Finite Group Databasebeta

← C139×#20087 #48014683

Subgroups — C139×#20087 #48014683

Order 35584.

628 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
1Q8×SD16×C139C211yesmaximal, characteristic, complemented
2#3368×C139C211yesmaximal, characteristic
3#3363×C139C211yesmaximal, characteristic, complemented
4#3278×C139C211yesmaximal, characteristic
5#1714×C139C211yesmaximal, characteristic, complemented
6#1703×C139C211yesmaximal, characteristic, complemented
7#1692×C139C211yesmaximal, characteristic, complemented
8#1682×C139C211yesmaximal, characteristic, complemented
9#1666×C139C211yesmaximal, characteristic, complemented
10#1649×C139C211yesmaximal, characteristic, complemented
11#1648×C139C211yesmaximal, characteristic, complemented
12#1631×C139C211yesmaximal, characteristic
13#1623×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1587×C139C211yesmaximal, characteristic, complemented
16C2×#137×C139—21no—
17Q82×C139C2211yescharacteristic
18#557×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20D4×Q8×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#498×C139—21no—
23#498×C139C2211yescharacteristic
24#492×C139C2211yescharacteristic
25#492×C139C2211yescharacteristic
26#490×C139—21no—
27#487×C139—21no—
28#487×C139C2211yescharacteristic
29#486×C139C2211yescharacteristic
30#478×C139—21no—
31#477×C139—21no—
32#477×C139C2211yescharacteristic
33#476×C139—21no—
34#476×C139C2211yescharacteristic
35#475×C139—21no—
36#475×C139C2211yescharacteristic
37#474×C139C2211yescharacteristic
38#468×C139—21no—
39#462×C139—21no—
40#462×C139C2211yescharacteristic
41#462×C139C2211yescharacteristic
42#460×C139—21no—
43#460×C139C2211yescharacteristic
44#460×C139C2211yescharacteristic
45#452×C139—21no—
46#448×C139—21no—
47#446×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49C8×Q8×C139C2211yescharacteristic
50#440×C139—21no—
51C4×Q16×C139—21no—
52C4×Q16×C139C2211yescharacteristic
53C4×SD16×C139—21no—
54C4×SD16×C139C2211yescharacteristic
55#436×C139C2211yescharacteristic
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
67C2×#41×C139—21no—
68C22×Q8×C139—21no—
69#137×C139—44no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139D411yescharacteristic
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139—41no—
78C2×SD16×C139D411yescharacteristic
79C2×M16×C139—21no—
80C4⋊Q8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139—21no—
83C4⋊Q8×C139—21no—
84C4⋊Q8×C139—41no—
85C4⋊Q8×C139C2311yescharacteristic
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88#127×C139—21no—
89#127×C139C2311yescharacteristic
90#125×C139—21no—
91#125×C139—41no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—41no—
94#121×C139—21no—
95#121×C139—41no—
96C4×Q8×C139—21no—
97C4×Q8×C139—21no—
98C4×Q8×C139—21no—
99C4×Q8×C139—21no—
100C4×Q8×C139C2311yescharacteristic
101C4×Q8×C139C2311yescharacteristic
102C4×Q8×C139C2311yescharacteristic
103C4×D4×C139—21no—
104C4×D4×C139—21no—
105C4×D4×C139C2311yescharacteristic
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×C139—21no—
114#106×C139D411yescharacteristic
115C4⋊C8×C139—21no—
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×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×C139—21no—
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139#97×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—41no—
151C2×Q8×C139—41no—
152C2×Q8×C139—42no—
153C2×Q8×C139—81no—
154C2×Q8×C139C2×D411yescharacteristic
155C2×Q8×C139C2×D411yescharacteristic
156C2×Q8×C139C2×D411yescharacteristic
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—41no—
161C2×D4×C139—41no—
162C2×D4×C139C2×D411yescharacteristic
163C22×C4×C139—21no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166Q16×C139—22no—
167Q16×C139—42no—
168Q16×C139—42no—
169SD16×C139—22no—
170SD16×C139—42no—
171SD16×C139—42no—
172SD16×C139—42no—
173SD16×C139—81no—
174SD16×C139—82no—
175M16×C139—42no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139C2×D411yescharacteristic
182C2×C8×C139C2×D411yescharacteristic
183C2×C8×C139C2×D411yescharacteristic
184C2×C8×C139C2×D411yescharacteristic
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—21no—
193C4⋊C4×C139—21no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C4⋊C4×C139C2×D411yescharacteristic
204C22⋊C4×C139—21no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C42×C139—21no—
208C42×C139—21no—
209C42×C139—21no—
210C42×C139—41no—
211C42×C139—41no—
212C42×C139C2411yescharacteristic
213C23×C139—21no—
214C23×C139—41no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—21no—
218Q8×C139—21no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—41no—
223Q8×C139—82no—
224Q8×C139—81no—
225Q8×C139—161no—
226Q8×C139AGL(1,ℤ/8)12yes—
227Q8×C139#13712yescomplemented
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—41no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—41no—
234D4×C139—81no—
235D4×C139—82no—
236D4×C139—161no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—21no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—82no—
250C2×C4×C139—82no—
251C2×C4×C139C22×D411yescharacteristic
252C2×C4×C139C22×D411yescharacteristic
253C2×C4×C139H(5,𝔽2)11yescharacteristic
254C8×C139—22no—
255C8×C139—21no—
256C8×C139—21no—
257C8×C139—21no—
258C8×C139—21no—
259C8×C139—41no—
260C8×C139—41no—
261C8×C139—41no—
262C8×C139—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—81no—
267C22×C139—81no—
268C22×C139—81no—
269C22×C139D4211yescharacteristic
270C4×C139—22no—
271C4×C139—22no—
272C4×C139—21no—
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×C139C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C139C2×#13711yescharacteristic
283C4×C139#57711yescharacteristic
284C4×C139#57811yescharacteristic
285C2×C139—81no—
286C2×C139—161no—
287C2×C139#326511yescharacteristic
288C2×C139#327011yescharacteristic
289C2×C139#329111yescharacteristic
290#20087C13911yesmaximal, characteristic, direct product factor, Sylow
291C139#2008711yescharacteristic, direct product factor, Sylow
292Q8×SD16C2×C13911yescharacteristic, complemented
293#3368C2×C13911yescharacteristic
294#3363C2×C13911yescharacteristic, complemented
295#3278C2×C13911yescharacteristic
296#1714C2×C13911yescharacteristic, complemented
297#1703C2×C13911yescharacteristic, complemented
298#1692C2×C13911yescharacteristic, complemented
299#1682C2×C13911yescharacteristic, complemented
300#1666C2×C13911yescharacteristic, complemented
301#1649C2×C13911yescharacteristic, complemented
302#1648C2×C13911yescharacteristic, complemented
303#1631C2×C13911yescharacteristic
304#1623C2×C13911yescharacteristic, complemented
305#1588C2×C13911yescharacteristic, complemented
306#1587C2×C13911yescharacteristic, complemented
307C2×#137—21no—
308Q82C22×C13911yescharacteristic
309#557C22×C13911yescharacteristic
310#550C22×C13911yescharacteristic
311D4×Q8C22×C13911yescharacteristic
312#500C22×C13911yescharacteristic
313#498—21no—
314#498C22×C13911yescharacteristic
315#492C22×C13911yescharacteristic
316#492C22×C13911yescharacteristic
317#490—21no—
318#487—21no—
319#487C22×C13911yescharacteristic
320#486C22×C13911yescharacteristic
321#478—21no—
322#477—21no—
323#477C22×C13911yescharacteristic
324#476—21no—
325#476C22×C13911yescharacteristic
326#475—21no—
327#475C22×C13911yescharacteristic
328#474C22×C13911yescharacteristic
329#468—21no—
330#462—21no—
331#462C22×C13911yescharacteristic
332#462C22×C13911yescharacteristic
333#460—21no—
334#460C22×C13911yescharacteristic
335#460C22×C13911yescharacteristic
336#452—21no—
337#448—21no—
338#446C22×C13911yescharacteristic
339C8×Q8C22×C13911yescharacteristic
340C8×Q8C22×C13911yescharacteristic
341#440—21no—
342C4×Q16—21no—
343C4×Q16C22×C13911yescharacteristic
344C4×SD16—21no—
345C4×SD16C22×C13911yescharacteristic
346#436C22×C13911yescharacteristic
347#335C22×C13911yescharacteristic
348#334C22×C13911yescharacteristic
349#333C22×C13911yescharacteristic
350#332C22×C13911yescharacteristic
351#332C22×C13911yescharacteristic
352#331C22×C13911yescharacteristic
353Q8⋊C8C22×C13911yescharacteristic
354Q8⋊C8C22×C13911yescharacteristic
355Q8⋊C8C22×C13911yescharacteristic
356D4⋊C8C22×C13911yescharacteristic
357#322C22×C13911yescharacteristic
358C2×#41—21no—
359C22×Q8—21no—
360#137—44no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16D4×C13911yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—41no—
369C2×SD16D4×C13911yescharacteristic
370C2×M16—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—41no—
376C4⋊Q8C23×C13911yescharacteristic
377C4⋊Q8C23×C13911yescharacteristic
378C4⋊Q8C23×C13911yescharacteristic
379#127—21no—
380#127C23×C13911yescharacteristic
381#125—21no—
382#125—41no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385#121—21no—
386#121—41no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C23×C13911yescharacteristic
392C4×Q8C23×C13911yescharacteristic
393C4×Q8C23×C13911yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C13911yescharacteristic
397#107—21no—
398#107—21no—
399#107—41no—
400#107D4×C13911yescharacteristic
401#106—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106D4×C13911yescharacteristic
406C4⋊C8—21no—
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#103D4×C13911yescharacteristic
420#103D4×C13911yescharacteristic
421#103D4×C13911yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102D4×C13911yescharacteristic
429C22⋊C8—21no—
430#97—21no—
431C4×C8—21no—
432C4×C8—21no—
433C4×C8C23×C13911yescharacteristic
434C4×C8C23×C13911yescharacteristic
435C4×C8C23×C13911yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C13911yescharacteristic
446C2×Q8C2×D4×C13911yescharacteristic
447C2×Q8C2×D4×C13911yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C13911yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457Q16—22no—
458Q16—42no—
459Q16—42no—
460SD16—22no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—81no—
465SD16—82no—
466M16—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8C2×D4×C13911yescharacteristic
473C2×C8C2×D4×C13911yescharacteristic
474C2×C8C2×D4×C13911yescharacteristic
475C2×C8C2×D4×C13911yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C13911yescharacteristic
492C4⋊C4C2×D4×C13911yescharacteristic
493C4⋊C4C2×D4×C13911yescharacteristic
494C4⋊C4C2×D4×C13911yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42—41no—
503C42C24×C13911yescharacteristic
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—82no—
515Q8—81no—
516Q8—161no—
517Q8AGL(1,ℤ/8)×C13912yes—
518Q8#137×C13912yescomplemented
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—82no—
527D4—161no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4C22×D4×C13911yescharacteristic
543C2×C4C22×D4×C13911yescharacteristic
544C2×C4H(5,𝔽2)×C13911yescharacteristic
545C8—22no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22D42×C13911yescharacteristic
561C4—21no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
573C4C2×#137×C13911yescharacteristic
574C4#577×C13911yescharacteristic
575C4#578×C13911yescharacteristic
576C2—81no—
577C2—161no—
578C2#3265×C13911yescharacteristic
579C2#3270×C13911yescharacteristic
580C2#3291×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#550×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. Q8×SD16×C139C2semidirect
3. #3363×C139C2semidirect
5. #1714×C139C2semidirect
6. #1703×C139C2semidirect
7. #1692×C139C2semidirect
8. #1682×C139C2semidirect
9. #1666×C139C2semidirect
10. #1649×C139C2semidirect
11. #1648×C139C2semidirect
13. #1623×C139C2semidirect
14. #1588×C139C2semidirect
15. #1587×C139C2semidirect
227. Q8×C139#137semidirect
290. #20087C139direct (N × H)
291. C139#20087direct (N × H)
292. Q8×SD16C2×C139semidirect
294. #3363C2×C139semidirect
296. #1714C2×C139semidirect
297. #1703C2×C139semidirect
298. #1692C2×C139semidirect
299. #1682C2×C139semidirect
300. #1666C2×C139semidirect
301. #1649C2×C139semidirect
302. #1648C2×C139semidirect
304. #1623C2×C139semidirect
305. #1588C2×C139semidirect
306. #1587C2×C139semidirect
518. Q8#137×C139semidirect

Maximal subgroups

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

subgroupindex
Q8×SD16×C1392
#3368×C1392
#3363×C1392
#3278×C1392
#1714×C1392
#1703×C1392
#1692×C1392
#1682×C1392
#1666×C1392
#1649×C1392
#1648×C1392
#1631×C1392
#1623×C1392
#1588×C1392
#1587×C1392
#20087139