Finite Group Databasebeta

← C139×#20089 #48014685

Subgroups — C139×#20089 #48014685

Order 35584.

618 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3364×C139C211yesmaximal, characteristic, complemented
2#3359×C139C211yesmaximal, characteristic, complemented
3#3353×C139C211yesmaximal, characteristic
4#3276×C139C211yesmaximal, characteristic
5#1723×C139C211yesmaximal, characteristic, complemented
6#1699×C139C211yesmaximal, characteristic, complemented
7#1699×C139C211yesmaximal, characteristic, complemented
8#1674×C139C211yesmaximal, characteristic, complemented
9#1670×C139C211yesmaximal, characteristic, complemented
10#1654×C139C211yesmaximal, characteristic
11#1653×C139C211yesmaximal, characteristic, complemented
12#1650×C139C211yesmaximal, characteristic, complemented
13#1649×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1588×C139C211yesmaximal, characteristic, complemented
16C2×#137×C139—21no—
17#557×C139C2211yescharacteristic
18#556×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#500×C139C2211yescharacteristic
23#498×C139C2211yescharacteristic
24#494×C139C2211yescharacteristic
25#488×C139—21no—
26#487×C139—21no—
27#487×C139C2211yescharacteristic
28#487×C139C2211yescharacteristic
29#484×C139—21no—
30#482×C139—21no—
31#479×C139—21no—
32#475×C139—21no—
33#475×C139C2211yescharacteristic
34#475×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#470×C139—21no—
38#468×C139—21no—
39#464×C139—21no—
40#462×C139C2211yescharacteristic
41#462×C139C2211yescharacteristic
42#461×C139—21no—
43#461×C139C2211yescharacteristic
44#461×C139C2211yescharacteristic
45#452×C139—21no—
46#451×C139—21no—
47C8×Q8×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49C4×Q16×C139—21no—
50C4×SD16×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54#436×C139C2211yescharacteristic
55#428×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C22×Q8×C139—21no—
69#137×C139—44no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139—21no—
73C2×Q16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139D411yescharacteristic
77C2×SD16×C139D411yescharacteristic
78C2×M16×C139—21no—
79C2×M16×C139—21no—
80C4⋊Q8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139C2311yescharacteristic
83C4⋊Q8×C139C2311yescharacteristic
84C4⋊Q8×C139C2311yescharacteristic
85C4⋊Q8×C139C2311yescharacteristic
86#126×C139—41no—
87#125×C139—21no—
88#125×C139—41no—
89#124×C139—21no—
90#123×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—21no—
94C22⋊Q8×C139—41no—
95#121×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139—21no—
98C4×Q8×C139—21no—
99C4×Q8×C139C2311yescharacteristic
100C4×Q8×C139C2311yescharacteristic
101C4×D4×C139—21no—
102C4×D4×C139C2311yescharacteristic
103C4×D4×C139C2311yescharacteristic
104#117×C139—21no—
105C2×C4⋊C4×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—21no—
110#107×C139—41no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139—41no—
114#106×C139D411yescharacteristic
115#106×C139D411yescharacteristic
116C4⋊C8×C139—21no—
117C4⋊C8×C139—21no—
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
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×C139—21no—
129#103×C139—21no—
130#103×C139—21no—
131#103×C139—21no—
132#103×C139D411yescharacteristic
133#103×C139D411yescharacteristic
134#102×C139—21no—
135#102×C139—21no—
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145#41×C139—42no—
146#41×C139—81no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—41no—
152C2×Q8×C139—42no—
153C2×Q8×C139—81no—
154C2×Q8×C139C2×D411yescharacteristic
155C2×Q8×C139C2×D411yescharacteristic
156C2×D4×C139—41no—
157C2×D4×C139C2×D411yescharacteristic
158C2×D4×C139C2×D411yescharacteristic
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—41no—
162C22×C4×C139—41no—
163Q16×C139—42no—
164Q16×C139—42no—
165Q16×C139—42no—
166Q16×C139—81no—
167SD16×C139—22no—
168SD16×C139—41no—
169SD16×C139—42no—
170SD16×C139—42no—
171M16×C139—42no—
172M16×C139—42no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
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—21no—
191C4⋊C4×C139—21no—
192C4⋊C4×C139—41no—
193C4⋊C4×C139—41no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139C2×D411yescharacteristic
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C22⋊C4×C139—21no—
203C22⋊C4×C139—21no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C22⋊C4×C139—41no—
208C42×C139—21no—
209C42×C139—21no—
210C42×C139—41no—
211C42×C139—41no—
212C42×C139C2411yescharacteristic
213C23×C139—21no—
214C23×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—41no—
223Q8×C139—41no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—82no—
227Q8×C139AGL(1,ℤ/8)12yes—
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—21no—
231D4×C139—21no—
232D4×C139—82no—
233C2×C4×C139—21no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—41no—
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—82no—
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×C139D4211yescharacteristic
268C4×C139—22no—
269C4×C139—21no—
270C4×C139—41no—
271C4×C139—41no—
272C4×C139—41no—
273C4×C139—41no—
274C4×C139—41no—
275C4×C139—81no—
276C4×C139—81no—
277C4×C139—81no—
278C4×C139—81no—
279C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C139#57511yescharacteristic
281C4×C139#57711yescharacteristic
282C4×C139#57811yescharacteristic
283C2×C139—81no—
284C2×C139—81no—
285C2×C139#326511yescharacteristic
286C2×C139#326911yescharacteristic
287C2×C139#329311yescharacteristic
288#20089C13911yesmaximal, characteristic, direct product factor, Sylow
289C139#2008911yescharacteristic, direct product factor, Sylow
290#3364C2×C13911yescharacteristic, complemented
291#3359C2×C13911yescharacteristic, complemented
292#3353C2×C13911yescharacteristic
293#3276C2×C13911yescharacteristic
294#1723C2×C13911yescharacteristic, complemented
295#1699C2×C13911yescharacteristic, complemented
296#1699C2×C13911yescharacteristic, complemented
297#1674C2×C13911yescharacteristic, complemented
298#1670C2×C13911yescharacteristic, complemented
299#1654C2×C13911yescharacteristic
300#1653C2×C13911yescharacteristic, complemented
301#1650C2×C13911yescharacteristic, complemented
302#1649C2×C13911yescharacteristic, complemented
303#1588C2×C13911yescharacteristic, complemented
304#1588C2×C13911yescharacteristic, complemented
305C2×#137—21no—
306#557C22×C13911yescharacteristic
307#556C22×C13911yescharacteristic
308D4×Q8C22×C13911yescharacteristic
309#547C22×C13911yescharacteristic
310#500C22×C13911yescharacteristic
311#500C22×C13911yescharacteristic
312#498C22×C13911yescharacteristic
313#494C22×C13911yescharacteristic
314#488—21no—
315#487—21no—
316#487C22×C13911yescharacteristic
317#487C22×C13911yescharacteristic
318#484—21no—
319#482—21no—
320#479—21no—
321#475—21no—
322#475C22×C13911yescharacteristic
323#475C22×C13911yescharacteristic
324#474C22×C13911yescharacteristic
325#474C22×C13911yescharacteristic
326#470—21no—
327#468—21no—
328#464—21no—
329#462C22×C13911yescharacteristic
330#462C22×C13911yescharacteristic
331#461—21no—
332#461C22×C13911yescharacteristic
333#461C22×C13911yescharacteristic
334#452—21no—
335#451—21no—
336C8×Q8C22×C13911yescharacteristic
337C8×Q8C22×C13911yescharacteristic
338C4×Q16—21no—
339C4×SD16—21no—
340C4×SD16C22×C13911yescharacteristic
341C4×SD16C22×C13911yescharacteristic
342#436C22×C13911yescharacteristic
343#436C22×C13911yescharacteristic
344#428—21no—
345#335C22×C13911yescharacteristic
346#335C22×C13911yescharacteristic
347#332C22×C13911yescharacteristic
348#332C22×C13911yescharacteristic
349#332C22×C13911yescharacteristic
350#332C22×C13911yescharacteristic
351Q8⋊C8C22×C13911yescharacteristic
352Q8⋊C8C22×C13911yescharacteristic
353D4⋊C8C22×C13911yescharacteristic
354D4⋊C8C22×C13911yescharacteristic
355#322C22×C13911yescharacteristic
356C2×#41—21no—
357C22×Q8—21no—
358#137—44no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16D4×C13911yescharacteristic
366C2×SD16D4×C13911yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C13911yescharacteristic
372C4⋊Q8C23×C13911yescharacteristic
373C4⋊Q8C23×C13911yescharacteristic
374C4⋊Q8C23×C13911yescharacteristic
375#126—41no—
376#125—21no—
377#125—41no—
378#124—21no—
379#123—41no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384#121—21no—
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—
394C2×C4⋊C4—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—41no—
400#106—21no—
401#106—21no—
402#106—41no—
403#106D4×C13911yescharacteristic
404#106D4×C13911yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C13911yescharacteristic
408C4⋊C8C23×C13911yescharacteristic
409C4⋊C8C23×C13911yescharacteristic
410C4⋊C8C23×C13911yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103D4×C13911yescharacteristic
422#103D4×C13911yescharacteristic
423#102—21no—
424#102—21no—
425#102D4×C13911yescharacteristic
426#102D4×C13911yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8C23×C13911yescharacteristic
432C4×C8C23×C13911yescharacteristic
433C4×C8C23×C13911yescharacteristic
434#41—42no—
435#41—81no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8C2×D4×C13911yescharacteristic
444C2×Q8C2×D4×C13911yescharacteristic
445C2×D4—41no—
446C2×D4C2×D4×C13911yescharacteristic
447C2×D4C2×D4×C13911yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—42no—
453Q16—42no—
454Q16—42no—
455Q16—81no—
456SD16—22no—
457SD16—41no—
458SD16—42no—
459SD16—42no—
460M16—42no—
461M16—42no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C2×D4×C13911yescharacteristic
468C2×C8C2×D4×C13911yescharacteristic
469C2×C8C2×D4×C13911yescharacteristic
470C2×C8C2×D4×C13911yescharacteristic
471C4⋊C4—21no—
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—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4C2×D4×C13911yescharacteristic
488C4⋊C4C2×D4×C13911yescharacteristic
489C4⋊C4C2×D4×C13911yescharacteristic
490C4⋊C4C2×D4×C13911yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42C24×C13911yescharacteristic
502C23—21no—
503C23—21no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—82no—
516Q8AGL(1,ℤ/8)×C13912yes—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—82no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4C22×D4×C13911yescharacteristic
539C2×C4C22×D4×C13911yescharacteristic
540C2×C4H(5,𝔽2)×C13911yescharacteristic
541C8—22no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22D42×C13911yescharacteristic
557C4—21no—
558C4—22no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
569C4#575×C13911yescharacteristic
570C4#577×C13911yescharacteristic
571C4#578×C13911yescharacteristic
572C2—81no—
573C2—81no—
574C2#3265×C13911yescharacteristic
575C2#3269×C13911yescharacteristic
576C2#3293×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#547×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. #3364×C139C2semidirect
2. #3359×C139C2semidirect
5. #1723×C139C2semidirect
6. #1699×C139C2semidirect
7. #1699×C139C2semidirect
8. #1674×C139C2semidirect
9. #1670×C139C2semidirect
11. #1653×C139C2semidirect
12. #1650×C139C2semidirect
13. #1649×C139C2semidirect
14. #1588×C139C2semidirect
15. #1588×C139C2semidirect
288. #20089C139direct (N × H)
289. C139#20089direct (N × H)
290. #3364C2×C139semidirect
291. #3359C2×C139semidirect
294. #1723C2×C139semidirect
295. #1699C2×C139semidirect
296. #1699C2×C139semidirect
297. #1674C2×C139semidirect
298. #1670C2×C139semidirect
300. #1653C2×C139semidirect
301. #1650C2×C139semidirect
302. #1649C2×C139semidirect
303. #1588C2×C139semidirect
304. #1588C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3364×C1392
#3359×C1392
#3353×C1392
#3276×C1392
#1723×C1392
#1699×C1392
#1674×C1392
#1670×C1392
#1654×C1392
#1653×C1392
#1650×C1392
#1649×C1392
#1588×C1392
#20089139