Finite Group Databasebeta

← C151×#19896 #50324821

Subgroups — C151×#19896 #50324821

Order 38656.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3387×C151C211yesmaximal, characteristic, complemented
2#3362×C151C211yesmaximal, characteristic
3#3359×C151C211yesmaximal, characteristic, complemented
4#3278×C151C211yesmaximal, characteristic
5#1708×C151C211yesmaximal, characteristic, complemented
6#1691×C151C211yesmaximal, characteristic, complemented
7#1686×C151C211yesmaximal, characteristic, complemented
8#1680×C151C211yesmaximal, characteristic, complemented
9#1678×C151C211yesmaximal, characteristic, complemented
10#1645×C151C211yesmaximal, characteristic, complemented
11#1642×C151C211yesmaximal, characteristic
12#1637×C151C211yesmaximal, characteristic, complemented
13#1626×C151C211yesmaximal, characteristic, complemented
14#1590×C151C211yesmaximal, characteristic, complemented
15C8×Q16×C151C211yesmaximal, characteristic, complemented
16C2×#137×C151—21no—
17Q82×C151C2211yescharacteristic
18#557×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20D4×Q8×C151C2211yescharacteristic
21#501×C151—21no—
22#498×C151C2211yescharacteristic
23#492×C151C2211yescharacteristic
24#487×C151—21no—
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#486×C151—21no—
28#486×C151C2211yescharacteristic
29#486×C151C2211yescharacteristic
30#479×C151—21no—
31#477×C151C2211yescharacteristic
32#476×C151—21no—
33#476×C151C2211yescharacteristic
34#475×C151—21no—
35#475×C151—21no—
36#475×C151C2211yescharacteristic
37#475×C151C2211yescharacteristic
38#468×C151—21no—
39#462×C151C2211yescharacteristic
40#461×C151—21no—
41#461×C151C2211yescharacteristic
42#460×C151—21no—
43#460×C151C2211yescharacteristic
44#460×C151C2211yescharacteristic
45#452×C151—21no—
46#448×C151—21no—
47#446×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49C8×Q8×C151C2211yescharacteristic
50#441×C151—21no—
51C4×Q16×C151C2211yescharacteristic
52C4×SD16×C151—21no—
53C4×SD16×C151—21no—
54C4×SD16×C151C2211yescharacteristic
55#436×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C22×Q8×C151—21no—
69#137×C151—44no—
70C2×Q16×C151—21no—
71C2×Q16×C151D411yescharacteristic
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C2×SD16×C151D411yescharacteristic
78C2×M16×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151—21no—
83C4⋊Q8×C151—41no—
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151—21no—
88#127×C151C2311yescharacteristic
89#125×C151—21no—
90#125×C151—41no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—41no—
93#121×C151—21no—
94#121×C151—41no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×Q8×C151C2311yescharacteristic
100C4×Q8×C151C2311yescharacteristic
101C4×Q8×C151C2311yescharacteristic
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151C2311yescharacteristic
105#107×C151—21no—
106#107×C151D411yescharacteristic
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111#106×C151—21no—
112#106×C151D411yescharacteristic
113C4⋊C8×C151—21no—
114C4⋊C8×C151—21no—
115C4⋊C8×C151—21no—
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#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—41no—
128#103×C151D411yescharacteristic
129#103×C151D411yescharacteristic
130#103×C151D411yescharacteristic
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135#102×C151—21no—
136#102×C151—41no—
137#102×C151D411yescharacteristic
138C22⋊C8×C151—21no—
139#97×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—81no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—41no—
151C2×Q8×C151—41no—
152C2×Q8×C151—42no—
153C2×Q8×C151—81no—
154C2×Q8×C151C2×D411yescharacteristic
155C2×Q8×C151C2×D411yescharacteristic
156C2×Q8×C151C2×D411yescharacteristic
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151C2×D411yescharacteristic
163C22×C4×C151—21no—
164C22×C4×C151—41no—
165C22×C4×C151—41no—
166Q16×C151—42no—
167Q16×C151SD1614yescomplemented
168SD16×C151—41no—
169SD16×C151—42no—
170SD16×C151—42no—
171SD16×C151—42no—
172SD16×C151—42no—
173SD16×C151—81no—
174M16×C151—42no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151C2×D411yescharacteristic
181C2×C8×C151C2×D411yescharacteristic
182C2×C8×C151C2×D411yescharacteristic
183C2×C8×C151C2×D411yescharacteristic
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
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—41no—
194C4⋊C4×C151—41no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151C2×D411yescharacteristic
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C4⋊C4×C151C2×D411yescharacteristic
203C22⋊C4×C151—21no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—41no—
210C42×C151—41no—
211C42×C151C2411yescharacteristic
212C23×C151—21no—
213C23×C151—41no—
214Q8×C151—21no—
215Q8×C151—21no—
216Q8×C151—21no—
217Q8×C151—21no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—82no—
223Q8×C151—81no—
224Q8×C151—161no—
225Q8×C151C2×SD1612yes—
226Q8×C151C2×SD1612yes—
227D4×C151—21no—
228D4×C151—21no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—41no—
233D4×C151—82no—
234D4×C151—81no—
235D4×C151—161no—
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—21no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—82no—
249C2×C4×C151—82no—
250C2×C4×C151C22×D411yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151H(5,𝔽2)11yescharacteristic
253C8×C151—21no—
254C8×C151—21no—
255C8×C151—21no—
256C8×C151—41no—
257C8×C151—41no—
258C8×C151—41no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151C2×SD1612yes—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—41no—
265C22×C151—81no—
266C22×C151—81no—
267C22×C151—81no—
268C22×C151D4211yescharacteristic
269C4×C151—22no—
270C4×C151—22no—
271C4×C151—21no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—41no—
275C4×C151—41no—
276C4×C151—41no—
277C4×C151—81no—
278C4×C151—81no—
279C4×C151—81no—
280C4×C151C22×SD1611yescharacteristic
281C4×C151#57511yescharacteristic
282C4×C151#57711yescharacteristic
283C4×C151#57811yescharacteristic
284C2×C151—81no—
285C2×C151—161no—
286C2×C151#327711yescharacteristic
287C2×C151D4×SD1611yescharacteristic
288C2×C151#329011yescharacteristic
289#19896C15111yesmaximal, characteristic, direct product factor, Sylow
290C151#1989611yescharacteristic, direct product factor, Sylow
291#3387C2×C15111yescharacteristic, complemented
292#3362C2×C15111yescharacteristic
293#3359C2×C15111yescharacteristic, complemented
294#3278C2×C15111yescharacteristic
295#1708C2×C15111yescharacteristic, complemented
296#1691C2×C15111yescharacteristic, complemented
297#1686C2×C15111yescharacteristic, complemented
298#1680C2×C15111yescharacteristic, complemented
299#1678C2×C15111yescharacteristic, complemented
300#1645C2×C15111yescharacteristic, complemented
301#1642C2×C15111yescharacteristic
302#1637C2×C15111yescharacteristic, complemented
303#1626C2×C15111yescharacteristic, complemented
304#1590C2×C15111yescharacteristic, complemented
305C8×Q16C2×C15111yescharacteristic, complemented
306C2×#137—21no—
307Q82C22×C15111yescharacteristic
308#557C22×C15111yescharacteristic
309#550C22×C15111yescharacteristic
310D4×Q8C22×C15111yescharacteristic
311#501—21no—
312#498C22×C15111yescharacteristic
313#492C22×C15111yescharacteristic
314#487—21no—
315#487C22×C15111yescharacteristic
316#487C22×C15111yescharacteristic
317#486—21no—
318#486C22×C15111yescharacteristic
319#486C22×C15111yescharacteristic
320#479—21no—
321#477C22×C15111yescharacteristic
322#476—21no—
323#476C22×C15111yescharacteristic
324#475—21no—
325#475—21no—
326#475C22×C15111yescharacteristic
327#475C22×C15111yescharacteristic
328#468—21no—
329#462C22×C15111yescharacteristic
330#461—21no—
331#461C22×C15111yescharacteristic
332#460—21no—
333#460C22×C15111yescharacteristic
334#460C22×C15111yescharacteristic
335#452—21no—
336#448—21no—
337#446C22×C15111yescharacteristic
338C8×Q8C22×C15111yescharacteristic
339C8×Q8C22×C15111yescharacteristic
340#441—21no—
341C4×Q16C22×C15111yescharacteristic
342C4×SD16—21no—
343C4×SD16—21no—
344C4×SD16C22×C15111yescharacteristic
345#436C22×C15111yescharacteristic
346#335C22×C15111yescharacteristic
347#334C22×C15111yescharacteristic
348#333C22×C15111yescharacteristic
349#332C22×C15111yescharacteristic
350#332C22×C15111yescharacteristic
351#331C22×C15111yescharacteristic
352Q8⋊C8C22×C15111yescharacteristic
353Q8⋊C8C22×C15111yescharacteristic
354Q8⋊C8C22×C15111yescharacteristic
355D4⋊C8C22×C15111yescharacteristic
356C82C22×C15111yescharacteristic
357C2×#41—21no—
358C22×Q8—21no—
359#137—44no—
360C2×Q16—21no—
361C2×Q16D4×C15111yescharacteristic
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16D4×C15111yescharacteristic
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—41no—
374C4⋊Q8C23×C15111yescharacteristic
375C4⋊Q8C23×C15111yescharacteristic
376C4⋊Q8C23×C15111yescharacteristic
377#127—21no—
378#127C23×C15111yescharacteristic
379#125—21no—
380#125—41no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C15111yescharacteristic
390C4×Q8C23×C15111yescharacteristic
391C4×Q8C23×C15111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C15111yescharacteristic
395#107—21no—
396#107D4×C15111yescharacteristic
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106D4×C15111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C15111yescharacteristic
407C4⋊C8C23×C15111yescharacteristic
408C4⋊C8C23×C15111yescharacteristic
409C4⋊C8C23×C15111yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C15111yescharacteristic
419#103D4×C15111yescharacteristic
420#103D4×C15111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—41no—
427#102D4×C15111yescharacteristic
428C22⋊C8—21no—
429#97—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C15111yescharacteristic
433C4×C8C23×C15111yescharacteristic
434C4×C8C23×C15111yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C15111yescharacteristic
445C2×Q8C2×D4×C15111yescharacteristic
446C2×Q8C2×D4×C15111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C15111yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—42no—
457Q16SD16×C15114yescomplemented
458SD16—41no—
459SD16—42no—
460SD16—42no—
461SD16—42no—
462SD16—42no—
463SD16—81no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×D4×C15111yescharacteristic
471C2×C8C2×D4×C15111yescharacteristic
472C2×C8C2×D4×C15111yescharacteristic
473C2×C8C2×D4×C15111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C15111yescharacteristic
490C4⋊C4C2×D4×C15111yescharacteristic
491C4⋊C4C2×D4×C15111yescharacteristic
492C4⋊C4C2×D4×C15111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42C24×C15111yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—82no—
513Q8—81no—
514Q8—161no—
515Q8C2×SD16×C15112yes—
516Q8C2×SD16×C15112yes—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C22×D4×C15111yescharacteristic
541C2×C4C22×D4×C15111yescharacteristic
542C2×C4H(5,𝔽2)×C15111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8C2×SD16×C15112yes—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D42×C15111yescharacteristic
559C4—22no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4C22×SD16×C15111yescharacteristic
571C4#575×C15111yescharacteristic
572C4#577×C15111yescharacteristic
573C4#578×C15111yescharacteristic
574C2—81no—
575C2—161no—
576C2#3277×C15111yescharacteristic
577C2D4×SD16×C15111yescharacteristic
578C2#3290×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#550×C151C22
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. #3387×C151C2semidirect
3. #3359×C151C2semidirect
5. #1708×C151C2semidirect
6. #1691×C151C2semidirect
7. #1686×C151C2semidirect
8. #1680×C151C2semidirect
9. #1678×C151C2semidirect
10. #1645×C151C2semidirect
12. #1637×C151C2semidirect
13. #1626×C151C2semidirect
14. #1590×C151C2semidirect
15. C8×Q16×C151C2semidirect
167. Q16×C151SD16semidirect
289. #19896C151direct (N × H)
290. C151#19896direct (N × H)
291. #3387C2×C151semidirect
293. #3359C2×C151semidirect
295. #1708C2×C151semidirect
296. #1691C2×C151semidirect
297. #1686C2×C151semidirect
298. #1680C2×C151semidirect
299. #1678C2×C151semidirect
300. #1645C2×C151semidirect
302. #1637C2×C151semidirect
303. #1626C2×C151semidirect
304. #1590C2×C151semidirect
305. C8×Q16C2×C151semidirect
457. Q16SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3387×C1512
#3362×C1512
#3359×C1512
#3278×C1512
#1708×C1512
#1691×C1512
#1686×C1512
#1680×C1512
#1678×C1512
#1645×C1512
#1642×C1512
#1637×C1512
#1626×C1512
#1590×C1512
C8×Q16×C1512
#19896151