Finite Group Databasebeta

← C139×#20124 #48014720

Subgroups — C139×#20124 #48014720

Order 35584.

594 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3398×C139C211yesmaximal, characteristic, complemented
2#3368×C139C211yesmaximal, characteristic, complemented
3#3340×C139C211yesmaximal, characteristic, complemented
4#3305×C139C211yesmaximal, characteristic
5#1720×C139C211yesmaximal, characteristic, complemented
6#1698×C139C211yesmaximal, characteristic, complemented
7#1692×C139C211yesmaximal, characteristic, complemented
8#1681×C139C211yesmaximal, characteristic, complemented
9#1669×C139C211yesmaximal, characteristic, complemented
10#1646×C139C211yesmaximal, characteristic, complemented
11#1641×C139C211yesmaximal, characteristic, complemented
12#1636×C139C211yesmaximal, characteristic, complemented
13#1628×C139C211yesmaximal, characteristic, complemented
14#1585×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16#557×C139C2211yescharacteristic
17#556×C139C2211yescharacteristic
18#555×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#498×C139C2211yescharacteristic
21#497×C139—21no—
22#494×C139C2211yescharacteristic
23#490×C139—21no—
24#487×C139C2211yescharacteristic
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#485×C139—21no—
29#482×C139—21no—
30#482×C139—21no—
31#478×C139—21no—
32#477×C139C2211yescharacteristic
33#477×C139C2211yescharacteristic
34#474×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#466×C139—21no—
37#465×C139—21no—
38#464×C139—21no—
39#462×C139—21no—
40#462×C139C2211yescharacteristic
41#461×C139C2211yescharacteristic
42#460×C139—21no—
43#460×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#449×C139—21no—
46#446×C139C2211yescharacteristic
47#446×C139C2211yescharacteristic
48#441×C139—21no—
49#440×C139—21no—
50C4×SD16×C139C2211yescharacteristic
51C4×SD16×C139C2211yescharacteristic
52C8×D4×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#427×C139—21no—
55#416×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×Q16×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139D411yescharacteristic
74C2×SD16×C139D411yescharacteristic
75C2×D8×C139—21no—
76C22×C8×C139—21no—
77C22×C8×C139—21no—
78C4⋊Q8×C139—21no—
79C4⋊Q8×C139C2311yescharacteristic
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82#127×C139—21no—
83#127×C139C2311yescharacteristic
84#126×C139—41no—
85#125×C139—21no—
86#125×C139—41no—
87#124×C139—21no—
88#124×C139—41no—
89C22⋊Q8×C139—21no—
90#121×C139—21no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—41no—
94C4×Q8×C139—21no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139C2311yescharacteristic
98C4×Q8×C139C2311yescharacteristic
99C4×D4×C139—21no—
100C4×D4×C139C2311yescharacteristic
101C4×D4×C139C2311yescharacteristic
102#117×C139—21no—
103#117×C139—21no—
104#117×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#106×C139—21no—
110#106×C139—21no—
111#106×C139D411yescharacteristic
112#106×C139D411yescharacteristic
113C4⋊C8×C139—21no—
114C4⋊C8×C139—21no—
115C4⋊C8×C139C2311yescharacteristic
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119#103×C139—21no—
120#103×C139—21no—
121#103×C139—21no—
122#103×C139—21no—
123#103×C139—41no—
124#103×C139D411yescharacteristic
125#103×C139D411yescharacteristic
126#102×C139—21no—
127#102×C139—21no—
128#102×C139—21no—
129#102×C139—21no—
130#102×C139—21no—
131#102×C139—21no—
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—41no—
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139#97×C139—21no—
140#97×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144#41×C139—42no—
145#41×C139—81no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139C2×D411yescharacteristic
150C2×Q8×C139C2×D411yescharacteristic
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—41no—
155C2×D4×C139—41no—
156C2×D4×C139—41no—
157C2×D4×C139C2×D411yescharacteristic
158C2×D4×C139C2×D411yescharacteristic
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—41no—
162Q16×C139—42no—
163Q16×C139—81no—
164Q16×C139—81no—
165SD16×C139—41no—
166SD16×C139—41no—
167SD16×C139—42no—
168SD16×C139—81no—
169D8×C139—81no—
170C2×C8×C139—21no—
171C2×C8×C139—21no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—42no—
176C2×C8×C139—81no—
177C2×C8×C139C2×D411yescharacteristic
178C2×C8×C139C2×D411yescharacteristic
179C2×C8×C139C2×D411yescharacteristic
180C2×C8×C139C2×D411yescharacteristic
181C4⋊C4×C139—21no—
182C4⋊C4×C139—21no—
183C4⋊C4×C139—21no—
184C4⋊C4×C139—21no—
185C4⋊C4×C139—21no—
186C4⋊C4×C139—21no—
187C4⋊C4×C139—21no—
188C4⋊C4×C139—21no—
189C4⋊C4×C139—41no—
190C4⋊C4×C139—41no—
191C4⋊C4×C139—41no—
192C4⋊C4×C139—41no—
193C4⋊C4×C139C2×D411yescharacteristic
194C4⋊C4×C139C2×D411yescharacteristic
195C4⋊C4×C139C2×D411yescharacteristic
196C4⋊C4×C139C2×D411yescharacteristic
197C22⋊C4×C139—21no—
198C22⋊C4×C139—21no—
199C22⋊C4×C139—41no—
200C22⋊C4×C139—41no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C22⋊C4×C139—41no—
204C42×C139—21no—
205C42×C139—21no—
206C42×C139—41no—
207C42×C139—41no—
208C42×C139—41no—
209C42×C139C2411yescharacteristic
210C23×C139—21no—
211C23×C139—21no—
212C23×C139—41no—
213Q8×C139—21no—
214Q8×C139—21no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—81no—
222D4×C139—21no—
223D4×C139—21no—
224D4×C139—21no—
225D4×C139—21no—
226D4×C139—41no—
227D4×C139—41no—
228D4×C139—41no—
229D4×C139—41no—
230D4×C139—81no—
231D4×C139—82no—
232D4×C139—161no—
233D4×C139—161no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—82no—
248C2×C4×C139C22×D411yescharacteristic
249C2×C4×C139C22×D411yescharacteristic
250C2×C4×C139H(5,𝔽2)11yescharacteristic
251C8×C139—21no—
252C8×C139—21no—
253C8×C139—21no—
254C8×C139—21no—
255C8×C139—41no—
256C8×C139—41no—
257C8×C139—41no—
258C8×C139—41no—
259C8×C139—41no—
260C22×C139—41no—
261C22×C139—41no—
262C22×C139—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—81no—
267C22×C139—81no—
268C22×C139—81no—
269C22×C139D4211yescharacteristic
270C4×C139—21no—
271C4×C139—41no—
272C4×C139—41no—
273C4×C139—41no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—41no—
277C4×C139—81no—
278C4×C139—81no—
279C4×C139—81no—
280C4×C139#57511yescharacteristic
281C4×C139#57511yescharacteristic
282C4×C139#57611yescharacteristic
283C4×C139#57811yescharacteristic
284C2×C139—81no—
285C2×C139—81no—
286C2×C139—161no—
287C2×C139#326811yescharacteristic
288C2×C139#326911yescharacteristic
289C2×C139#329011yescharacteristic
290#20124C13911yesmaximal, characteristic, direct product factor, Sylow
291C139#2012411yescharacteristic, direct product factor, Sylow
292#3398C2×C13911yescharacteristic, complemented
293#3368C2×C13911yescharacteristic, complemented
294#3340C2×C13911yescharacteristic, complemented
295#3305C2×C13911yescharacteristic
296#1720C2×C13911yescharacteristic, complemented
297#1698C2×C13911yescharacteristic, complemented
298#1692C2×C13911yescharacteristic, complemented
299#1681C2×C13911yescharacteristic, complemented
300#1669C2×C13911yescharacteristic, complemented
301#1646C2×C13911yescharacteristic, complemented
302#1641C2×C13911yescharacteristic, complemented
303#1636C2×C13911yescharacteristic, complemented
304#1628C2×C13911yescharacteristic, complemented
305#1585C2×C13911yescharacteristic, complemented
306#1585C2×C13911yescharacteristic, complemented
307#557C22×C13911yescharacteristic
308#556C22×C13911yescharacteristic
309#555C22×C13911yescharacteristic
310#550C22×C13911yescharacteristic
311#498C22×C13911yescharacteristic
312#497—21no—
313#494C22×C13911yescharacteristic
314#490—21no—
315#487C22×C13911yescharacteristic
316#486C22×C13911yescharacteristic
317#486C22×C13911yescharacteristic
318#486C22×C13911yescharacteristic
319#485—21no—
320#482—21no—
321#482—21no—
322#478—21no—
323#477C22×C13911yescharacteristic
324#477C22×C13911yescharacteristic
325#474C22×C13911yescharacteristic
326#474C22×C13911yescharacteristic
327#466—21no—
328#465—21no—
329#464—21no—
330#462—21no—
331#462C22×C13911yescharacteristic
332#461C22×C13911yescharacteristic
333#460—21no—
334#460C22×C13911yescharacteristic
335#459C22×C13911yescharacteristic
336#449—21no—
337#446C22×C13911yescharacteristic
338#446C22×C13911yescharacteristic
339#441—21no—
340#440—21no—
341C4×SD16C22×C13911yescharacteristic
342C4×SD16C22×C13911yescharacteristic
343C8×D4C22×C13911yescharacteristic
344C8×D4C22×C13911yescharacteristic
345#427—21no—
346#416—21no—
347#335C22×C13911yescharacteristic
348#335C22×C13911yescharacteristic
349#333C22×C13911yescharacteristic
350#332C22×C13911yescharacteristic
351#332C22×C13911yescharacteristic
352#331C22×C13911yescharacteristic
353Q8⋊C8C22×C13911yescharacteristic
354Q8⋊C8C22×C13911yescharacteristic
355D4⋊C8C22×C13911yescharacteristic
356D4⋊C8C22×C13911yescharacteristic
357#322C22×C13911yescharacteristic
358C2×#41—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16D4×C13911yescharacteristic
365C2×SD16D4×C13911yescharacteristic
366C2×D8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C23×C13911yescharacteristic
371C4⋊Q8C23×C13911yescharacteristic
372C4⋊Q8C23×C13911yescharacteristic
373#127—21no—
374#127C23×C13911yescharacteristic
375#126—41no—
376#125—21no—
377#125—41no—
378#124—21no—
379#124—41no—
380C22⋊Q8—21no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C23×C13911yescharacteristic
389C4×Q8C23×C13911yescharacteristic
390C4×D4—21no—
391C4×D4C23×C13911yescharacteristic
392C4×D4C23×C13911yescharacteristic
393#117—21no—
394#117—21no—
395#117—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402#106D4×C13911yescharacteristic
403#106D4×C13911yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C13911yescharacteristic
407C4⋊C8C23×C13911yescharacteristic
408C4⋊C8C23×C13911yescharacteristic
409C4⋊C8C23×C13911yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C13911yescharacteristic
416#103D4×C13911yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—41no—
426#102D4×C13911yescharacteristic
427#102D4×C13911yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430#97—21no—
431#97—21no—
432C4×C8C23×C13911yescharacteristic
433C4×C8C23×C13911yescharacteristic
434C4×C8C23×C13911yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×D4×C13911yescharacteristic
441C2×Q8C2×D4×C13911yescharacteristic
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4C2×D4×C13911yescharacteristic
449C2×D4C2×D4×C13911yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453Q16—42no—
454Q16—81no—
455Q16—81no—
456SD16—41no—
457SD16—41no—
458SD16—42no—
459SD16—81no—
460D8—81no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—81no—
468C2×C8C2×D4×C13911yescharacteristic
469C2×C8C2×D4×C13911yescharacteristic
470C2×C8C2×D4×C13911yescharacteristic
471C2×C8C2×D4×C13911yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C13911yescharacteristic
485C4⋊C4C2×D4×C13911yescharacteristic
486C4⋊C4C2×D4×C13911yescharacteristic
487C4⋊C4C2×D4×C13911yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—41no—
499C42—41no—
500C42C24×C13911yescharacteristic
501C23—21no—
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—81no—
522D4—82no—
523D4—161no—
524D4—161no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4C22×D4×C13911yescharacteristic
540C2×C4C22×D4×C13911yescharacteristic
541C2×C4H(5,𝔽2)×C13911yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22D42×C13911yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4#575×C13911yescharacteristic
572C4#575×C13911yescharacteristic
573C4#576×C13911yescharacteristic
574C4#578×C13911yescharacteristic
575C2—81no—
576C2—81no—
577C2—161no—
578C2#3268×C13911yescharacteristic
579C2#3269×C13911yescharacteristic
580C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3305×C139C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3398×C139C2semidirect
2. #3368×C139C2semidirect
3. #3340×C139C2semidirect
5. #1720×C139C2semidirect
6. #1698×C139C2semidirect
7. #1692×C139C2semidirect
8. #1681×C139C2semidirect
9. #1669×C139C2semidirect
10. #1646×C139C2semidirect
11. #1641×C139C2semidirect
12. #1636×C139C2semidirect
13. #1628×C139C2semidirect
14. #1585×C139C2semidirect
15. #1585×C139C2semidirect
290. #20124C139direct (N × H)
291. C139#20124direct (N × H)
292. #3398C2×C139semidirect
293. #3368C2×C139semidirect
294. #3340C2×C139semidirect
296. #1720C2×C139semidirect
297. #1698C2×C139semidirect
298. #1692C2×C139semidirect
299. #1681C2×C139semidirect
300. #1669C2×C139semidirect
301. #1646C2×C139semidirect
302. #1641C2×C139semidirect
303. #1636C2×C139semidirect
304. #1628C2×C139semidirect
305. #1585C2×C139semidirect
306. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3398×C1392
#3368×C1392
#3340×C1392
#3305×C1392
#1720×C1392
#1698×C1392
#1692×C1392
#1681×C1392
#1669×C1392
#1646×C1392
#1641×C1392
#1636×C1392
#1628×C1392
#1585×C1392
#20124139