Finite Group Databasebeta

← C139×#20139 #48014735

Subgroups — C139×#20139 #48014735

Order 35584.

628 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C139C211yesmaximal, characteristic, complemented
2#3394×C139C211yesmaximal, characteristic, complemented
3#3332×C139C211yesmaximal, characteristic, complemented
4#3302×C139C211yesmaximal, characteristic, complemented
5#1717×C139C211yesmaximal, characteristic, complemented
6#1700×C139C211yesmaximal, characteristic, complemented
7#1685×C139C211yesmaximal, characteristic, complemented
8#1682×C139C211yesmaximal, characteristic, complemented
9#1667×C139C211yesmaximal, characteristic, complemented
10#1641×C139C211yesmaximal, characteristic, complemented
11#1640×C139C211yesmaximal, characteristic, complemented
12#1628×C139C211yesmaximal, characteristic, complemented
13#1625×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic
17#556×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19#547×C139C2211yescharacteristic
20#496×C139—21no—
21#495×C139—21no—
22#493×C139C2211yescharacteristic
23#492×C139C2211yescharacteristic
24#487×C139C2211yescharacteristic
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#485×C139—21no—
29#481×C139—21no—
30#475×C139C2211yescharacteristic
31#474×C139C2211yescharacteristic
32#469×C139—21no—
33#467×C139—21no—
34#464×C139—21no—
35#463×C139—21no—
36#463×C139—21no—
37#462×C139C2211yescharacteristic
38#462×C139C2211yescharacteristic
39#460×C139C2211yescharacteristic
40#459×C139—21no—
41#459×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#452×C139—21no—
45#449×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#417×C139—21no—
55#416×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139D411yescharacteristic
75C2×SD16×C139D411yescharacteristic
76C2×D8×C139—21no—
77C2×D8×C139—21no—
78C2×D8×C139—21no—
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×M16×C139—21no—
82C22×C8×C139—21no—
83C4⋊Q8×C139C2311yescharacteristic
84C4⋊Q8×C139C2311yescharacteristic
85#127×C139—21no—
86#127×C139C2311yescharacteristic
87#127×C139C2311yescharacteristic
88#126×C139—41no—
89#124×C139—21no—
90#124×C139—21no—
91#124×C139—21no—
92#123×C139—41no—
93#123×C139—41no—
94C22⋊Q8×C139—21no—
95C22⋊Q8×C139—21no—
96#121×C139—21no—
97#121×C139—21no—
98#121×C139—41no—
99C4×Q8×C139—21no—
100C4×Q8×C139C2311yescharacteristic
101C4×Q8×C139C2311yescharacteristic
102C4×D4×C139—21no—
103C4×D4×C139—21no—
104C4×D4×C139—21no—
105C4×D4×C139C2311yescharacteristic
106C4×D4×C139C2311yescharacteristic
107#117×C139—21no—
108C2×C4⋊C4×C139—21no—
109#107×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—21no—
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—41no—
134#102×C139—41no—
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
144#41×C139—42no—
145#41×C139—42no—
146#41×C139—81no—
147#41×C139—81no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139C2×D411yescharacteristic
151C2×Q8×C139C2×D411yescharacteristic
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—41no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139C2×D411yescharacteristic
162C2×D4×C139C2×D411yescharacteristic
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167C22×C4×C139—41no—
168Q16×C139—81no—
169Q16×C139—81no—
170SD16×C139—41no—
171SD16×C139—41no—
172SD16×C139—42no—
173SD16×C139—81no—
174SD16×C139—81no—
175D8×C139—42no—
176D8×C139—81no—
177D8×C139—81no—
178D8×C139—81no—
179D8×C139—81no—
180M16×C139—81no—
181C2×C8×C139—21no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—81no—
187C2×C8×C139C2×D411yescharacteristic
188C2×C8×C139C2×D411yescharacteristic
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
191C4⋊C4×C139—21no—
192C4⋊C4×C139—21no—
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C22⋊C4×C139—21no—
204C22⋊C4×C139—21no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C22⋊C4×C139—41no—
208C22⋊C4×C139—41no—
209C22⋊C4×C139—41no—
210C22⋊C4×C139—41no—
211C22⋊C4×C139—41no—
212C42×C139—21no—
213C42×C139—21no—
214C42×C139—41no—
215C42×C139C2411yescharacteristic
216C23×C139—21no—
217C23×C139—21no—
218C23×C139—41no—
219C23×C139—41no—
220Q8×C139—21no—
221Q8×C139—21no—
222Q8×C139—21no—
223Q8×C139—21no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—41no—
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—21no—
231D4×C139—21no—
232D4×C139—41no—
233D4×C139—41no—
234D4×C139—41no—
235D4×C139—41no—
236D4×C139—41no—
237D4×C139—41no—
238D4×C139—41no—
239D4×C139—41no—
240D4×C139—81no—
241D4×C139—81no—
242D4×C139—82no—
243D4×C139—82no—
244D4×C139—161no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—82no—
258C2×C4×C139—82no—
259C2×C4×C139—161no—
260C2×C4×C139C22×D411yescharacteristic
261C2×C4×C139C22×D411yescharacteristic
262C2×C4×C139H(5,𝔽2)11yescharacteristic
263C8×C139—21no—
264C8×C139—21no—
265C8×C139—21no—
266C8×C139—21no—
267C8×C139—41no—
268C8×C139—41no—
269C8×C139—41no—
270C8×C139—41no—
271C8×C139—41no—
272C22×C139—41no—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139—81no—
284C22×C139D4211yescharacteristic
285C4×C139—21no—
286C4×C139—41no—
287C4×C139—41no—
288C4×C139—41no—
289C4×C139—41no—
290C4×C139—41no—
291C4×C139—41no—
292C4×C139—81no—
293C4×C139—81no—
294C4×C139#57511yescharacteristic
295C4×C139#57511yescharacteristic
296C4×C139#57611yescharacteristic
297C4×C139#57611yescharacteristic
298C2×C139—81no—
299C2×C139—81no—
300C2×C139—161no—
301C2×C139—161no—
302C2×C139#326811yescharacteristic
303C2×C139#326811yescharacteristic
304C2×C139#329011yescharacteristic
305#20139C13911yesmaximal, characteristic, direct product factor, Sylow
306C139#2013911yescharacteristic, direct product factor, Sylow
307#3399C2×C13911yescharacteristic, complemented
308#3394C2×C13911yescharacteristic, complemented
309#3332C2×C13911yescharacteristic, complemented
310#3302C2×C13911yescharacteristic, complemented
311#1717C2×C13911yescharacteristic, complemented
312#1700C2×C13911yescharacteristic, complemented
313#1685C2×C13911yescharacteristic, complemented
314#1682C2×C13911yescharacteristic, complemented
315#1667C2×C13911yescharacteristic, complemented
316#1641C2×C13911yescharacteristic, complemented
317#1640C2×C13911yescharacteristic, complemented
318#1628C2×C13911yescharacteristic, complemented
319#1625C2×C13911yescharacteristic, complemented
320#1588C2×C13911yescharacteristic, complemented
321#1585C2×C13911yescharacteristic, complemented
322#559C22×C13911yescharacteristic
323#556C22×C13911yescharacteristic
324#550C22×C13911yescharacteristic
325#547C22×C13911yescharacteristic
326#496—21no—
327#495—21no—
328#493C22×C13911yescharacteristic
329#492C22×C13911yescharacteristic
330#487C22×C13911yescharacteristic
331#486C22×C13911yescharacteristic
332#486C22×C13911yescharacteristic
333#486C22×C13911yescharacteristic
334#485—21no—
335#481—21no—
336#475C22×C13911yescharacteristic
337#474C22×C13911yescharacteristic
338#469—21no—
339#467—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#462C22×C13911yescharacteristic
344#462C22×C13911yescharacteristic
345#460C22×C13911yescharacteristic
346#459—21no—
347#459C22×C13911yescharacteristic
348#459C22×C13911yescharacteristic
349#459C22×C13911yescharacteristic
350#452—21no—
351#449—21no—
352#446C22×C13911yescharacteristic
353C8×Q8C22×C13911yescharacteristic
354#442—21no—
355C4×SD16—21no—
356C4×SD16C22×C13911yescharacteristic
357C4×SD16C22×C13911yescharacteristic
358#436C22×C13911yescharacteristic
359C8×D4C22×C13911yescharacteristic
360#417—21no—
361#416—21no—
362#335C22×C13911yescharacteristic
363#335C22×C13911yescharacteristic
364#332C22×C13911yescharacteristic
365#332C22×C13911yescharacteristic
366#331C22×C13911yescharacteristic
367#331C22×C13911yescharacteristic
368Q8⋊C8C22×C13911yescharacteristic
369Q8⋊C8C22×C13911yescharacteristic
370D4⋊C8C22×C13911yescharacteristic
371D4⋊C8C22×C13911yescharacteristic
372#322C22×C13911yescharacteristic
373C2×#41—21no—
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16D4×C13911yescharacteristic
381C2×SD16D4×C13911yescharacteristic
382C2×D8—21no—
383C2×D8—21no—
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×M16—21no—
388C22×C8—21no—
389C4⋊Q8C23×C13911yescharacteristic
390C4⋊Q8C23×C13911yescharacteristic
391#127—21no—
392#127C23×C13911yescharacteristic
393#127C23×C13911yescharacteristic
394#126—41no—
395#124—21no—
396#124—21no—
397#124—21no—
398#123—41no—
399#123—41no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402#121—21no—
403#121—21no—
404#121—41no—
405C4×Q8—21no—
406C4×Q8C23×C13911yescharacteristic
407C4×Q8C23×C13911yescharacteristic
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4C23×C13911yescharacteristic
412C4×D4C23×C13911yescharacteristic
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#106—21no—
417#106D4×C13911yescharacteristic
418#106D4×C13911yescharacteristic
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C13911yescharacteristic
422C4⋊C8C23×C13911yescharacteristic
423C4⋊C8C23×C13911yescharacteristic
424C4⋊C8C23×C13911yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103D4×C13911yescharacteristic
431#103D4×C13911yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—41no—
440#102—41no—
441#102D4×C13911yescharacteristic
442#102D4×C13911yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8C23×C13911yescharacteristic
448C4×C8C23×C13911yescharacteristic
449C4×C8C23×C13911yescharacteristic
450#41—42no—
451#41—42no—
452#41—81no—
453#41—81no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C13911yescharacteristic
457C2×Q8C2×D4×C13911yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4C2×D4×C13911yescharacteristic
468C2×D4C2×D4×C13911yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474Q16—81no—
475Q16—81no—
476SD16—41no—
477SD16—41no—
478SD16—42no—
479SD16—81no—
480SD16—81no—
481D8—42no—
482D8—81no—
483D8—81no—
484D8—81no—
485D8—81no—
486M16—81no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8C2×D4×C13911yescharacteristic
494C2×C8C2×D4×C13911yescharacteristic
495C2×C8C2×D4×C13911yescharacteristic
496C2×C8C2×D4×C13911yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C13911yescharacteristic
506C4⋊C4C2×D4×C13911yescharacteristic
507C4⋊C4C2×D4×C13911yescharacteristic
508C4⋊C4C2×D4×C13911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—21no—
519C42—21no—
520C42—41no—
521C42C24×C13911yescharacteristic
522C23—21no—
523C23—21no—
524C23—41no—
525C23—41no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—81no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—161no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—161no—
566C2×C4C22×D4×C13911yescharacteristic
567C2×C4C22×D4×C13911yescharacteristic
568C2×C4H(5,𝔽2)×C13911yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22D42×C13911yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4#575×C13911yescharacteristic
601C4#575×C13911yescharacteristic
602C4#576×C13911yescharacteristic
603C4#576×C13911yescharacteristic
604C2—81no—
605C2—81no—
606C2—161no—
607C2—161no—
608C2#3268×C13911yescharacteristic
609C2#3268×C13911yescharacteristic
610C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
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. #3399×C139C2semidirect
2. #3394×C139C2semidirect
3. #3332×C139C2semidirect
4. #3302×C139C2semidirect
5. #1717×C139C2semidirect
6. #1700×C139C2semidirect
7. #1685×C139C2semidirect
8. #1682×C139C2semidirect
9. #1667×C139C2semidirect
10. #1641×C139C2semidirect
11. #1640×C139C2semidirect
12. #1628×C139C2semidirect
13. #1625×C139C2semidirect
14. #1588×C139C2semidirect
15. #1585×C139C2semidirect
305. #20139C139direct (N × H)
306. C139#20139direct (N × H)
307. #3399C2×C139semidirect
308. #3394C2×C139semidirect
309. #3332C2×C139semidirect
310. #3302C2×C139semidirect
311. #1717C2×C139semidirect
312. #1700C2×C139semidirect
313. #1685C2×C139semidirect
314. #1682C2×C139semidirect
315. #1667C2×C139semidirect
316. #1641C2×C139semidirect
317. #1640C2×C139semidirect
318. #1628C2×C139semidirect
319. #1625C2×C139semidirect
320. #1588C2×C139semidirect
321. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3399×C1392
#3394×C1392
#3332×C1392
#3302×C1392
#1717×C1392
#1700×C1392
#1685×C1392
#1682×C1392
#1667×C1392
#1641×C1392
#1640×C1392
#1628×C1392
#1625×C1392
#1588×C1392
#1585×C1392
#20139139