Finite Group Databasebeta

← C151×#19768 #50324693

Subgroups — C151×#19768 #50324693

Order 38656.

642 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3385×C151C211yesmaximal, characteristic, complemented
2#3362×C151C211yesmaximal, characteristic, complemented
3#3335×C151C211yesmaximal, characteristic, complemented
4#3284×C151C211yesmaximal, characteristic
5#1714×C151C211yesmaximal, characteristic, complemented
6#1686×C151C211yesmaximal, characteristic, complemented
7#1677×C151C211yesmaximal, characteristic, complemented
8#1675×C151C211yesmaximal, characteristic, complemented
9#1672×C151C211yesmaximal, characteristic, complemented
10#1645×C151C211yesmaximal, characteristic, complemented
11#1635×C151C211yesmaximal, characteristic, complemented
12#1631×C151C211yesmaximal, characteristic, complemented
13#1622×C151C211yesmaximal, characteristic, complemented
14#1582×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151—21no—
17Q82×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20#547×C151C2211yescharacteristic
21#501×C151—21no—
22#500×C151C2211yescharacteristic
23#498×C151C2211yescharacteristic
24#492×C151C2211yescharacteristic
25#492×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#486×C151—21no—
28#486×C151C2211yescharacteristic
29#483×C151—21no—
30#481×C151—21no—
31#479×C151—21no—
32#477×C151C2211yescharacteristic
33#476×C151—21no—
34#476×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#476×C151C2211yescharacteristic
37#475×C151C2211yescharacteristic
38#474×C151—21no—
39#465×C151—21no—
40#465×C151—21no—
41#462×C151C2211yescharacteristic
42#460×C151—21no—
43#460×C151C2211yescharacteristic
44#459×C151C2211yescharacteristic
45#452×C151—21no—
46#449×C151—21no—
47#446×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#440×C151—21no—
50C4×SD16×C151—21no—
51C4×SD16×C151C2211yescharacteristic
52C4×SD16×C151C2211yescharacteristic
53C8×D4×C151C2211yescharacteristic
54C8×D4×C151C2211yescharacteristic
55C2×#106×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#332×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—
69#135×C151—44no—
70C2×Q16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—41no—
75C2×SD16×C151D411yescharacteristic
76C2×SD16×C151D411yescharacteristic
77C2×D8×C151—21no—
78C22×C8×C151—21no—
79C22×C8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151—41no—
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151—21no—
87#127×C151C2311yescharacteristic
88#125×C151—21no—
89#123×C151—41no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—41no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151—41no—
96C4×Q8×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151C2311yescharacteristic
99C4×Q8×C151C2311yescharacteristic
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151C2311yescharacteristic
103C4×D4×C151C2311yescharacteristic
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115#106×C151D411yescharacteristic
116#106×C151D411yescharacteristic
117C4⋊C8×C151—21no—
118C4⋊C8×C151—21no—
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—41no—
127#103×C151D411yescharacteristic
128#103×C151D411yescharacteristic
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—
140#97×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—81no—
148#41×C151—81no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—41no—
153C2×Q8×C151C2×D411yescharacteristic
154C2×Q8×C151C2×D411yescharacteristic
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—41no—
159C2×D4×C151—41no—
160C2×D4×C151—41no—
161C2×D4×C151C2×D411yescharacteristic
162C2×D4×C151C2×D411yescharacteristic
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—41no—
166C22×C4×C151—41no—
167C22×C4×C151—41no—
168Q16×C151—42no—
169SD16×C151—41no—
170SD16×C151—42no—
171SD16×C151—42no—
172SD16×C151—81no—
173SD16×C151—82no—
174SD16×C151SD1614yescomplemented
175D8×C151—42no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—42no—
182C2×C8×C151—42no—
183C2×C8×C151C2×D411yescharacteristic
184C2×C8×C151C2×D411yescharacteristic
185C2×C8×C151C2×D411yescharacteristic
186C2×C8×C151C2×D411yescharacteristic
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
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—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D411yescharacteristic
204C22⋊C4×C151—21no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—41no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—41no—
212C42×C151C2411yescharacteristic
213C23×C151—21no—
214C23×C151—21no—
215C23×C151—41no—
216Q8×C151—21no—
217Q8×C151—21no—
218Q8×C151—21no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—81no—
222Q8×C151—81no—
223Q8×C151—161no—
224Q8×C151C2×SD1612yes—
225D4×C151—21no—
226D4×C151—21no—
227D4×C151—21no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—82no—
233D4×C151—81no—
234D4×C151—82no—
235D4×C151—161no—
236D4×C151C2×SD1612yes—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
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—82no—
252C2×C4×C151—161no—
253C2×C4×C151C22×D411yescharacteristic
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151H(5,𝔽2)11yescharacteristic
256C8×C151—21no—
257C8×C151—21no—
258C8×C151—21no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151—41no—
264C8×C151C2×SD1612yes—
265C22×C151—22no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—81no—
272C22×C151—81no—
273C22×C151—81no—
274C22×C151D4211yescharacteristic
275C4×C151—22no—
276C4×C151—21no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—41no—
280C4×C151—41no—
281C4×C151—41no—
282C4×C151—81no—
283C4×C151—81no—
284C4×C151—81no—
285C4×C151C22×SD1611yescharacteristic
286C4×C151#57511yescharacteristic
287C4×C151#57711yescharacteristic
288C4×C151#57811yescharacteristic
289C2×C151—42no—
290C2×C151—81no—
291C2×C151—161no—
292C2×C151#326911yescharacteristic
293C2×C151D4×SD1611yescharacteristic
294C2×C151#328811yescharacteristic
295#19768C15111yesmaximal, characteristic, direct product factor, Sylow
296C151#1976811yescharacteristic, direct product factor, Sylow
297#3385C2×C15111yescharacteristic, complemented
298#3362C2×C15111yescharacteristic, complemented
299#3335C2×C15111yescharacteristic, complemented
300#3284C2×C15111yescharacteristic
301#1714C2×C15111yescharacteristic, complemented
302#1686C2×C15111yescharacteristic, complemented
303#1677C2×C15111yescharacteristic, complemented
304#1675C2×C15111yescharacteristic, complemented
305#1672C2×C15111yescharacteristic, complemented
306#1645C2×C15111yescharacteristic, complemented
307#1635C2×C15111yescharacteristic, complemented
308#1631C2×C15111yescharacteristic, complemented
309#1622C2×C15111yescharacteristic, complemented
310#1582C2×C15111yescharacteristic, complemented
311SD16⋊C8C2×C15111yescharacteristic, complemented
312C2×#135—21no—
313Q82C22×C15111yescharacteristic
314#554C22×C15111yescharacteristic
315#550C22×C15111yescharacteristic
316#547C22×C15111yescharacteristic
317#501—21no—
318#500C22×C15111yescharacteristic
319#498C22×C15111yescharacteristic
320#492C22×C15111yescharacteristic
321#492C22×C15111yescharacteristic
322#487C22×C15111yescharacteristic
323#486—21no—
324#486C22×C15111yescharacteristic
325#483—21no—
326#481—21no—
327#479—21no—
328#477C22×C15111yescharacteristic
329#476—21no—
330#476C22×C15111yescharacteristic
331#476C22×C15111yescharacteristic
332#476C22×C15111yescharacteristic
333#475C22×C15111yescharacteristic
334#474—21no—
335#465—21no—
336#465—21no—
337#462C22×C15111yescharacteristic
338#460—21no—
339#460C22×C15111yescharacteristic
340#459C22×C15111yescharacteristic
341#452—21no—
342#449—21no—
343#446C22×C15111yescharacteristic
344C8×Q8C22×C15111yescharacteristic
345#440—21no—
346C4×SD16—21no—
347C4×SD16C22×C15111yescharacteristic
348C4×SD16C22×C15111yescharacteristic
349C8×D4C22×C15111yescharacteristic
350C8×D4C22×C15111yescharacteristic
351C2×#106—21no—
352#335C22×C15111yescharacteristic
353#334C22×C15111yescharacteristic
354#333C22×C15111yescharacteristic
355#333C22×C15111yescharacteristic
356#332C22×C15111yescharacteristic
357#331C22×C15111yescharacteristic
358Q8⋊C8C22×C15111yescharacteristic
359Q8⋊C8C22×C15111yescharacteristic
360D4⋊C8C22×C15111yescharacteristic
361D4⋊C8C22×C15111yescharacteristic
362#322C22×C15111yescharacteristic
363C2×#41—21no—
364C2×#41—21no—
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—41no—
371C2×SD16D4×C15111yescharacteristic
372C2×SD16D4×C15111yescharacteristic
373C2×D8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—41no—
379C4⋊Q8C23×C15111yescharacteristic
380C4⋊Q8C23×C15111yescharacteristic
381C4⋊Q8C23×C15111yescharacteristic
382#127—21no—
383#127C23×C15111yescharacteristic
384#125—21no—
385#123—41no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8C23×C15111yescharacteristic
395C4×Q8C23×C15111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C15111yescharacteristic
399C4×D4C23×C15111yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402#107—21no—
403#107—21no—
404#107—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C15111yescharacteristic
412#106D4×C15111yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C15111yescharacteristic
416C4⋊C8C23×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418C4⋊C8C23×C15111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C15111yescharacteristic
424#103D4×C15111yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102D4×C15111yescharacteristic
433#102D4×C15111yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437C4×C8—21no—
438C4×C8C23×C15111yescharacteristic
439C4×C8C23×C15111yescharacteristic
440C4×C8C23×C15111yescharacteristic
441#41—42no—
442#41—42no—
443#41—81no—
444#41—81no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8C2×D4×C15111yescharacteristic
450C2×Q8C2×D4×C15111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C2×D4×C15111yescharacteristic
458C2×D4C2×D4×C15111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464Q16—42no—
465SD16—41no—
466SD16—42no—
467SD16—42no—
468SD16—81no—
469SD16—82no—
470SD16SD16×C15114yescomplemented
471D8—42no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—42no—
479C2×C8C2×D4×C15111yescharacteristic
480C2×C8C2×D4×C15111yescharacteristic
481C2×C8C2×D4×C15111yescharacteristic
482C2×C8C2×D4×C15111yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C15111yescharacteristic
497C4⋊C4C2×D4×C15111yescharacteristic
498C4⋊C4C2×D4×C15111yescharacteristic
499C4⋊C4C2×D4×C15111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C24×C15111yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—81no—
519Q8—161no—
520Q8C2×SD16×C15112yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—82no—
529D4—81no—
530D4—82no—
531D4—161no—
532D4C2×SD16×C15112yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4C22×D4×C15111yescharacteristic
550C2×C4C22×D4×C15111yescharacteristic
551C2×C4H(5,𝔽2)×C15111yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8C2×SD16×C15112yes—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C15111yescharacteristic
571C4—22no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C22×SD16×C15111yescharacteristic
582C4#575×C15111yescharacteristic
583C4#577×C15111yescharacteristic
584C4#578×C15111yescharacteristic
585C2—42no—
586C2—81no—
587C2—161no—
588C2#3269×C15111yescharacteristic
589C2D4×SD16×C15111yescharacteristic
590C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#3284×C151C2
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. #3385×C151C2semidirect
2. #3362×C151C2semidirect
3. #3335×C151C2semidirect
5. #1714×C151C2semidirect
6. #1686×C151C2semidirect
7. #1677×C151C2semidirect
8. #1675×C151C2semidirect
9. #1672×C151C2semidirect
10. #1645×C151C2semidirect
11. #1635×C151C2semidirect
12. #1631×C151C2semidirect
13. #1622×C151C2semidirect
14. #1582×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
174. SD16×C151SD16semidirect
295. #19768C151direct (N × H)
296. C151#19768direct (N × H)
297. #3385C2×C151semidirect
298. #3362C2×C151semidirect
299. #3335C2×C151semidirect
301. #1714C2×C151semidirect
302. #1686C2×C151semidirect
303. #1677C2×C151semidirect
304. #1675C2×C151semidirect
305. #1672C2×C151semidirect
306. #1645C2×C151semidirect
307. #1635C2×C151semidirect
308. #1631C2×C151semidirect
309. #1622C2×C151semidirect
310. #1582C2×C151semidirect
311. SD16⋊C8C2×C151semidirect
470. SD16SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3385×C1512
#3362×C1512
#3335×C1512
#3284×C1512
#1714×C1512
#1686×C1512
#1677×C1512
#1675×C1512
#1672×C1512
#1645×C1512
#1635×C1512
#1631×C1512
#1622×C1512
#1582×C1512
SD16⋊C8×C1512
#19768151