Finite Group Databasebeta

← C139×#20115 #48014711

Subgroups — C139×#20115 #48014711

Order 35584.

594 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3400×C139C211yesmaximal, characteristic, complemented
2#3381×C139C211yesmaximal, characteristic, complemented
3#3373×C139C211yesmaximal, characteristic
4#3299×C139C211yesmaximal, characteristic, complemented
5#1714×C139C211yesmaximal, characteristic, complemented
6#1704×C139C211yesmaximal, characteristic, complemented
7#1692×C139C211yesmaximal, characteristic, complemented
8#1682×C139C211yesmaximal, characteristic, complemented
9#1665×C139C211yesmaximal, characteristic
10#1649×C139C211yesmaximal, characteristic, complemented
11#1648×C139C211yesmaximal, characteristic, complemented
12#1630×C139C211yesmaximal, characteristic, complemented
13#1622×C139C211yesmaximal, characteristic
14#1587×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic
17#557×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#500×C139C2211yescharacteristic
21#499×C139—21no—
22#498×C139C2211yescharacteristic
23#497×C139—21no—
24#492×C139C2211yescharacteristic
25#492×C139C2211yescharacteristic
26#489×C139—21no—
27#487×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#484×C139—21no—
30#479×C139—21no—
31#478×C139—21no—
32#477×C139C2211yescharacteristic
33#477×C139C2211yescharacteristic
34#476×C139—21no—
35#475×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#467×C139—21no—
38#464×C139—21no—
39#463×C139—21no—
40#462×C139C2211yescharacteristic
41#462×C139C2211yescharacteristic
42#461×C139—21no—
43#460×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#451×C139—21no—
46#446×C139C2211yescharacteristic
47#446×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49#442×C139—21no—
50#440×C139—21no—
51C4×Q16×C139C2211yescharacteristic
52C4×SD16×C139—21no—
53C4×SD16×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55C2×#103×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C22×Q8×C139—21no—
68C2×Q16×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139D411yescharacteristic
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—41no—
75C2×SD16×C139D411yescharacteristic
76C2×D8×C139—21no—
77C22×C8×C139—21no—
78C4⋊Q8×C139—21no—
79C4⋊Q8×C139—21no—
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83#127×C139C2311yescharacteristic
84#125×C139—21no—
85#125×C139—21no—
86#125×C139—41no—
87#124×C139—21no—
88#124×C139—21no—
89#123×C139—41no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—41no—
93C22⋊Q8×C139—41no—
94C4×Q8×C139—21no—
95C4×Q8×C139—21no—
96C4×Q8×C139C2311yescharacteristic
97C4×Q8×C139C2311yescharacteristic
98C4×Q8×C139C2311yescharacteristic
99C4×D4×C139—21no—
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139C2311yescharacteristic
104C2×C4⋊C4×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—41no—
109#107×C139D411yescharacteristic
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139D411yescharacteristic
114C4⋊C8×C139—21no—
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#103×C139D411yescharacteristic
131#102×C139—21no—
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—21no—
135#102×C139—21no—
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138#97×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×Q8×C139C2×D411yescharacteristic
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139C2×D411yescharacteristic
157C22×C4×C139—21no—
158C22×C4×C139—41no—
159C22×C4×C139—41no—
160C22×C4×C139—41no—
161Q16×C139—41no—
162Q16×C139—81no—
163Q16×C139—81no—
164SD16×C139—22no—
165SD16×C139—42no—
166SD16×C139—81no—
167SD16×C139—82no—
168SD16×C139—81no—
169D8×C139—42no—
170C2×C8×C139—21no—
171C2×C8×C139—21no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—81no—
176C2×C8×C139C2×D411yescharacteristic
177C2×C8×C139C2×D411yescharacteristic
178C2×C8×C139C2×D411yescharacteristic
179C2×C8×C139C2×D411yescharacteristic
180C4⋊C4×C139—21no—
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×C139—41no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139C2×D411yescharacteristic
196C4⋊C4×C139C2×D411yescharacteristic
197C4⋊C4×C139C2×D411yescharacteristic
198C4⋊C4×C139C2×D411yescharacteristic
199C22⋊C4×C139—21no—
200C22⋊C4×C139—41no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C42×C139—21no—
206C42×C139—21no—
207C42×C139—21no—
208C42×C139—41no—
209C42×C139C2411yescharacteristic
210C23×C139—21no—
211C23×C139—41no—
212Q8×C139—21no—
213Q8×C139—21no—
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—41no—
226D4×C139—41no—
227D4×C139—41no—
228D4×C139—41no—
229D4×C139—81no—
230D4×C139#13712yes—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—82no—
244C2×C4×C139—161no—
245C2×C4×C139—161no—
246C2×C4×C139C22×D411yescharacteristic
247C2×C4×C139C22×D411yescharacteristic
248C2×C4×C139H(5,𝔽2)11yescharacteristic
249C8×C139—22no—
250C8×C139—21no—
251C8×C139—21no—
252C8×C139—21no—
253C8×C139—21no—
254C8×C139—41no—
255C8×C139—41no—
256C8×C139—41no—
257C8×C139—41no—
258C22×C139—22no—
259C22×C139—41no—
260C22×C139—41no—
261C22×C139—81no—
262C22×C139—81no—
263C22×C139—81no—
264C22×C139D4211yescharacteristic
265C4×C139—21no—
266C4×C139—41no—
267C4×C139—41no—
268C4×C139—41no—
269C4×C139—41no—
270C4×C139—41no—
271C4×C139—41no—
272C4×C139—41no—
273C4×C139—81no—
274C4×C139—81no—
275C4×C139—81no—
276C4×C139C2×#13711yescharacteristic
277C4×C139#57511yescharacteristic
278C4×C139#57611yescharacteristic
279C4×C139#57811yescharacteristic
280C2×C139—42no—
281C2×C139—161no—
282C2×C139#326811yescharacteristic
283C2×C139#327011yescharacteristic
284C2×C139#329111yescharacteristic
285#20115C13911yesmaximal, characteristic, direct product factor, Sylow
286C139#2011511yescharacteristic, direct product factor, Sylow
287#3400C2×C13911yescharacteristic, complemented
288#3381C2×C13911yescharacteristic, complemented
289#3373C2×C13911yescharacteristic
290#3299C2×C13911yescharacteristic, complemented
291#1714C2×C13911yescharacteristic, complemented
292#1704C2×C13911yescharacteristic, complemented
293#1692C2×C13911yescharacteristic, complemented
294#1682C2×C13911yescharacteristic, complemented
295#1665C2×C13911yescharacteristic
296#1649C2×C13911yescharacteristic, complemented
297#1648C2×C13911yescharacteristic, complemented
298#1630C2×C13911yescharacteristic, complemented
299#1622C2×C13911yescharacteristic
300#1587C2×C13911yescharacteristic, complemented
301#1585C2×C13911yescharacteristic, complemented
302#559C22×C13911yescharacteristic
303#557C22×C13911yescharacteristic
304#554C22×C13911yescharacteristic
305D4×Q8C22×C13911yescharacteristic
306#500C22×C13911yescharacteristic
307#499—21no—
308#498C22×C13911yescharacteristic
309#497—21no—
310#492C22×C13911yescharacteristic
311#492C22×C13911yescharacteristic
312#489—21no—
313#487C22×C13911yescharacteristic
314#486C22×C13911yescharacteristic
315#484—21no—
316#479—21no—
317#478—21no—
318#477C22×C13911yescharacteristic
319#477C22×C13911yescharacteristic
320#476—21no—
321#475C22×C13911yescharacteristic
322#474C22×C13911yescharacteristic
323#467—21no—
324#464—21no—
325#463—21no—
326#462C22×C13911yescharacteristic
327#462C22×C13911yescharacteristic
328#461—21no—
329#460C22×C13911yescharacteristic
330#459C22×C13911yescharacteristic
331#451—21no—
332#446C22×C13911yescharacteristic
333#446C22×C13911yescharacteristic
334C8×Q8C22×C13911yescharacteristic
335#442—21no—
336#440—21no—
337C4×Q16C22×C13911yescharacteristic
338C4×SD16—21no—
339C4×SD16C22×C13911yescharacteristic
340C8×D4C22×C13911yescharacteristic
341C2×#103—21no—
342#335C22×C13911yescharacteristic
343#334C22×C13911yescharacteristic
344#333C22×C13911yescharacteristic
345#332C22×C13911yescharacteristic
346#332C22×C13911yescharacteristic
347#331C22×C13911yescharacteristic
348Q8⋊C8C22×C13911yescharacteristic
349Q8⋊C8C22×C13911yescharacteristic
350Q8⋊C8C22×C13911yescharacteristic
351D4⋊C8C22×C13911yescharacteristic
352#322C22×C13911yescharacteristic
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16D4×C13911yescharacteristic
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—41no—
361C2×SD16D4×C13911yescharacteristic
362C2×D8—21no—
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C13911yescharacteristic
367C4⋊Q8C23×C13911yescharacteristic
368C4⋊Q8C23×C13911yescharacteristic
369#127C23×C13911yescharacteristic
370#125—21no—
371#125—21no—
372#125—41no—
373#124—21no—
374#124—21no—
375#123—41no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—41no—
379C22⋊Q8—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C23×C13911yescharacteristic
383C4×Q8C23×C13911yescharacteristic
384C4×Q8C23×C13911yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C23×C13911yescharacteristic
390C2×C4⋊C4—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#107—41no—
395#107D4×C13911yescharacteristic
396#106—21no—
397#106—21no—
398#106—21no—
399#106D4×C13911yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C13911yescharacteristic
404C4⋊C8C23×C13911yescharacteristic
405C4⋊C8C23×C13911yescharacteristic
406C4⋊C8C23×C13911yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103D4×C13911yescharacteristic
415#103D4×C13911yescharacteristic
416#103D4×C13911yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102D4×C13911yescharacteristic
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8C23×C13911yescharacteristic
428C4×C8C23×C13911yescharacteristic
429C4×C8C23×C13911yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8C2×D4×C13911yescharacteristic
437C2×Q8C2×D4×C13911yescharacteristic
438C2×Q8C2×D4×C13911yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×D4×C13911yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447Q16—41no—
448Q16—81no—
449Q16—81no—
450SD16—22no—
451SD16—42no—
452SD16—81no—
453SD16—82no—
454SD16—81no—
455D8—42no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8C2×D4×C13911yescharacteristic
463C2×C8C2×D4×C13911yescharacteristic
464C2×C8C2×D4×C13911yescharacteristic
465C2×C8C2×D4×C13911yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C13911yescharacteristic
482C4⋊C4C2×D4×C13911yescharacteristic
483C4⋊C4C2×D4×C13911yescharacteristic
484C4⋊C4C2×D4×C13911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42C24×C13911yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—82no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4#137×C13912yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—161no—
531C2×C4—161no—
532C2×C4C22×D4×C13911yescharacteristic
533C2×C4C22×D4×C13911yescharacteristic
534C2×C4H(5,𝔽2)×C13911yescharacteristic
535C8—22no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C13911yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×#137×C13911yescharacteristic
563C4#575×C13911yescharacteristic
564C4#576×C13911yescharacteristic
565C4#578×C13911yescharacteristic
566C2—42no—
567C2—161no—
568C2#3268×C13911yescharacteristic
569C2#3270×C13911yescharacteristic
570C2#3291×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#459×C139C22
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. #3400×C139C2semidirect
2. #3381×C139C2semidirect
4. #3299×C139C2semidirect
5. #1714×C139C2semidirect
6. #1704×C139C2semidirect
7. #1692×C139C2semidirect
8. #1682×C139C2semidirect
10. #1649×C139C2semidirect
11. #1648×C139C2semidirect
12. #1630×C139C2semidirect
14. #1587×C139C2semidirect
15. #1585×C139C2semidirect
285. #20115C139direct (N × H)
286. C139#20115direct (N × H)
287. #3400C2×C139semidirect
288. #3381C2×C139semidirect
290. #3299C2×C139semidirect
291. #1714C2×C139semidirect
292. #1704C2×C139semidirect
293. #1692C2×C139semidirect
294. #1682C2×C139semidirect
296. #1649C2×C139semidirect
297. #1648C2×C139semidirect
298. #1630C2×C139semidirect
300. #1587C2×C139semidirect
301. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3400×C1392
#3381×C1392
#3373×C1392
#3299×C1392
#1714×C1392
#1704×C1392
#1692×C1392
#1682×C1392
#1665×C1392
#1649×C1392
#1648×C1392
#1630×C1392
#1622×C1392
#1587×C1392
#1585×C1392
#20115139