Finite Group Databasebeta

← C139×#19947 #48014543

Subgroups — C139×#19947 #48014543

Order 35584.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 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#3353×C139C211yesmaximal, characteristic, complemented
4#3284×C139C211yesmaximal, characteristic, complemented
5#1706×C139C211yesmaximal, characteristic, complemented
6#1694×C139C211yesmaximal, characteristic, complemented
7#1687×C139C211yesmaximal, characteristic, complemented
8#1666×C139C211yesmaximal, characteristic, complemented
9#1665×C139C211yesmaximal, characteristic, complemented
10#1641×C139C211yesmaximal, characteristic, complemented
11#1640×C139C211yesmaximal, characteristic, complemented
12#1628×C139C211yesmaximal, characteristic, complemented
13#1625×C139C211yesmaximal, characteristic, complemented
14#1590×C139C211yesmaximal, characteristic, complemented
15C8×SD16×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#559×C139C2211yescharacteristic
18#556×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#496×C139—21no—
23#495×C139—21no—
24#493×C139C2211yescharacteristic
25#492×C139C2211yescharacteristic
26#492×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#484×C139—21no—
30#482×C139—21no—
31#475×C139C2211yescharacteristic
32#474×C139C2211yescharacteristic
33#468×C139—21no—
34#465×C139—21no—
35#464×C139—21no—
36#463×C139—21no—
37#463×C139—21no—
38#462×C139C2211yescharacteristic
39#462×C139C2211yescharacteristic
40#460×C139C2211yescharacteristic
41#459×C139—21no—
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#452×C139—21no—
46#449×C139—21no—
47#446×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49#442×C139—21no—
50C4×SD16×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55#428×C139—21no—
56#334×C139C2211yescharacteristic
57#334×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
66C82×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69#135×C139—44no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139D411yescharacteristic
78C2×SD16×C139D411yescharacteristic
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139—21no—
83C2×D8×C139—21no—
84C2×M16×C139—21no—
85C22×C8×C139—21no—
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88#127×C139—21no—
89#127×C139C2311yescharacteristic
90#127×C139C2311yescharacteristic
91#126×C139—41no—
92#124×C139—21no—
93#124×C139—21no—
94#124×C139—21no—
95#123×C139—41no—
96#123×C139—41no—
97C22⋊Q8×C139—21no—
98C22⋊Q8×C139—21no—
99#121×C139—21no—
100#121×C139—21no—
101#121×C139—41no—
102C4×Q8×C139—21no—
103C4×Q8×C139C2311yescharacteristic
104C4×Q8×C139C2311yescharacteristic
105C4×D4×C139—21no—
106C4×D4×C139—21no—
107C4×D4×C139—21no—
108C4×D4×C139C2311yescharacteristic
109C4×D4×C139C2311yescharacteristic
110#117×C139—21no—
111C2×C4⋊C4×C139—21no—
112#107×C139—21no—
113#107×C139—21no—
114#107×C139—21no—
115#106×C139—21no—
116#106×C139D411yescharacteristic
117#106×C139D411yescharacteristic
118C4⋊C8×C139—21no—
119C4⋊C8×C139—21no—
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122C4⋊C8×C139C2311yescharacteristic
123C4⋊C8×C139C2311yescharacteristic
124#103×C139—21no—
125#103×C139—21no—
126#103×C139—21no—
127#103×C139D411yescharacteristic
128#103×C139D411yescharacteristic
129#102×C139—21no—
130#102×C139—21no—
131#102×C139—21no—
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—41no—
135#102×C139—41no—
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140#97×C139—21no—
141C4×C8×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145#41×C139—42no—
146#41×C139—42no—
147#41×C139—81no—
148#41×C139—81no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139C2×D411yescharacteristic
152C2×Q8×C139C2×D411yescharacteristic
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139—41no—
162C2×D4×C139C2×D411yescharacteristic
163C2×D4×C139C2×D411yescharacteristic
164C22×C4×C139—21no—
165C22×C4×C139—21no—
166C22×C4×C139—41no—
167C22×C4×C139—41no—
168C22×C4×C139—41no—
169Q16×C139—42no—
170Q16×C139—81no—
171SD16×C139—22no—
172SD16×C139—22no—
173SD16×C139—42no—
174SD16×C139—42no—
175SD16×C139—81no—
176SD16×C139—81no—
177SD16×C139—81no—
178D8×C139—42no—
179D8×C139—42no—
180D8×C139—81no—
181D8×C139—81no—
182D8×C139—81no—
183M16×C139—42no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—42no—
190C2×C8×C139C2×D411yescharacteristic
191C2×C8×C139C2×D411yescharacteristic
192C2×C8×C139C2×D411yescharacteristic
193C2×C8×C139C2×D411yescharacteristic
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—41no—
201C4⋊C4×C139—41no—
202C4⋊C4×C139C2×D411yescharacteristic
203C4⋊C4×C139C2×D411yescharacteristic
204C4⋊C4×C139C2×D411yescharacteristic
205C4⋊C4×C139C2×D411yescharacteristic
206C22⋊C4×C139—21no—
207C22⋊C4×C139—21no—
208C22⋊C4×C139—41no—
209C22⋊C4×C139—41no—
210C22⋊C4×C139—41no—
211C22⋊C4×C139—41no—
212C22⋊C4×C139—41no—
213C22⋊C4×C139—41no—
214C22⋊C4×C139—41no—
215C42×C139—21no—
216C42×C139—21no—
217C42×C139—41no—
218C42×C139C2411yescharacteristic
219C23×C139—21no—
220C23×C139—21no—
221C23×C139—41no—
222C23×C139—41no—
223Q8×C139—21no—
224Q8×C139—21no—
225Q8×C139—21no—
226Q8×C139—21no—
227Q8×C139—41no—
228Q8×C139—41no—
229Q8×C139—41no—
230Q8×C139—41no—
231D4×C139—21no—
232D4×C139—21no—
233D4×C139—21no—
234D4×C139—21no—
235D4×C139—41no—
236D4×C139—41no—
237D4×C139—41no—
238D4×C139—41no—
239D4×C139—41no—
240D4×C139—41no—
241D4×C139—41no—
242D4×C139—41no—
243D4×C139—81no—
244D4×C139—81no—
245D4×C139—82no—
246D4×C139—82no—
247D4×C139—161no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—21no—
253C2×C4×C139—21no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—82no—
261C2×C4×C139—82no—
262C2×C4×C139—161no—
263C2×C4×C139C22×D411yescharacteristic
264C2×C4×C139C22×D411yescharacteristic
265C2×C4×C139H(5,𝔽2)11yescharacteristic
266C8×C139—21no—
267C8×C139—21no—
268C8×C139—41no—
269C8×C139—41no—
270C8×C139—41no—
271C8×C139—41no—
272C8×C139—41no—
273C8×C139#13512yescomplemented
274C8×C139AGL(1,ℤ/8)12yes—
275C22×C139—41no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139—81no—
284C22×C139—81no—
285C22×C139—81no—
286C22×C139—81no—
287C22×C139D4211yescharacteristic
288C4×C139—21no—
289C4×C139—41no—
290C4×C139—41no—
291C4×C139—41no—
292C4×C139—41no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—81no—
296C4×C139—81no—
297C4×C139C2×#13511yescharacteristic
298C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C139#57611yescharacteristic
300C4×C139#57711yescharacteristic
301C2×C139—81no—
302C2×C139—81no—
303C2×C139—161no—
304C2×C139—161no—
305C2×C139#327411yescharacteristic
306C2×C139#328411yescharacteristic
307C2×C139#329011yescharacteristic
308#19947C13911yesmaximal, characteristic, direct product factor, Sylow
309C139#1994711yescharacteristic, direct product factor, Sylow
310#3399C2×C13911yescharacteristic, complemented
311#3394C2×C13911yescharacteristic, complemented
312#3353C2×C13911yescharacteristic, complemented
313#3284C2×C13911yescharacteristic, complemented
314#1706C2×C13911yescharacteristic, complemented
315#1694C2×C13911yescharacteristic, complemented
316#1687C2×C13911yescharacteristic, complemented
317#1666C2×C13911yescharacteristic, complemented
318#1665C2×C13911yescharacteristic, complemented
319#1641C2×C13911yescharacteristic, complemented
320#1640C2×C13911yescharacteristic, complemented
321#1628C2×C13911yescharacteristic, complemented
322#1625C2×C13911yescharacteristic, complemented
323#1590C2×C13911yescharacteristic, complemented
324C8×SD16C2×C13911yescharacteristic, complemented
325C2×#135—21no—
326#559C22×C13911yescharacteristic
327#556C22×C13911yescharacteristic
328#550C22×C13911yescharacteristic
329#547C22×C13911yescharacteristic
330#500C22×C13911yescharacteristic
331#496—21no—
332#495—21no—
333#493C22×C13911yescharacteristic
334#492C22×C13911yescharacteristic
335#492C22×C13911yescharacteristic
336#486C22×C13911yescharacteristic
337#486C22×C13911yescharacteristic
338#484—21no—
339#482—21no—
340#475C22×C13911yescharacteristic
341#474C22×C13911yescharacteristic
342#468—21no—
343#465—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462C22×C13911yescharacteristic
348#462C22×C13911yescharacteristic
349#460C22×C13911yescharacteristic
350#459—21no—
351#459C22×C13911yescharacteristic
352#459C22×C13911yescharacteristic
353#459C22×C13911yescharacteristic
354#452—21no—
355#449—21no—
356#446C22×C13911yescharacteristic
357C8×Q8C22×C13911yescharacteristic
358#442—21no—
359C4×SD16—21no—
360C4×SD16C22×C13911yescharacteristic
361C4×SD16C22×C13911yescharacteristic
362#436C22×C13911yescharacteristic
363C8×D4C22×C13911yescharacteristic
364#428—21no—
365#334C22×C13911yescharacteristic
366#334C22×C13911yescharacteristic
367#332C22×C13911yescharacteristic
368#332C22×C13911yescharacteristic
369#331C22×C13911yescharacteristic
370#331C22×C13911yescharacteristic
371Q8⋊C8C22×C13911yescharacteristic
372Q8⋊C8C22×C13911yescharacteristic
373D4⋊C8C22×C13911yescharacteristic
374D4⋊C8C22×C13911yescharacteristic
375C82C22×C13911yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16D4×C13911yescharacteristic
387C2×SD16D4×C13911yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×M16—21no—
394C22×C8—21no—
395C4⋊Q8C23×C13911yescharacteristic
396C4⋊Q8C23×C13911yescharacteristic
397#127—21no—
398#127C23×C13911yescharacteristic
399#127C23×C13911yescharacteristic
400#126—41no—
401#124—21no—
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8—21no—
412C4×Q8C23×C13911yescharacteristic
413C4×Q8C23×C13911yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C13911yescharacteristic
418C4×D4C23×C13911yescharacteristic
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106D4×C13911yescharacteristic
426#106D4×C13911yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C13911yescharacteristic
430C4⋊C8C23×C13911yescharacteristic
431C4⋊C8C23×C13911yescharacteristic
432C4⋊C8C23×C13911yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C13911yescharacteristic
437#103D4×C13911yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102—41no—
445#102D4×C13911yescharacteristic
446#102D4×C13911yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C13911yescharacteristic
452C4×C8C23×C13911yescharacteristic
453C4×C8C23×C13911yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C13911yescharacteristic
461C2×Q8C2×D4×C13911yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C13911yescharacteristic
472C2×D4C2×D4×C13911yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C13911yescharacteristic
500C2×C8C2×D4×C13911yescharacteristic
501C2×C8C2×D4×C13911yescharacteristic
502C2×C8C2×D4×C13911yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C13911yescharacteristic
512C4⋊C4C2×D4×C13911yescharacteristic
513C4⋊C4C2×D4×C13911yescharacteristic
514C4⋊C4C2×D4×C13911yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C13911yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C13911yescharacteristic
573C2×C4C22×D4×C13911yescharacteristic
574C2×C4H(5,𝔽2)×C13911yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8#135×C13912yescomplemented
583C8AGL(1,ℤ/8)×C13912yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C13911yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C13911yescharacteristic
607C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
608C4#576×C13911yescharacteristic
609C4#577×C13911yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2#3274×C13911yescharacteristic
615C2#3284×C13911yescharacteristic
616C2#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. #3353×C139C2semidirect
4. #3284×C139C2semidirect
5. #1706×C139C2semidirect
6. #1694×C139C2semidirect
7. #1687×C139C2semidirect
8. #1666×C139C2semidirect
9. #1665×C139C2semidirect
10. #1641×C139C2semidirect
11. #1640×C139C2semidirect
12. #1628×C139C2semidirect
13. #1625×C139C2semidirect
14. #1590×C139C2semidirect
15. C8×SD16×C139C2semidirect
273. C8×C139#135semidirect
308. #19947C139direct (N × H)
309. C139#19947direct (N × H)
310. #3399C2×C139semidirect
311. #3394C2×C139semidirect
312. #3353C2×C139semidirect
313. #3284C2×C139semidirect
314. #1706C2×C139semidirect
315. #1694C2×C139semidirect
316. #1687C2×C139semidirect
317. #1666C2×C139semidirect
318. #1665C2×C139semidirect
319. #1641C2×C139semidirect
320. #1640C2×C139semidirect
321. #1628C2×C139semidirect
322. #1625C2×C139semidirect
323. #1590C2×C139semidirect
324. C8×SD16C2×C139semidirect
582. C8#135×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
#3353×C1392
#3284×C1392
#1706×C1392
#1694×C1392
#1687×C1392
#1666×C1392
#1665×C1392
#1641×C1392
#1640×C1392
#1628×C1392
#1625×C1392
#1590×C1392
C8×SD16×C1392
#19947139