Finite Group Databasebeta

← C139×#19871 #48014467

Subgroups — C139×#19871 #48014467

Order 35584.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C139C211yesmaximal, characteristic, complemented
2#3396×C139C211yesmaximal, characteristic, complemented
3#3394×C139C211yesmaximal, characteristic, complemented
4#3304×C139C211yesmaximal, characteristic, complemented
5#1721×C139C211yesmaximal, characteristic, complemented
6#1686×C139C211yesmaximal, characteristic, complemented
7#1682×C139C211yesmaximal, characteristic, complemented
8#1668×C139C211yesmaximal, characteristic, complemented
9#1667×C139C211yesmaximal, characteristic, complemented
10#1640×C139C211yesmaximal, characteristic, complemented
11#1628×C139C211yesmaximal, characteristic, complemented
12#1621×C139C211yesmaximal, characteristic, complemented
13#1620×C139C211yesmaximal, characteristic, complemented
14#1584×C139C211yesmaximal, characteristic, complemented
15SD16⋊C8×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic
17#559×C139C2211yescharacteristic
18#556×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#496×C139—21no—
21#495×C139—21no—
22#495×C139—21no—
23#493×C139C2211yescharacteristic
24#493×C139C2211yescharacteristic
25#493×C139C2211yescharacteristic
26#492×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#482×C139—21no—
30#475×C139C2211yescharacteristic
31#465×C139—21no—
32#464×C139—21no—
33#463×C139—21no—
34#463×C139—21no—
35#463×C139—21no—
36#463×C139—21no—
37#462×C139C2211yescharacteristic
38#460×C139C2211yescharacteristic
39#460×C139C2211yescharacteristic
40#460×C139C2211yescharacteristic
41#460×C139C2211yescharacteristic
42#459×C139—21no—
43#459×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#452×C139—21no—
46#446×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49#442×C139—21no—
50C4×Q16×C139C2211yescharacteristic
51C4×SD16×C139—21no—
52C4×SD16×C139C2211yescharacteristic
53C4×D8×C139—21no—
54C8×D4×C139C2211yescharacteristic
55#416×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#331×C139C2211yescharacteristic
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×Q16×C139—21no—
69C2×Q16×C139D411yescharacteristic
70C2×SD16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139D411yescharacteristic
77C2×D8×C139—21no—
78C2×D8×C139—21no—
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139—21no—
83C2×D8×C139—41no—
84C22×C8×C139—21no—
85C4⋊Q8×C139C2311yescharacteristic
86#127×C139—21no—
87#127×C139C2311yescharacteristic
88#127×C139C2311yescharacteristic
89#127×C139C2311yescharacteristic
90#126×C139—41no—
91#124×C139—21no—
92#124×C139—21no—
93#124×C139—21no—
94#124×C139—21no—
95#124×C139—21no—
96#123×C139—41no—
97#123×C139—41no—
98C22⋊Q8×C139—21no—
99#121×C139—21no—
100#121×C139—41no—
101C4×Q8×C139—21no—
102C4×Q8×C139C2311yescharacteristic
103C4×Q8×C139C2311yescharacteristic
104C4×Q8×C139C2311yescharacteristic
105C4×D4×C139—21no—
106C4×D4×C139—21no—
107C4×D4×C139—21no—
108C4×D4×C139—21no—
109C4×D4×C139—21no—
110C4×D4×C139C2311yescharacteristic
111#117×C139—21no—
112#107×C139D411yescharacteristic
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×C139D411yescharacteristic
125#103×C139D411yescharacteristic
126#103×C139D411yescharacteristic
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—21no—
134#102×C139—21no—
135#102×C139—41no—
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138#97×C139—21no—
139C4×C8×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144#41×C139—42no—
145#41×C139—81no—
146C2×Q8×C139—21no—
147C2×Q8×C139C2×D411yescharacteristic
148C2×Q8×C139C2×D411yescharacteristic
149C2×Q8×C139C2×D411yescharacteristic
150C2×D4×C139—21no—
151C2×D4×C139—21no—
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—21no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139C2×D411yescharacteristic
162C22×C4×C139—21no—
163C22×C4×C139—41no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166Q16×C139—41no—
167Q16×C139—81no—
168SD16×C139—22no—
169SD16×C139—42no—
170SD16×C139—81no—
171SD16×C139—81no—
172SD16×C139—81no—
173SD16×C139—81no—
174SD16×C139—81no—
175D8×C139—42no—
176D8×C139—42no—
177D8×C139—81no—
178D8×C139—81no—
179D8×C139—81no—
180D8×C139—81no—
181D8×C139—82no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—81no—
188C2×C8×C139C2×D411yescharacteristic
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
191C2×C8×C139C2×D411yescharacteristic
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×C139C2×D411yescharacteristic
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C22⋊C4×C139—21no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
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—21no—
215C42×C139—41no—
216C42×C139C2411yescharacteristic
217C23×C139—21no—
218C23×C139—41no—
219C23×C139—41no—
220C23×C139—41no—
221Q8×C139—21no—
222Q8×C139—21no—
223Q8×C139—21no—
224Q8×C139—21no—
225Q8×C139—21no—
226Q8×C139—21no—
227Q8×C139—41no—
228Q8×C139—41no—
229D4×C139—21no—
230D4×C139—21no—
231D4×C139—41no—
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—41no—
241D4×C139—41no—
242D4×C139—41no—
243D4×C139—81no—
244D4×C139—81no—
245D4×C139—81no—
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—21no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—82no—
259C2×C4×C139—161no—
260C2×C4×C139—161no—
261C2×C4×C139C22×D411yescharacteristic
262C2×C4×C139C22×D411yescharacteristic
263C2×C4×C139H(5,𝔽2)11yescharacteristic
264C8×C139—21no—
265C8×C139—21no—
266C8×C139—21no—
267C8×C139—41no—
268C8×C139—41no—
269C8×C139—41no—
270C8×C139—41no—
271C8×C139—41no—
272C8×C139#13512yes—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—81no—
277C22×C139—81no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139—81no—
284C22×C139—81no—
285C22×C139D4211yescharacteristic
286C4×C139—21no—
287C4×C139—41no—
288C4×C139—41no—
289C4×C139—41no—
290C4×C139—41no—
291C4×C139—41no—
292C4×C139—41no—
293C4×C139—41no—
294C4×C139—81no—
295C4×C139C2×#13511yescharacteristic
296C4×C139#57511yescharacteristic
297C4×C139#57611yescharacteristic
298C4×C139#57611yescharacteristic
299C2×C139—81no—
300C2×C139—161no—
301C2×C139—161no—
302C2×C139—161no—
303C2×C139#326811yescharacteristic
304C2×C139#328711yescharacteristic
305C2×C139#328811yescharacteristic
306#19871C13911yesmaximal, characteristic, direct product factor, Sylow
307C139#1987111yescharacteristic, direct product factor, Sylow
308#3399C2×C13911yescharacteristic, complemented
309#3396C2×C13911yescharacteristic, complemented
310#3394C2×C13911yescharacteristic, complemented
311#3304C2×C13911yescharacteristic, complemented
312#1721C2×C13911yescharacteristic, complemented
313#1686C2×C13911yescharacteristic, complemented
314#1682C2×C13911yescharacteristic, complemented
315#1668C2×C13911yescharacteristic, complemented
316#1667C2×C13911yescharacteristic, complemented
317#1640C2×C13911yescharacteristic, complemented
318#1628C2×C13911yescharacteristic, complemented
319#1621C2×C13911yescharacteristic, complemented
320#1620C2×C13911yescharacteristic, complemented
321#1584C2×C13911yescharacteristic, complemented
322SD16⋊C8C2×C13911yescharacteristic, complemented
323#559C22×C13911yescharacteristic
324#559C22×C13911yescharacteristic
325#556C22×C13911yescharacteristic
326#550C22×C13911yescharacteristic
327#496—21no—
328#495—21no—
329#495—21no—
330#493C22×C13911yescharacteristic
331#493C22×C13911yescharacteristic
332#493C22×C13911yescharacteristic
333#492C22×C13911yescharacteristic
334#486C22×C13911yescharacteristic
335#486C22×C13911yescharacteristic
336#482—21no—
337#475C22×C13911yescharacteristic
338#465—21no—
339#464—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#462C22×C13911yescharacteristic
345#460C22×C13911yescharacteristic
346#460C22×C13911yescharacteristic
347#460C22×C13911yescharacteristic
348#460C22×C13911yescharacteristic
349#459—21no—
350#459C22×C13911yescharacteristic
351#459C22×C13911yescharacteristic
352#452—21no—
353#446C22×C13911yescharacteristic
354C8×Q8C22×C13911yescharacteristic
355C8×Q8C22×C13911yescharacteristic
356#442—21no—
357C4×Q16C22×C13911yescharacteristic
358C4×SD16—21no—
359C4×SD16C22×C13911yescharacteristic
360C4×D8—21no—
361C8×D4C22×C13911yescharacteristic
362#416—21no—
363#335C22×C13911yescharacteristic
364#335C22×C13911yescharacteristic
365#332C22×C13911yescharacteristic
366#331C22×C13911yescharacteristic
367#331C22×C13911yescharacteristic
368#331C22×C13911yescharacteristic
369Q8⋊C8C22×C13911yescharacteristic
370Q8⋊C8C22×C13911yescharacteristic
371Q8⋊C8C22×C13911yescharacteristic
372D4⋊C8C22×C13911yescharacteristic
373#322C22×C13911yescharacteristic
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C13911yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C13911yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C13911yescharacteristic
393#127—21no—
394#127C23×C13911yescharacteristic
395#127C23×C13911yescharacteristic
396#127C23×C13911yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C13911yescharacteristic
410C4×Q8C23×C13911yescharacteristic
411C4×Q8C23×C13911yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C13911yescharacteristic
418#117—21no—
419#107D4×C13911yescharacteristic
420#106—21no—
421#106D4×C13911yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C13911yescharacteristic
426C4⋊C8C23×C13911yescharacteristic
427C4⋊C8C23×C13911yescharacteristic
428C4⋊C8C23×C13911yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C13911yescharacteristic
432#103D4×C13911yescharacteristic
433#103D4×C13911yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C13911yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C13911yescharacteristic
449C4×C8C23×C13911yescharacteristic
450C4×C8C23×C13911yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C13911yescharacteristic
455C2×Q8C2×D4×C13911yescharacteristic
456C2×Q8C2×D4×C13911yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C13911yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C13911yescharacteristic
496C2×C8C2×D4×C13911yescharacteristic
497C2×C8C2×D4×C13911yescharacteristic
498C2×C8C2×D4×C13911yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C13911yescharacteristic
506C4⋊C4C2×D4×C13911yescharacteristic
507C4⋊C4C2×D4×C13911yescharacteristic
508C4⋊C4C2×D4×C13911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C13911yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C13911yescharacteristic
569C2×C4C22×D4×C13911yescharacteristic
570C2×C4H(5,𝔽2)×C13911yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C13912yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C13911yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C13911yescharacteristic
603C4#575×C13911yescharacteristic
604C4#576×C13911yescharacteristic
605C4#576×C13911yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2#3268×C13911yescharacteristic
611C2#3287×C13911yescharacteristic
612C2#3288×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. #3396×C139C2semidirect
3. #3394×C139C2semidirect
4. #3304×C139C2semidirect
5. #1721×C139C2semidirect
6. #1686×C139C2semidirect
7. #1682×C139C2semidirect
8. #1668×C139C2semidirect
9. #1667×C139C2semidirect
10. #1640×C139C2semidirect
11. #1628×C139C2semidirect
12. #1621×C139C2semidirect
13. #1620×C139C2semidirect
14. #1584×C139C2semidirect
15. SD16⋊C8×C139C2semidirect
306. #19871C139direct (N × H)
307. C139#19871direct (N × H)
308. #3399C2×C139semidirect
309. #3396C2×C139semidirect
310. #3394C2×C139semidirect
311. #3304C2×C139semidirect
312. #1721C2×C139semidirect
313. #1686C2×C139semidirect
314. #1682C2×C139semidirect
315. #1668C2×C139semidirect
316. #1667C2×C139semidirect
317. #1640C2×C139semidirect
318. #1628C2×C139semidirect
319. #1621C2×C139semidirect
320. #1620C2×C139semidirect
321. #1584C2×C139semidirect
322. SD16⋊C8C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3399×C1392
#3396×C1392
#3394×C1392
#3304×C1392
#1721×C1392
#1686×C1392
#1682×C1392
#1668×C1392
#1667×C1392
#1640×C1392
#1628×C1392
#1621×C1392
#1620×C1392
#1584×C1392
SD16⋊C8×C1392
#19871139