Finite Group Databasebeta

← C139×#20126 #48014722

Subgroups — C139×#20126 #48014722

Order 35584.

600 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3394×C139C211yesmaximal, characteristic, complemented
2#3373×C139C211yesmaximal, characteristic, complemented
3#3340×C139C211yesmaximal, characteristic, complemented
4#3329×C139C211yesmaximal, characteristic, complemented
5#1714×C139C211yesmaximal, characteristic, complemented
6#1692×C139C211yesmaximal, characteristic, complemented
7#1685×C139C211yesmaximal, characteristic, complemented
8#1684×C139C211yesmaximal, characteristic, complemented
9#1681×C139C211yesmaximal, characteristic, complemented
10#1650×C139C211yesmaximal, characteristic, complemented
11#1649×C139C211yesmaximal, characteristic, complemented
12#1630×C139C211yesmaximal, characteristic, complemented
13#1624×C139C211yesmaximal, characteristic
14#1588×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic
17#556×C139C2211yescharacteristic
18#555×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#500×C139C2211yescharacteristic
21#498×C139C2211yescharacteristic
22#495×C139—21no—
23#492×C139C2211yescharacteristic
24#492×C139C2211yescharacteristic
25#489×C139—21no—
26#487×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#485×C139—21no—
29#485×C139—21no—
30#482×C139—21no—
31#477×C139C2211yescharacteristic
32#477×C139C2211yescharacteristic
33#476×C139—21no—
34#475×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#468×C139—21no—
37#465×C139—21no—
38#464×C139—21no—
39#463×C139—21no—
40#463×C139—21no—
41#462×C139C2211yescharacteristic
42#461×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#448×C139—21no—
46#446×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48#442×C139—21no—
49C4×SD16×C139—21no—
50C4×SD16×C139C2211yescharacteristic
51C4×SD16×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#427×C139—21no—
55#419×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
67C22×Q8×C139—21no—
68C2×Q16×C139—21no—
69C2×SD16×C139—21no—
70C2×SD16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—41no—
73C2×SD16×C139D411yescharacteristic
74C2×SD16×C139D411yescharacteristic
75C2×D8×C139—21no—
76C2×D8×C139—21no—
77C2×M16×C139—21no—
78C22×C8×C139—21no—
79C4⋊Q8×C139—21no—
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83#127×C139C2311yescharacteristic
84#126×C139—41no—
85#124×C139—21no—
86#124×C139—21no—
87#124×C139—21no—
88#124×C139—41no—
89#123×C139—41no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—41no—
93#121×C139—21no—
94#121×C139—21no—
95C4×Q8×C139—21no—
96C4×Q8×C139C2311yescharacteristic
97C4×Q8×C139C2311yescharacteristic
98C4×D4×C139—21no—
99C4×D4×C139—21no—
100C4×D4×C139—21no—
101C4×D4×C139C2311yescharacteristic
102C4×D4×C139C2311yescharacteristic
103#117×C139—21no—
104#117×C139—21no—
105#117×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—41no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139D411yescharacteristic
114#106×C139D411yescharacteristic
115C4⋊C8×C139—21no—
116C4⋊C8×C139—21no—
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121#103×C139—21no—
122#103×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#103×C139—21no—
126#103×C139—21no—
127#103×C139—21no—
128#103×C139D411yescharacteristic
129#103×C139D411yescharacteristic
130#102×C139—21no—
131#102×C139—21no—
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—21no—
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139#97×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C2×Q8×C139—21no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—41no—
148C2×Q8×C139—42no—
149C2×Q8×C139—81no—
150C2×Q8×C139C2×D411yescharacteristic
151C2×Q8×C139C2×D411yescharacteristic
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—41no—
156C2×D4×C139C2×D411yescharacteristic
157C2×D4×C139C2×D411yescharacteristic
158C22×C4×C139—21no—
159C22×C4×C139—21no—
160C22×C4×C139—41no—
161C22×C4×C139—41no—
162Q16×C139—81no—
163SD16×C139—41no—
164SD16×C139—41no—
165SD16×C139—42no—
166SD16×C139—81no—
167SD16×C139—82no—
168SD16×C139—81no—
169D8×C139—42no—
170D8×C139—81no—
171M16×C139—81no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—42no—
178C2×C8×C139C2×D411yescharacteristic
179C2×C8×C139C2×D411yescharacteristic
180C2×C8×C139C2×D411yescharacteristic
181C2×C8×C139C2×D411yescharacteristic
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—21no—
190C4⋊C4×C139—41no—
191C4⋊C4×C139—41no—
192C4⋊C4×C139C2×D411yescharacteristic
193C4⋊C4×C139C2×D411yescharacteristic
194C4⋊C4×C139C2×D411yescharacteristic
195C4⋊C4×C139C2×D411yescharacteristic
196C22⋊C4×C139—21no—
197C22⋊C4×C139—21no—
198C22⋊C4×C139—41no—
199C22⋊C4×C139—41no—
200C22⋊C4×C139—41no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C42×C139—21no—
207C42×C139—21no—
208C42×C139—41no—
209C42×C139—41no—
210C42×C139C2411yescharacteristic
211C23×C139—21no—
212C23×C139—21no—
213C23×C139—41no—
214Q8×C139—21no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—21no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—81no—
223Q8×C139—82no—
224D4×C139—21no—
225D4×C139—21no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—41no—
229D4×C139—41no—
230D4×C139—41no—
231D4×C139—41no—
232D4×C139—81no—
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×C139—161no—
249C2×C4×C139C22×D411yescharacteristic
250C2×C4×C139C22×D411yescharacteristic
251C2×C4×C139H(5,𝔽2)11yescharacteristic
252C8×C139—22no—
253C8×C139—21no—
254C8×C139—21no—
255C8×C139—21no—
256C8×C139—21no—
257C8×C139—41no—
258C8×C139—41no—
259C8×C139—41no—
260C8×C139—41no—
261C22×C139—41no—
262C22×C139—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—81no—
268C22×C139—81no—
269C22×C139—81no—
270C22×C139D4211yescharacteristic
271C4×C139—21no—
272C4×C139—41no—
273C4×C139—41no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—81no—
279C4×C139—81no—
280C4×C139—81no—
281C4×C139#57511yescharacteristic
282C4×C139#57511yescharacteristic
283C4×C139#57611yescharacteristic
284C4×C139#57811yescharacteristic
285C2×C139—81no—
286C2×C139—81no—
287C2×C139—161no—
288C2×C139#326811yescharacteristic
289C2×C139#326911yescharacteristic
290C2×C139#329111yescharacteristic
291#20126C13911yesmaximal, characteristic, direct product factor, Sylow
292C139#2012611yescharacteristic, direct product factor, Sylow
293#3394C2×C13911yescharacteristic, complemented
294#3373C2×C13911yescharacteristic, complemented
295#3340C2×C13911yescharacteristic, complemented
296#3329C2×C13911yescharacteristic, complemented
297#1714C2×C13911yescharacteristic, complemented
298#1692C2×C13911yescharacteristic, complemented
299#1685C2×C13911yescharacteristic, complemented
300#1684C2×C13911yescharacteristic, complemented
301#1681C2×C13911yescharacteristic, complemented
302#1650C2×C13911yescharacteristic, complemented
303#1649C2×C13911yescharacteristic, complemented
304#1630C2×C13911yescharacteristic, complemented
305#1624C2×C13911yescharacteristic
306#1588C2×C13911yescharacteristic, complemented
307#1585C2×C13911yescharacteristic, complemented
308#559C22×C13911yescharacteristic
309#556C22×C13911yescharacteristic
310#555C22×C13911yescharacteristic
311D4×Q8C22×C13911yescharacteristic
312#500C22×C13911yescharacteristic
313#498C22×C13911yescharacteristic
314#495—21no—
315#492C22×C13911yescharacteristic
316#492C22×C13911yescharacteristic
317#489—21no—
318#487C22×C13911yescharacteristic
319#486C22×C13911yescharacteristic
320#485—21no—
321#485—21no—
322#482—21no—
323#477C22×C13911yescharacteristic
324#477C22×C13911yescharacteristic
325#476—21no—
326#475C22×C13911yescharacteristic
327#474C22×C13911yescharacteristic
328#468—21no—
329#465—21no—
330#464—21no—
331#463—21no—
332#463—21no—
333#462C22×C13911yescharacteristic
334#461C22×C13911yescharacteristic
335#459C22×C13911yescharacteristic
336#459C22×C13911yescharacteristic
337#448—21no—
338#446C22×C13911yescharacteristic
339C8×Q8C22×C13911yescharacteristic
340#442—21no—
341C4×SD16—21no—
342C4×SD16C22×C13911yescharacteristic
343C4×SD16C22×C13911yescharacteristic
344#436C22×C13911yescharacteristic
345C8×D4C22×C13911yescharacteristic
346#427—21no—
347#419—21no—
348#335C22×C13911yescharacteristic
349#335C22×C13911yescharacteristic
350#333C22×C13911yescharacteristic
351#332C22×C13911yescharacteristic
352#332C22×C13911yescharacteristic
353#331C22×C13911yescharacteristic
354Q8⋊C8C22×C13911yescharacteristic
355Q8⋊C8C22×C13911yescharacteristic
356D4⋊C8C22×C13911yescharacteristic
357D4⋊C8C22×C13911yescharacteristic
358#322C22×C13911yescharacteristic
359C22×Q8—21no—
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—41no—
365C2×SD16D4×C13911yescharacteristic
366C2×SD16D4×C13911yescharacteristic
367C2×D8—21no—
368C2×D8—21no—
369C2×M16—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8C23×C13911yescharacteristic
373C4⋊Q8C23×C13911yescharacteristic
374C4⋊Q8C23×C13911yescharacteristic
375#127C23×C13911yescharacteristic
376#126—41no—
377#124—21no—
378#124—21no—
379#124—21no—
380#124—41no—
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385#121—21no—
386#121—21no—
387C4×Q8—21no—
388C4×Q8C23×C13911yescharacteristic
389C4×Q8C23×C13911yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C23×C13911yescharacteristic
394C4×D4C23×C13911yescharacteristic
395#117—21no—
396#117—21no—
397#117—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—41no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106D4×C13911yescharacteristic
406#106D4×C13911yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C13911yescharacteristic
410C4⋊C8C23×C13911yescharacteristic
411C4⋊C8C23×C13911yescharacteristic
412C4⋊C8C23×C13911yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103D4×C13911yescharacteristic
421#103D4×C13911yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102D4×C13911yescharacteristic
428#102D4×C13911yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431#97—21no—
432C4×C8—21no—
433C4×C8C23×C13911yescharacteristic
434C4×C8C23×C13911yescharacteristic
435C4×C8C23×C13911yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8C2×D4×C13911yescharacteristic
443C2×Q8C2×D4×C13911yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C13911yescharacteristic
449C2×D4C2×D4×C13911yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—41no—
454Q16—81no—
455SD16—41no—
456SD16—41no—
457SD16—42no—
458SD16—81no—
459SD16—82no—
460SD16—81no—
461D8—42no—
462D8—81no—
463M16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—42no—
470C2×C8C2×D4×C13911yescharacteristic
471C2×C8C2×D4×C13911yescharacteristic
472C2×C8C2×D4×C13911yescharacteristic
473C2×C8C2×D4×C13911yescharacteristic
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—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—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—41no—
501C42—41no—
502C42C24×C13911yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8—82no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—161no—
541C2×C4C22×D4×C13911yescharacteristic
542C2×C4C22×D4×C13911yescharacteristic
543C2×C4H(5,𝔽2)×C13911yescharacteristic
544C8—22no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22D42×C13911yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4#575×C13911yescharacteristic
574C4#575×C13911yescharacteristic
575C4#576×C13911yescharacteristic
576C4#578×C13911yescharacteristic
577C2—81no—
578C2—81no—
579C2—161no—
580C2#3268×C13911yescharacteristic
581C2#3269×C13911yescharacteristic
582C2#3291×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#1624×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. #3394×C139C2semidirect
2. #3373×C139C2semidirect
3. #3340×C139C2semidirect
4. #3329×C139C2semidirect
5. #1714×C139C2semidirect
6. #1692×C139C2semidirect
7. #1685×C139C2semidirect
8. #1684×C139C2semidirect
9. #1681×C139C2semidirect
10. #1650×C139C2semidirect
11. #1649×C139C2semidirect
12. #1630×C139C2semidirect
14. #1588×C139C2semidirect
15. #1585×C139C2semidirect
291. #20126C139direct (N × H)
292. C139#20126direct (N × H)
293. #3394C2×C139semidirect
294. #3373C2×C139semidirect
295. #3340C2×C139semidirect
296. #3329C2×C139semidirect
297. #1714C2×C139semidirect
298. #1692C2×C139semidirect
299. #1685C2×C139semidirect
300. #1684C2×C139semidirect
301. #1681C2×C139semidirect
302. #1650C2×C139semidirect
303. #1649C2×C139semidirect
304. #1630C2×C139semidirect
306. #1588C2×C139semidirect
307. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3394×C1392
#3373×C1392
#3340×C1392
#3329×C1392
#1714×C1392
#1692×C1392
#1685×C1392
#1684×C1392
#1681×C1392
#1650×C1392
#1649×C1392
#1630×C1392
#1624×C1392
#1588×C1392
#1585×C1392
#20126139