Finite Group Databasebeta

← C151×#19899 #50324824

Subgroups — C151×#19899 #50324824

Order 38656.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3330×C151C211yesmaximal, characteristic, complemented
2#3325×C151C211yesmaximal, characteristic, complemented
3#3303×C151C211yesmaximal, characteristic, complemented
4#3294×C151C211yesmaximal, characteristic, complemented
5#1711×C151C211yesmaximal, characteristic, complemented
6#1699×C151C211yesmaximal, characteristic, complemented
7#1697×C151C211yesmaximal, characteristic, complemented
8#1683×C151C211yesmaximal, characteristic, complemented
9#1681×C151C211yesmaximal, characteristic, complemented
10#1646×C151C211yesmaximal, characteristic, complemented
11#1639×C151C211yesmaximal, characteristic, complemented
12#1635×C151C211yesmaximal, characteristic, complemented
13#1625×C151C211yesmaximal, characteristic, complemented
14#1589×C151C211yesmaximal, characteristic, complemented
15C8×D8×C151C211yesmaximal, characteristic, complemented
16#555×C151C2211yescharacteristic
17#547×C151C2211yescharacteristic
18#547×C151C2211yescharacteristic, complemented
19D42×C151C2211yescharacteristic
20#487×C151C2211yescharacteristic, complemented
21#487×C151C2211yescharacteristic, complemented
22#487×C151C2211yescharacteristic, complemented
23#486×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#486×C151C2211yescharacteristic
26#485×C151—21no—
27#484×C151—21no—
28#482×C151—21no—
29#480×C151—21no—
30#476×C151C2211yescharacteristic
31#476×C151C2211yescharacteristic, complemented
32#474×C151C2211yescharacteristic
33#474×C151C2211yescharacteristic
34#469×C151—21no—
35#468×C151—21no—
36#466×C151—21no—
37#465×C151—21no—
38#461×C151C2211yescharacteristic
39#461×C151C2211yescharacteristic, complemented
40#459×C151C2211yescharacteristic
41#459×C151C2211yescharacteristic
42#449×C151—21no—
43#449×C151—21no—
44#447×C151—21no—
45#447×C151—21no—
46C4×D8×C151C2211yescharacteristic
47C4×D8×C151C2211yescharacteristic
48#436×C151C2211yescharacteristic
49#436×C151C2211yescharacteristic, complemented
50C8×D4×C151C2211yescharacteristic
51C8×D4×C151C2211yescharacteristic, complemented
52#418×C151—21no—
53#417×C151—21no—
54#416×C151—21no—
55C2×#102×C151—21no—
56#335×C151C2211yescharacteristic, complemented
57#335×C151C2211yescharacteristic, complemented
58#333×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#332×C151C2211yescharacteristic, complemented
61#331×C151C2211yescharacteristic
62D4⋊C8×C151C2211yescharacteristic
63D4⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic, complemented
65D4⋊C8×C151C2211yescharacteristic, complemented
66C82×C151C2211yescharacteristic, complemented
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×D8×C151—21no—
74C2×D8×C151—21no—
75C2×D8×C151D411yescharacteristic
76C2×D8×C151D411yescharacteristic
77C2×M16×C151—21no—
78C2×M16×C151—21no—
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#127×C151C2311yescharacteristic
85#124×C151—41no—
86#123×C151—41no—
87#123×C151—41no—
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—
95#121×C151—21no—
96#120×C151—41no—
97C4×D4×C151C2311yescharacteristic
98C4×D4×C151C2311yescharacteristic
99C4×D4×C151C2311yescharacteristic
100C4×D4×C151C2311yescharacteristic
101#117×C151—21no—
102#117×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151D411yescharacteristic
108#107×C151D411yescharacteristic
109#106×C151—21no—
110#106×C151—21no—
111C4⋊C8×C151C2311yescharacteristic
112C4⋊C8×C151C2311yescharacteristic
113C4⋊C8×C151C2311yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115#103×C151—21no—
116#103×C151—21no—
117#103×C151—21no—
118#103×C151—21no—
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—41no—
122#102×C151—21no—
123#102×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—
132#102×C151—41no—
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
144C24×C151—41no—
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×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—41no—
156C2×D4×C151—41no—
157C2×D4×C151—42no—
158C2×D4×C151—42no—
159C2×D4×C151—41no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151—81no—
163C2×D4×C151—81no—
164C2×D4×C151C2×D411yescharacteristic
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C2×D4×C151C2×D411yescharacteristic
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—41no—
173C22×C4×C151—41no—
174SD16×C151—81no—
175SD16×C151—81no—
176D8×C151—22no—
177D8×C151—41no—
178D8×C151—81no—
179D8×C151—81no—
180M16×C151—81no—
181M16×C151—81no—
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×C151—81no—
189C2×C8×C151C2×D411yescharacteristic
190C2×C8×C151C2×D411yescharacteristic
191C2×C8×C151C2×D411yescharacteristic
192C2×C8×C151C2×D411yescharacteristic
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151—41no—
201C4⋊C4×C151C2×D411yescharacteristic
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D411yescharacteristic
204C4⋊C4×C151C2×D411yescharacteristic
205C22⋊C4×C151—21no—
206C22⋊C4×C151—21no—
207C22⋊C4×C151—21no—
208C22⋊C4×C151—21no—
209C22⋊C4×C151—41no—
210C22⋊C4×C151—41no—
211C22⋊C4×C151—41no—
212C22⋊C4×C151—41no—
213C22⋊C4×C151—41no—
214C42×C151—41no—
215C42×C151C2411yescharacteristic
216C23×C151—21no—
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—21no—
220C23×C151—41no—
221C23×C151—82no—
222C23×C151—82no—
223C23×C151—161no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—41no—
228Q8×C151—81no—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—21no—
232D4×C151—21no—
233D4×C151—21no—
234D4×C151—21no—
235D4×C151—21no—
236D4×C151—41no—
237D4×C151—41no—
238D4×C151—41no—
239D4×C151—41no—
240D4×C151—81no—
241D4×C151—82no—
242D4×C151—82no—
243D4×C151—82no—
244D4×C151—82no—
245D4×C151—161no—
246D4×C151#13512yes—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
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—41no—
262C2×C4×C151—82no—
263C2×C4×C151—82no—
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151C22×D411yescharacteristic
266C2×C4×C151H(5,𝔽2)11yescharacteristic
267C8×C151—21no—
268C8×C151—21no—
269C8×C151—21no—
270C8×C151—21no—
271C8×C151—41no—
272C8×C151—41no—
273C8×C151—41no—
274C8×C151—41no—
275C8×C151—41no—
276C22×C151—22no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
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—164no—
292C22×C151D4211yescharacteristic
293C4×C151—21no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—41no—
297C4×C151—41no—
298C4×C151—81no—
299C4×C151—81no—
300C4×C151—81no—
301C4×C151C2×#13511yescharacteristic
302C4×C151#57511yescharacteristic
303C4×C151#57611yescharacteristic
304C4×C151#57611yescharacteristic
305C2×C151—42no—
306C2×C151—81no—
307C2×C151—81no—
308C2×C151—81no—
309C2×C151—161no—
310C2×C151#327311yescharacteristic
311C2×C151#328011yescharacteristic
312C2×C151#329011yescharacteristic
313#19899C15111yesmaximal, characteristic, direct product factor, Sylow
314C151#1989911yescharacteristic, direct product factor, Sylow
315#3330C2×C15111yescharacteristic, complemented
316#3325C2×C15111yescharacteristic, complemented
317#3303C2×C15111yescharacteristic, complemented
318#3294C2×C15111yescharacteristic, complemented
319#1711C2×C15111yescharacteristic, complemented
320#1699C2×C15111yescharacteristic, complemented
321#1697C2×C15111yescharacteristic, complemented
322#1683C2×C15111yescharacteristic, complemented
323#1681C2×C15111yescharacteristic, complemented
324#1646C2×C15111yescharacteristic, complemented
325#1639C2×C15111yescharacteristic, complemented
326#1635C2×C15111yescharacteristic, complemented
327#1625C2×C15111yescharacteristic, complemented
328#1589C2×C15111yescharacteristic, complemented
329C8×D8C2×C15111yescharacteristic, complemented
330#555C22×C15111yescharacteristic
331#547C22×C15111yescharacteristic
332#547C22×C15111yescharacteristic, complemented
333D42C22×C15111yescharacteristic
334#487C22×C15111yescharacteristic, complemented
335#487C22×C15111yescharacteristic, complemented
336#487C22×C15111yescharacteristic, complemented
337#486C22×C15111yescharacteristic
338#486C22×C15111yescharacteristic
339#486C22×C15111yescharacteristic
340#485—21no—
341#484—21no—
342#482—21no—
343#480—21no—
344#476C22×C15111yescharacteristic
345#476C22×C15111yescharacteristic, complemented
346#474C22×C15111yescharacteristic
347#474C22×C15111yescharacteristic
348#469—21no—
349#468—21no—
350#466—21no—
351#465—21no—
352#461C22×C15111yescharacteristic
353#461C22×C15111yescharacteristic, complemented
354#459C22×C15111yescharacteristic
355#459C22×C15111yescharacteristic
356#449—21no—
357#449—21no—
358#447—21no—
359#447—21no—
360C4×D8C22×C15111yescharacteristic
361C4×D8C22×C15111yescharacteristic
362#436C22×C15111yescharacteristic
363#436C22×C15111yescharacteristic, complemented
364C8×D4C22×C15111yescharacteristic
365C8×D4C22×C15111yescharacteristic, complemented
366#418—21no—
367#417—21no—
368#416—21no—
369C2×#102—21no—
370#335C22×C15111yescharacteristic, complemented
371#335C22×C15111yescharacteristic, complemented
372#333C22×C15111yescharacteristic, complemented
373#332C22×C15111yescharacteristic, complemented
374#332C22×C15111yescharacteristic, complemented
375#331C22×C15111yescharacteristic
376D4⋊C8C22×C15111yescharacteristic
377D4⋊C8C22×C15111yescharacteristic
378D4⋊C8C22×C15111yescharacteristic, complemented
379D4⋊C8C22×C15111yescharacteristic, complemented
380C82C22×C15111yescharacteristic, complemented
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C15111yescharacteristic
390C2×D8D4×C15111yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C15111yescharacteristic
396C4⋊Q8C23×C15111yescharacteristic
397C4⋊Q8C23×C15111yescharacteristic
398#127C23×C15111yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C15111yescharacteristic
412C4×D4C23×C15111yescharacteristic
413C4×D4C23×C15111yescharacteristic
414C4×D4C23×C15111yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C15111yescharacteristic
422#107D4×C15111yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C15111yescharacteristic
426C4⋊C8C23×C15111yescharacteristic
427C4⋊C8C23×C15111yescharacteristic
428C4⋊C8C23×C15111yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
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#102—21no—
446#102—41no—
447#102D4×C15111yescharacteristic
448#102D4×C15111yescharacteristic
449#102D4×C15111yescharacteristic
450#102D4×C15111yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C15111yescharacteristic
456C4×C8C23×C15111yescharacteristic
457C4×C8C23×C15111yescharacteristic
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C15111yescharacteristic
479C2×D4C2×D4×C15111yescharacteristic
480C2×D4C2×D4×C15111yescharacteristic
481C2×D4C2×D4×C15111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C15111yescharacteristic
504C2×C8C2×D4×C15111yescharacteristic
505C2×C8C2×D4×C15111yescharacteristic
506C2×C8C2×D4×C15111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C15111yescharacteristic
516C4⋊C4C2×D4×C15111yescharacteristic
517C4⋊C4C2×D4×C15111yescharacteristic
518C4⋊C4C2×D4×C15111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C15111yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4#135×C15112yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C15111yescharacteristic
579C2×C4C22×D4×C15111yescharacteristic
580C2×C4H(5,𝔽2)×C15111yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C15111yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C15111yescharacteristic
616C4#575×C15111yescharacteristic
617C4#576×C15111yescharacteristic
618C4#576×C15111yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2#3273×C15111yescharacteristic
625C2#3280×C15111yescharacteristic
626C2#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. #3330×C151C2semidirect
2. #3325×C151C2semidirect
3. #3303×C151C2semidirect
4. #3294×C151C2semidirect
5. #1711×C151C2semidirect
6. #1699×C151C2semidirect
7. #1697×C151C2semidirect
8. #1683×C151C2semidirect
9. #1681×C151C2semidirect
10. #1646×C151C2semidirect
11. #1639×C151C2semidirect
12. #1635×C151C2semidirect
13. #1625×C151C2semidirect
14. #1589×C151C2semidirect
15. C8×D8×C151C2semidirect
18. #547×C151C22semidirect
20. #487×C151C22semidirect
21. #487×C151C22semidirect
22. #487×C151C22semidirect
31. #476×C151C22semidirect
39. #461×C151C22semidirect
49. #436×C151C22semidirect
51. C8×D4×C151C22semidirect
56. #335×C151C22semidirect
57. #335×C151C22semidirect
58. #333×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
64. D4⋊C8×C151C22semidirect
65. D4⋊C8×C151C22semidirect
66. C82×C151C22semidirect
313. #19899C151direct (N × H)
314. C151#19899direct (N × H)
315. #3330C2×C151semidirect
316. #3325C2×C151semidirect
317. #3303C2×C151semidirect
318. #3294C2×C151semidirect
319. #1711C2×C151semidirect
320. #1699C2×C151semidirect
321. #1697C2×C151semidirect
322. #1683C2×C151semidirect
323. #1681C2×C151semidirect
324. #1646C2×C151semidirect
325. #1639C2×C151semidirect
326. #1635C2×C151semidirect
327. #1625C2×C151semidirect
328. #1589C2×C151semidirect
329. C8×D8C2×C151semidirect
332. #547C22×C151semidirect
334. #487C22×C151semidirect
335. #487C22×C151semidirect
336. #487C22×C151semidirect
345. #476C22×C151semidirect
353. #461C22×C151semidirect
363. #436C22×C151semidirect
365. C8×D4C22×C151semidirect
370. #335C22×C151semidirect
371. #335C22×C151semidirect
372. #333C22×C151semidirect
373. #332C22×C151semidirect
374. #332C22×C151semidirect
378. D4⋊C8C22×C151semidirect
379. D4⋊C8C22×C151semidirect
380. C82C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3330×C1512
#3325×C1512
#3303×C1512
#3294×C1512
#1711×C1512
#1699×C1512
#1697×C1512
#1683×C1512
#1681×C1512
#1646×C1512
#1639×C1512
#1635×C1512
#1625×C1512
#1589×C1512
C8×D8×C1512
#19899151