Finite Group Databasebeta

← C151×#19557 #50324482

Subgroups — C151×#19557 #50324482

Order 38656.

642 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3245×C151C211yesmaximal, characteristic, complemented
2#3214×C151C211yesmaximal, characteristic, complemented
3#3207×C151C211yesmaximal, characteristic, complemented
4#2979×C151C211yesmaximal, characteristic, complemented
5#1701×C151C211yesmaximal, characteristic, complemented
6#1699×C151C211yesmaximal, characteristic, complemented
7#1687×C151C211yesmaximal, characteristic, complemented
8#1685×C151C211yesmaximal, characteristic, complemented
9#1681×C151C211yesmaximal, characteristic, complemented
10#1679×C151C211yesmaximal, characteristic, complemented
11#1667×C151C211yesmaximal, characteristic, complemented
12#1665×C151C211yesmaximal, characteristic, complemented
13#1573×C151C211yesmaximal, characteristic, complemented
14#1553×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#532×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19#496×C151—21no—
20#493×C151C2211yescharacteristic
21#492×C151C2211yescharacteristic
22#489×C151—21no—
23#487×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#474×C151—21no—
26#474×C151C2211yescharacteristic
27#474×C151C2211yescharacteristic
28#466×C151—21no—
29#466×C151—21no—
30#463×C151—21no—
31#463×C151—21no—
32#461×C151C2211yescharacteristic
33#461×C151C2211yescharacteristic
34#459×C151—21no—
35#459×C151C2211yescharacteristic
36#459×C151C2211yescharacteristic
37#459×C151C2211yescharacteristic
38#459×C151C2211yescharacteristic
39#449×C151—21no—
40#449×C151—21no—
41#449×C151—21no—
42#449×C151—21no—
43#436×C151—21no—
44#436×C151C2211yescharacteristic
45#436×C151C2211yescharacteristic
46C8×D4×C151—21no—
47C8×D4×C151C2211yescharacteristic
48C8×D4×C151C2211yescharacteristic
49#432×C151C2211yescharacteristic
50#431×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#408×C151—21no—
54#408×C151—21no—
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#331×C151C2211yescharacteristic
64#331×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×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×SD16×C151—21no—
74C2×D8×C151—21no—
75C2×D8×C151—21no—
76C2×D8×C151—21no—
77C2×D8×C151—21no—
78C2×D8×C151—21no—
79C2×D8×C151—21no—
80C2×M16×C151—21no—
81C2×M16×C151—21no—
82C22×C8×C151—21no—
83C22×C8×C151—21no—
84C22×C8×C151—21no—
85C4⋊Q8×C151D411yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88#127×C151D411yescharacteristic
89#127×C151C2311yescharacteristic
90#127×C151C2311yescharacteristic
91#124×C151—21no—
92#124×C151—21no—
93#124×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97#121×C151—21no—
98#121×C151—21no—
99#121×C151D411yescharacteristic
100#121×C151D411yescharacteristic
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106C4×D4×C151C2311yescharacteristic
107C4×D4×C151C2311yescharacteristic
108C2×C42×C151C2311yescharacteristic
109#107×C151—21no—
110#107×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151D411yescharacteristic
113C4⋊C8×C151D411yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
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—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151—21no—
137C22⋊C8×C151—21no—
138C22⋊C8×C151D411yescharacteristic
139C22⋊C8×C151D411yescharacteristic
140#97×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—81no—
145#41×C151—81no—
146#41×C151—81no—
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×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—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—41no—
164C2×D4×C151—41no—
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—41no—
170C22×C4×C151—41no—
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151#4111yescharacteristic
174SD16×C151—81no—
175SD16×C151—81no—
176SD16×C151—81no—
177SD16×C151—81no—
178D8×C151—81no—
179D8×C151—81no—
180D8×C151—81no—
181D8×C151—81no—
182D8×C151—81no—
183D8×C151—81no—
184M16×C151—81no—
185M16×C151—81no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—81no—
193C2×C8×C151—81no—
194C2×C8×C151—81no—
195C2×C8×C151C2×D411yescharacteristic
196C2×C8×C151C2×D411yescharacteristic
197C2×C8×C151C2×D411yescharacteristic
198C2×C8×C151C2×D411yescharacteristic
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151C2×D411yescharacteristic
205C4⋊C4×C151C2×D411yescharacteristic
206C22⋊C4×C151—21no—
207C22⋊C4×C151—21no—
208C22⋊C4×C151—21no—
209C22⋊C4×C151—21no—
210C22⋊C4×C151—41no—
211C22⋊C4×C151—41no—
212C22⋊C4×C151—41no—
213C22⋊C4×C151—41no—
214C42×C151C2×D411yescharacteristic
215C42×C151C2×D411yescharacteristic
216C42×C151#4111yescharacteristic
217C42×C151C2411yescharacteristic
218C23×C151—21no—
219C23×C151—21no—
220C23×C151—41no—
221C23×C151—41no—
222C23×C151#12111yescharacteristic
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—81no—
228D4×C151—21no—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—21no—
232D4×C151—42no—
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—81no—
242D4×C151—81no—
243D4×C151—81no—
244D4×C151—81no—
245D4×C151—81no—
246D4×C151—82no—
247D4×C151—82no—
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—41no—
261C2×C4×C151—82no—
262C2×C4×C151—82no—
263C2×C4×C151#12111yescharacteristic
264C2×C4×C151#12111yescharacteristic
265C2×C4×C151#12111yescharacteristic
266C2×C4×C151C22×D411yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C2×#4111yescharacteristic
269C8×C151—21no—
270C8×C151—21no—
271C8×C151—21no—
272C8×C151—21no—
273C8×C151—41no—
274C8×C151—41no—
275C8×C151—41no—
276C8×C151—41no—
277C8×C151—41no—
278C8×C151—41no—
279C22×C151—21no—
280C22×C151—21no—
281C22×C151—21no—
282C22×C151—41no—
283C22×C151—41no—
284C22×C151—41no—
285C22×C151—41no—
286C22×C151—41no—
287C22×C151—41no—
288C22×C151—81no—
289C22×C151—81no—
290C22×C151—81no—
291C22×C151—81no—
292C22×C151—81no—
293C22×C151—81no—
294C22×C151C2×#12111yescharacteristic
295C4×C151—21no—
296C4×C151—21no—
297C4×C151—21no—
298C4×C151—21no—
299C4×C151—41no—
300C4×C151—41no—
301C4×C151—81no—
302C4×C151—81no—
303C4×C151#57611yescharacteristic
304C4×C151#57611yescharacteristic
305C4×C151#57611yescharacteristic
306C4×C151#57711yescharacteristic
307C2×C151—41no—
308C2×C151—81no—
309C2×C151—81no—
310C2×C151—161no—
311C2×C151—161no—
312C2×C151#304111yescharacteristic
313C2×C151#306211yescharacteristic
314C2×C151#306711yescharacteristic
315#19557C15111yesmaximal, characteristic, direct product factor, Sylow
316C151#1955711yescharacteristic, direct product factor, Sylow
317#3245C2×C15111yescharacteristic, complemented
318#3214C2×C15111yescharacteristic, complemented
319#3207C2×C15111yescharacteristic, complemented
320#2979C2×C15111yescharacteristic, complemented
321#1701C2×C15111yescharacteristic, complemented
322#1699C2×C15111yescharacteristic, complemented
323#1687C2×C15111yescharacteristic, complemented
324#1685C2×C15111yescharacteristic, complemented
325#1681C2×C15111yescharacteristic, complemented
326#1679C2×C15111yescharacteristic, complemented
327#1667C2×C15111yescharacteristic, complemented
328#1665C2×C15111yescharacteristic, complemented
329#1573C2×C15111yescharacteristic, complemented
330#1553C2×C15111yescharacteristic, complemented
331#1540C2×C15111yescharacteristic, complemented
332#532C22×C15111yescharacteristic
333#532C22×C15111yescharacteristic
334#532C22×C15111yescharacteristic
335#496—21no—
336#493C22×C15111yescharacteristic
337#492C22×C15111yescharacteristic
338#489—21no—
339#487C22×C15111yescharacteristic
340#486C22×C15111yescharacteristic
341#474—21no—
342#474C22×C15111yescharacteristic
343#474C22×C15111yescharacteristic
344#466—21no—
345#466—21no—
346#463—21no—
347#463—21no—
348#461C22×C15111yescharacteristic
349#461C22×C15111yescharacteristic
350#459—21no—
351#459C22×C15111yescharacteristic
352#459C22×C15111yescharacteristic
353#459C22×C15111yescharacteristic
354#459C22×C15111yescharacteristic
355#449—21no—
356#449—21no—
357#449—21no—
358#449—21no—
359#436—21no—
360#436C22×C15111yescharacteristic
361#436C22×C15111yescharacteristic
362C8×D4—21no—
363C8×D4C22×C15111yescharacteristic
364C8×D4C22×C15111yescharacteristic
365#432C22×C15111yescharacteristic
366#431C22×C15111yescharacteristic
367#431C22×C15111yescharacteristic
368C2×C4⋊C8C22×C15111yescharacteristic
369#408—21no—
370#408—21no—
371#335C22×C15111yescharacteristic
372#335C22×C15111yescharacteristic
373#334C22×C15111yescharacteristic
374#334C22×C15111yescharacteristic
375#332C22×C15111yescharacteristic
376#332C22×C15111yescharacteristic
377#332C22×C15111yescharacteristic
378#332C22×C15111yescharacteristic
379#331C22×C15111yescharacteristic
380#331C22×C15111yescharacteristic
381#331C22×C15111yescharacteristic
382#331C22×C15111yescharacteristic
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×M16—21no—
397C2×M16—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C4⋊Q8D4×C15111yescharacteristic
402C4⋊Q8C23×C15111yescharacteristic
403C4⋊Q8C23×C15111yescharacteristic
404#127D4×C15111yescharacteristic
405#127C23×C15111yescharacteristic
406#127C23×C15111yescharacteristic
407#124—21no—
408#124—21no—
409#124—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121D4×C15111yescharacteristic
416#121D4×C15111yescharacteristic
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4C23×C15111yescharacteristic
423C4×D4C23×C15111yescharacteristic
424C2×C42C23×C15111yescharacteristic
425#107—21no—
426#107—21no—
427C4⋊C8—21no—
428C4⋊C8D4×C15111yescharacteristic
429C4⋊C8D4×C15111yescharacteristic
430C4⋊C8C23×C15111yescharacteristic
431C4⋊C8C23×C15111yescharacteristic
432C4⋊C8C23×C15111yescharacteristic
433C4⋊C8C23×C15111yescharacteristic
434C4⋊C8C23×C15111yescharacteristic
435C4⋊C8C23×C15111yescharacteristic
436#103—21no—
437#103—21no—
438#103—21no—
439#103—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8D4×C15111yescharacteristic
455C22⋊C8D4×C15111yescharacteristic
456#97—21no—
457C4×C8—21no—
458C4×C8C23×C15111yescharacteristic
459C4×C8C23×C15111yescharacteristic
460#41—81no—
461#41—81no—
462#41—81no—
463#41—81no—
464#41—81no—
465#41—81no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4C2×D4×C15111yescharacteristic
482C2×D4C2×D4×C15111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4#41×C15111yescharacteristic
490SD16—81no—
491SD16—81no—
492SD16—81no—
493SD16—81no—
494D8—81no—
495D8—81no—
496D8—81no—
497D8—81no—
498D8—81no—
499D8—81no—
500M16—81no—
501M16—81no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—81no—
510C2×C8—81no—
511C2×C8C2×D4×C15111yescharacteristic
512C2×C8C2×D4×C15111yescharacteristic
513C2×C8C2×D4×C15111yescharacteristic
514C2×C8C2×D4×C15111yescharacteristic
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4C2×D4×C15111yescharacteristic
521C4⋊C4C2×D4×C15111yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C42C2×D4×C15111yescharacteristic
531C42C2×D4×C15111yescharacteristic
532C42#41×C15111yescharacteristic
533C42C24×C15111yescharacteristic
534C23—21no—
535C23—21no—
536C23—41no—
537C23—41no—
538C23#121×C15111yescharacteristic
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—81no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—81no—
558D4—81no—
559D4—81no—
560D4—81no—
561D4—81no—
562D4—82no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4#121×C15111yescharacteristic
580C2×C4#121×C15111yescharacteristic
581C2×C4#121×C15111yescharacteristic
582C2×C4C22×D4×C15111yescharacteristic
583C2×C4C22×D4×C15111yescharacteristic
584C2×C4C2×#41×C15111yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—21no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—41no—
593C8—41no—
594C8—41no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×#121×C15111yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4#576×C15111yescharacteristic
620C4#576×C15111yescharacteristic
621C4#576×C15111yescharacteristic
622C4#577×C15111yescharacteristic
623C2—41no—
624C2—81no—
625C2—81no—
626C2—161no—
627C2—161no—
628C2#3041×C15111yescharacteristic
629C2#3062×C15111yescharacteristic
630C2#3067×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3245×C151C2semidirect
2. #3214×C151C2semidirect
3. #3207×C151C2semidirect
4. #2979×C151C2semidirect
5. #1701×C151C2semidirect
6. #1699×C151C2semidirect
7. #1687×C151C2semidirect
8. #1685×C151C2semidirect
9. #1681×C151C2semidirect
10. #1679×C151C2semidirect
11. #1667×C151C2semidirect
12. #1665×C151C2semidirect
13. #1573×C151C2semidirect
14. #1553×C151C2semidirect
15. #1540×C151C2semidirect
315. #19557C151direct (N × H)
316. C151#19557direct (N × H)
317. #3245C2×C151semidirect
318. #3214C2×C151semidirect
319. #3207C2×C151semidirect
320. #2979C2×C151semidirect
321. #1701C2×C151semidirect
322. #1699C2×C151semidirect
323. #1687C2×C151semidirect
324. #1685C2×C151semidirect
325. #1681C2×C151semidirect
326. #1679C2×C151semidirect
327. #1667C2×C151semidirect
328. #1665C2×C151semidirect
329. #1573C2×C151semidirect
330. #1553C2×C151semidirect
331. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3245×C1512
#3214×C1512
#3207×C1512
#2979×C1512
#1701×C1512
#1699×C1512
#1687×C1512
#1685×C1512
#1681×C1512
#1679×C1512
#1667×C1512
#1665×C1512
#1573×C1512
#1553×C1512
#1540×C1512
#19557151