic
369#331C22×C15111yescharacteristic
370#331C22×C15111yescharacteristic
371Q8⋊C8C22×C15111yescharacteristic
372Q8⋊C8C22×C15111yescharacteristic
373D4⋊C8C22×C15111yescharacteristic
374D4⋊C8C22×C15111yescharacteristic
375#322C22×C15111yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379#135—44no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16D4×C15111yescharacteristic
386C2×SD16D4×C15111yescharacteristic
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—41no—
390C2×M16—21no—
391C22×C8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—41no—
395C4⋊Q8C23×C15111yescharacteristic
396C4⋊Q8C23×C15111yescharacteristic
397#127—21no—
398#127—21no—
399#127C23×C15111yescharacteristic
400#127C23×C15111yescharacteristic
401#123—41no—
402C22⋊Q8—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8C23×C15111yescharacteristic
411C4×Q8C23×C15111yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C23×C15111yescharacteristic
415C4×D4C23×C15111yescharacteristic
416C2×C4⋊C4—21no—
417#106—21no—
418#106—21no—
419#106—21no—
420#106D4×C15111yescharacteristic
421#106D4×C15111yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8C23×C15111yescharacteristic
425C4⋊C8C23×C15111yescharacteristic
426C4⋊C8C23×C15111yescharacteristic
427C4⋊C8C23×C15111yescharacteristic
428#103—21no—
429#103—21no—
430#103—41no—
431#103D4×C15111yescharacteristic
432#103D4×C15111yescharacteristic
433#102—21no—
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—21no—
443#102—21no—
444#102—21no—
445#102D4×C15111yescharacteristic
446#102D4×C15111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8C23×C15111yescharacteristic
452C4×C8C23×C15111yescharacteristic
453C4×C8C23×C15111yescharacteristic
454#41—42no—
455#41—42no—
456#41—42no—
457#41—81no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8C2×D4×C15111yescharacteristic
464C2×Q8C2×D4×C15111yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C15111yescharacteristic
477C2×D4C2×D4×C15111yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—42no—
484SD16—22no—
485SD16—22no—
486SD16—42no—
487SD16—42no—
488SD16—42no—
489SD16—81no—
490D8—42no—
491D8—81no—
492D8—82no—
493M16—81no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—42no—
500C2×C8C2×D4×C15111yescharacteristic
501C2×C8C2×D4×C15111yescharacteristic
502C2×C8C2×D4×C15111yescharacteristic
503C2×C8C2×D4×C15111yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C15111yescharacteristic
514C4⋊C4C2×D4×C15111yescharacteristic
515C4⋊C4C2×D4×C15111yescharacteristic
516C4⋊C4C2×D4×C15111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C42—21no—
523C42—21no—
524C42—41no—
525C42C24×C15111yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—161no—
536Q8#135×C15112yescomplemented
537Q8AGL(1,ℤ/8)×C15112yes—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—82no—
551D4—82no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—161no—
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—82no—
572C2×C4C22×D4×C15111yescharacteristic
573C2×C4C22×D4×C15111yescharacteristic
574C2×C4H(5,𝔽2)×C15111yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
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—22no—
598C4—22no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C15111yescharacteristic
607C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
608C4#577×C15111yescharacteristic
609C4#577×C15111yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2#3265×C15111yescharacteristic
615C2#3282×C15111yescharacteristic
616C2#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. #3362×C151C2semidirect
2. #3362×C151C2semidirect
3. #3332×C151C2semidirect
4. #3284×C151C2semidirect
5. #1717×C151C2semidirect
6. #1697×C151C2semidirect
7. #1682×C151C2semidirect
8. #1677×C151C2semidirect
9. #1666×C151C2semidirect
10. #1645×C151C2semidirect
11. #1635×C151C2semidirect
12. #1621×C151C2semidirect
13. #1621×C151C2semidirect
14. #1583×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
227. Q8×C151#135semidirect
308. #19827C151direct (N × H)
309. C151#19827direct (N × H)
310. #3362C2×C151semidirect
311. #3362C2×C151semidirect
312. #3332C2×C151semidirect
313. #3284C2×C151semidirect
314. #1717C2×C151semidirect
315. #1697C2×C151semidirect
316. #1682C2×C151semidirect
317. #1677C2×C151semidirect
318. #1666C2×C151semidirect
319. #1645C2×C151semidirect
320. #1635C2×C151semidirect
321. #1621C2×C151semidirect
322. #1621C2×C151semidirect
323. #1583C2×C151semidirect
324. SD16⋊C8C2×C151semidirect
536. Q8#135×C151semidirect

Maximal subgroups

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

subgroupindex
#3362×C1512
#3332×C1512
#3284×C1512
#1717×C1512
#1697×C1512
#1682×C1512
#1677×C1512
#1666×C1512
#1645×C1512
#1635×C1512
#1621×C1512
#1583×C1512
SD16⋊C8×C1512
#19827151