Finite Group Databasebeta

← C151×#19563 #50324488

Subgroups — C151×#19563 #50324488

Order 38656.

608 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3246×C151C211yesmaximal, characteristic, complemented
2#3228×C151C211yesmaximal, characteristic, complemented
3#3214×C151C211yesmaximal, characteristic
4#2979×C151C211yesmaximal, characteristic, complemented
5#1701×C151C211yesmaximal, characteristic, complemented
6#1697×C151C211yesmaximal, characteristic, complemented
7#1693×C151C211yesmaximal, characteristic, complemented
8#1691×C151C211yesmaximal, characteristic, complemented
9#1681×C151C211yesmaximal, characteristic, complemented
10#1677×C151C211yesmaximal, characteristic, complemented
11#1673×C151C211yesmaximal, characteristic, complemented
12#1671×C151C211yesmaximal, characteristic, complemented
13#1573×C151C211yesmaximal, characteristic, complemented
14#1554×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19#500×C151C2211yescharacteristic
20#498×C151C2211yescharacteristic
21#496×C151—21no—
22#489×C151—21no—
23#486×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#482×C151—21no—
26#482×C151—21no—
27#478×C151—21no—
28#478×C151—21no—
29#476×C151C2211yescharacteristic
30#476×C151C2211yescharacteristic
31#475×C151—21no—
32#465×C151—21no—
33#465×C151—21no—
34#461×C151C2211yescharacteristic
35#461×C151C2211yescharacteristic
36#461×C151C2211yescharacteristic
37#461×C151C2211yescharacteristic
38#460×C151—21no—
39#459×C151C2211yescharacteristic
40#459×C151C2211yescharacteristic
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#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×SD16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×D8×C151—21no—
74C2×D8×C151—21no—
75C2×M16×C151—21no—
76C2×M16×C151—21no—
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79C22×C8×C151—21no—
80C4⋊Q8×C151D411yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#127×C151D411yescharacteristic
85#127×C151C2311yescharacteristic
86#125×C151—21no—
87#124×C151—21no—
88#124×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151D411yescharacteristic
95#121×C151D411yescharacteristic
96C4×Q8×C151—21no—
97C4×Q8×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151C2311yescharacteristic
102C4×D4×C151C2311yescharacteristic
103#117×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#107×C151—21no—
106#107×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×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—
148C2×Q8×C151—21no—
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—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—41no—
160C2×D4×C151C2×D411yescharacteristic
161C2×D4×C151C2×D411yescharacteristic
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—41no—
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151#4111yescharacteristic
168SD16×C151—81no—
169SD16×C151—81no—
170SD16×C151—81no—
171SD16×C151—81no—
172D8×C151—81no—
173D8×C151—81no—
174M16×C151—81no—
175M16×C151—81no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—81no—
183C2×C8×C151—81no—
184C2×C8×C151—81no—
185C2×C8×C151C2×D411yescharacteristic
186C2×C8×C151C2×D411yescharacteristic
187C2×C8×C151C2×D411yescharacteristic
188C2×C8×C151C2×D411yescharacteristic
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D411yescharacteristic
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C42×C151—41no—
208C42×C151C2×D411yescharacteristic
209C42×C151C2×D411yescharacteristic
210C42×C151#4111yescharacteristic
211C42×C151C2411yescharacteristic
212C23×C151—21no—
213C23×C151—21no—
214C23×C151—41no—
215C23×C151#12111yescharacteristic
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—81no—
221Q8×C151—81no—
222D4×C151—21no—
223D4×C151—21no—
224D4×C151—21no—
225D4×C151—21no—
226D4×C151—42no—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—81no—
232D4×C151—81no—
233D4×C151—81no—
234D4×C151—81no—
235D4×C151—82no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—82no—
251C2×C4×C151#12111yescharacteristic
252C2×C4×C151#12111yescharacteristic
253C2×C4×C151#12111yescharacteristic
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151C22×D411yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C8×C151—21no—
258C8×C151—21no—
259C8×C151—21no—
260C8×C151—21no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—41no—
266C8×C151—41no—
267C22×C151—21no—
268C22×C151—21no—
269C22×C151—21no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151—81no—
279C22×C151C2×#12111yescharacteristic
280C4×C151—21no—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—41no—
285C4×C151—41no—
286C4×C151—81no—
287C4×C151—81no—
288C4×C151—81no—
289C4×C151#57611yescharacteristic
290C4×C151#57711yescharacteristic
291C4×C151#57711yescharacteristic
292C4×C151#57711yescharacteristic
293C2×C151—41no—
294C2×C151—81no—
295C2×C151—81no—
296C2×C151—161no—
297C2×C151#304211yescharacteristic
298C2×C151#306211yescharacteristic
299C2×C151#306711yescharacteristic
300#19563C15111yesmaximal, characteristic, direct product factor, Sylow
301C151#1956311yescharacteristic, direct product factor, Sylow
302#3246C2×C15111yescharacteristic, complemented
303#3228C2×C15111yescharacteristic, complemented
304#3214C2×C15111yescharacteristic
305#2979C2×C15111yescharacteristic, complemented
306#1701C2×C15111yescharacteristic, complemented
307#1697C2×C15111yescharacteristic, complemented
308#1693C2×C15111yescharacteristic, complemented
309#1691C2×C15111yescharacteristic, complemented
310#1681C2×C15111yescharacteristic, complemented
311#1677C2×C15111yescharacteristic, complemented
312#1673C2×C15111yescharacteristic, complemented
313#1671C2×C15111yescharacteristic, complemented
314#1573C2×C15111yescharacteristic, complemented
315#1554C2×C15111yescharacteristic, complemented
316#1540C2×C15111yescharacteristic, complemented
317#533C22×C15111yescharacteristic
318#532C22×C15111yescharacteristic
319#532C22×C15111yescharacteristic
320#500C22×C15111yescharacteristic
321#498C22×C15111yescharacteristic
322#496—21no—
323#489—21no—
324#486C22×C15111yescharacteristic
325#486C22×C15111yescharacteristic
326#482—21no—
327#482—21no—
328#478—21no—
329#478—21no—
330#476C22×C15111yescharacteristic
331#476C22×C15111yescharacteristic
332#475—21no—
333#465—21no—
334#465—21no—
335#461C22×C15111yescharacteristic
336#461C22×C15111yescharacteristic
337#461C22×C15111yescharacteristic
338#461C22×C15111yescharacteristic
339#460—21no—
340#459C22×C15111yescharacteristic
341#459C22×C15111yescharacteristic
342#449—21no—
343#449—21no—
344#436—21no—
345#436C22×C15111yescharacteristic
346#436C22×C15111yescharacteristic
347C8×D4—21no—
348C8×D4C22×C15111yescharacteristic
349C8×D4C22×C15111yescharacteristic
350#432C22×C15111yescharacteristic
351#431C22×C15111yescharacteristic
352#431C22×C15111yescharacteristic
353C2×C4⋊C8C22×C15111yescharacteristic
354#408—21no—
355#408—21no—
356#335C22×C15111yescharacteristic
357#335C22×C15111yescharacteristic
358#334C22×C15111yescharacteristic
359#334C22×C15111yescharacteristic
360#333C22×C15111yescharacteristic
361#333C22×C15111yescharacteristic
362#332C22×C15111yescharacteristic
363#332C22×C15111yescharacteristic
364#332C22×C15111yescharacteristic
365#332C22×C15111yescharacteristic
366#331C22×C15111yescharacteristic
367#331C22×C15111yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×M16—21no—
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C4⋊Q8D4×C15111yescharacteristic
382C4⋊Q8C23×C15111yescharacteristic
383C4⋊Q8C23×C15111yescharacteristic
384C4⋊Q8C23×C15111yescharacteristic
385#127D4×C15111yescharacteristic
386#127C23×C15111yescharacteristic
387#125—21no—
388#124—21no—
389#124—21no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121D4×C15111yescharacteristic
396#121D4×C15111yescharacteristic
397C4×Q8—21no—
398C4×Q8—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C15111yescharacteristic
403C4×D4C23×C15111yescharacteristic
404#117—21no—
405C2×C42C23×C15111yescharacteristic
406#107—21no—
407#107—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8D4×C15111yescharacteristic
414C4⋊C8D4×C15111yescharacteristic
415C4⋊C8C23×C15111yescharacteristic
416C4⋊C8C23×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418C4⋊C8C23×C15111yescharacteristic
419C4⋊C8C23×C15111yescharacteristic
420C4⋊C8C23×C15111yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8D4×C15111yescharacteristic
440C22⋊C8D4×C15111yescharacteristic
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C15111yescharacteristic
444C4×C8C23×C15111yescharacteristic
445#41—81no—
446#41—81no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C15111yescharacteristic
462C2×D4C2×D4×C15111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4#41×C15111yescharacteristic
469SD16—81no—
470SD16—81no—
471SD16—81no—
472SD16—81no—
473D8—81no—
474D8—81no—
475M16—81no—
476M16—81no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8C2×D4×C15111yescharacteristic
487C2×C8C2×D4×C15111yescharacteristic
488C2×C8C2×D4×C15111yescharacteristic
489C2×C8C2×D4×C15111yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C15111yescharacteristic
500C4⋊C4C2×D4×C15111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—41no—
509C42C2×D4×C15111yescharacteristic
510C42C2×D4×C15111yescharacteristic
511C42#41×C15111yescharacteristic
512C42C24×C15111yescharacteristic
513C23—21no—
514C23—21no—
515C23—41no—
516C23#121×C15111yescharacteristic
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—81no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4#121×C15111yescharacteristic
553C2×C4#121×C15111yescharacteristic
554C2×C4#121×C15111yescharacteristic
555C2×C4C22×D4×C15111yescharacteristic
556C2×C4C22×D4×C15111yescharacteristic
557C2×C4C2×#41×C15111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C15111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4#576×C15111yescharacteristic
591C4#577×C15111yescharacteristic
592C4#577×C15111yescharacteristic
593C4#577×C15111yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2#3042×C15111yescharacteristic
599C2#3062×C15111yescharacteristic
600C2#3067×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3214×C151C2
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. #3246×C151C2semidirect
2. #3228×C151C2semidirect
4. #2979×C151C2semidirect
5. #1701×C151C2semidirect
6. #1697×C151C2semidirect
7. #1693×C151C2semidirect
8. #1691×C151C2semidirect
9. #1681×C151C2semidirect
10. #1677×C151C2semidirect
11. #1673×C151C2semidirect
12. #1671×C151C2semidirect
13. #1573×C151C2semidirect
14. #1554×C151C2semidirect
15. #1540×C151C2semidirect
300. #19563C151direct (N × H)
301. C151#19563direct (N × H)
302. #3246C2×C151semidirect
303. #3228C2×C151semidirect
305. #2979C2×C151semidirect
306. #1701C2×C151semidirect
307. #1697C2×C151semidirect
308. #1693C2×C151semidirect
309. #1691C2×C151semidirect
310. #1681C2×C151semidirect
311. #1677C2×C151semidirect
312. #1673C2×C151semidirect
313. #1671C2×C151semidirect
314. #1573C2×C151semidirect
315. #1554C2×C151semidirect
316. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3246×C1512
#3228×C1512
#3214×C1512
#2979×C1512
#1701×C1512
#1697×C1512
#1693×C1512
#1691×C1512
#1681×C1512
#1677×C1512
#1673×C1512
#1671×C1512
#1573×C1512
#1554×C1512
#1540×C1512
#19563151