Finite Group Databasebeta

← C139×#20272 #48014868

Subgroups — C139×#20272 #48014868

Order 35584.

662 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3400×C139C211yesmaximal, characteristic, complemented
2#3399×C139C211yesmaximal, characteristic, complemented
3#3368×C139C211yesmaximal, characteristic, complemented
4#3287×C139C211yesmaximal, characteristic, complemented
5#1721×C139C211yesmaximal, characteristic, complemented
6#1702×C139C211yesmaximal, characteristic, complemented
7#1688×C139C211yesmaximal, characteristic, complemented
8#1688×C139C211yesmaximal, characteristic, complemented
9#1665×C139C211yesmaximal, characteristic, complemented
10#1641×C139C211yesmaximal, characteristic, complemented
11#1626×C139C211yesmaximal, characteristic, complemented
12#1621×C139C211yesmaximal, characteristic, complemented
13#1620×C139C211yesmaximal, characteristic, complemented
14#1593×C139C211yesmaximal, characteristic, complemented
15#1582×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#559×C139C2211yescharacteristic
18#557×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#550×C139C2211yescharacteristic
21#497×C139—21no—
22#496×C139—21no—
23#493×C139C2211yescharacteristic
24#493×C139C2211yescharacteristic
25#493×C139C2211yescharacteristic
26#492×C139C2211yescharacteristic
27#490×C139—21no—
28#486×C139C2211yescharacteristic
29#486×C139C2211yescharacteristic
30#478×C139—21no—
31#474×C139C2211yescharacteristic
32#466×C139—21no—
33#464×C139—21no—
34#463×C139—21no—
35#462×C139C2211yescharacteristic
36#461×C139—21no—
37#460×C139—21no—
38#460×C139C2211yescharacteristic
39#460×C139C2211yescharacteristic
40#460×C139C2211yescharacteristic
41#460×C139C2211yescharacteristic
42#460×C139C2211yescharacteristic
43#459×C139—21no—
44#459×C139C2211yescharacteristic
45#449×C139—21no—
46#449×C139—21no—
47#446×C139C2211yescharacteristic
48#446×C139C2211yescharacteristic
49#446×C139C2211yescharacteristic
50#442×C139—21no—
51#440×C139—21no—
52#440×C139—21no—
53C4×Q16×C139C2211yescharacteristic
54C4×SD16×C139C2211yescharacteristic
55C8×D4×C139C2211yescharacteristic
56#334×C139C2211yescharacteristic
57#334×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×#41×C139—21no—
69#135×C139—44no—
70C2×Q16×C139—21no—
71C2×Q16×C139D411yescharacteristic
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139—21no—
79C2×SD16×C139D411yescharacteristic
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139—21no—
83C2×D8×C139—21no—
84C2×D8×C139—21no—
85C2×D8×C139—41no—
86C22×C8×C139—21no—
87C4⋊Q8×C139—21no—
88C4⋊Q8×C139C2311yescharacteristic
89#127×C139—21no—
90#127×C139—21no—
91#127×C139C2311yescharacteristic
92#127×C139C2311yescharacteristic
93#127×C139C2311yescharacteristic
94#125×C139—21no—
95#125×C139—41no—
96#124×C139—21no—
97#124×C139—21no—
98#123×C139—41no—
99#121×C139—21no—
100#121×C139—21no—
101#121×C139—41no—
102#121×C139—41no—
103C4×Q8×C139—21no—
104C4×Q8×C139—21no—
105C4×Q8×C139C2311yescharacteristic
106C4×Q8×C139C2311yescharacteristic
107C4×Q8×C139C2311yescharacteristic
108C4×D4×C139—21no—
109C4×D4×C139—21no—
110C4×D4×C139—21no—
111C4×D4×C139—21no—
112C4×D4×C139C2311yescharacteristic
113#107×C139—21no—
114#107×C139D411yescharacteristic
115#106×C139D411yescharacteristic
116C4⋊C8×C139—21no—
117C4⋊C8×C139—21no—
118C4⋊C8×C139—21no—
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122C4⋊C8×C139C2311yescharacteristic
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—21no—
136#102×C139—41no—
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139#97×C139—21no—
140#97×C139—21no—
141#97×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×C139C2×D411yescharacteristic
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—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—41no—
163C2×D4×C139—41no—
164C2×D4×C139—41no—
165C2×D4×C139—41no—
166C2×D4×C139C2×D411yescharacteristic
167C22×C4×C139—21no—
168C22×C4×C139—41no—
169C22×C4×C139—41no—
170C22×C4×C139—41no—
171Q16×C139—22no—
172Q16×C139—81no—
173SD16×C139—41no—
174SD16×C139—42no—
175SD16×C139—42no—
176SD16×C139—42no—
177SD16×C139—42no—
178SD16×C139—81no—
179SD16×C139—81no—
180SD16×C139—81no—
181D8×C139—42no—
182D8×C139—42no—
183D8×C139—81no—
184D8×C139—81no—
185D8×C139—81no—
186D8×C139—82no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—21no—
190C2×C8×C139—21no—
191C2×C8×C139—21no—
192C2×C8×C139—42no—
193C2×C8×C139C2×D411yescharacteristic
194C2×C8×C139C2×D411yescharacteristic
195C2×C8×C139C2×D411yescharacteristic
196C2×C8×C139C2×D411yescharacteristic
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—21no—
201C4⋊C4×C139—21no—
202C4⋊C4×C139—41no—
203C4⋊C4×C139—41no—
204C4⋊C4×C139—41no—
205C4⋊C4×C139C2×D411yescharacteristic
206C4⋊C4×C139C2×D411yescharacteristic
207C4⋊C4×C139C2×D411yescharacteristic
208C4⋊C4×C139C2×D411yescharacteristic
209C22⋊C4×C139—21no—
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—21no—
218C42×C139—41no—
219C42×C139C2411yescharacteristic
220C23×C139—21no—
221C23×C139—41no—
222C23×C139—41no—
223C23×C139—41no—
224Q8×C139—21no—
225Q8×C139—21no—
226Q8×C139—21no—
227Q8×C139—21no—
228Q8×C139—21no—
229Q8×C139—21no—
230Q8×C139—41no—
231Q8×C139—41no—
232D4×C139—21no—
233D4×C139—21no—
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—41no—
244D4×C139—41no—
245D4×C139—41no—
246D4×C139—81no—
247D4×C139—81no—
248D4×C139—81no—
249D4×C139—82no—
250D4×C139—82no—
251D4×C139—161no—
252D4×C139—161no—
253C2×C4×C139—21no—
254C2×C4×C139—21no—
255C2×C4×C139—21no—
256C2×C4×C139—21no—
257C2×C4×C139—21no—
258C2×C4×C139—21no—
259C2×C4×C139—21no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—41no—
263C2×C4×C139—82no—
264C2×C4×C139—82no—
265C2×C4×C139—161no—
266C2×C4×C139C22×D411yescharacteristic
267C2×C4×C139C22×D411yescharacteristic
268C2×C4×C139H(5,𝔽2)11yescharacteristic
269C8×C139—21no—
270C8×C139—21no—
271C8×C139—21no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C8×C139—41no—
276C8×C139—41no—
277C8×C139AGL(1,ℤ/8)12yes—
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×C139—81no—
288C22×C139—81no—
289C22×C139—81no—
290C22×C139D4211yescharacteristic
291C4×C139—21no—
292C4×C139—41no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—41no—
296C4×C139—41no—
297C4×C139—41no—
298C4×C139—41no—
299C4×C139—81no—
300C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C139#57511yescharacteristic
302C4×C139#57611yescharacteristic
303C4×C139#57711yescharacteristic
304C2×C139—81no—
305C2×C139—161no—
306C2×C139—161no—
307C2×C139—161no—
308C2×C139#327111yescharacteristic
309C2×C139#327411yescharacteristic
310C2×C139#328811yescharacteristic
311#20272C13911yesmaximal, characteristic, direct product factor, Sylow
312C139#2027211yescharacteristic, direct product factor, Sylow
313#3400C2×C13911yescharacteristic, complemented
314#3399C2×C13911yescharacteristic, complemented
315#3368C2×C13911yescharacteristic, complemented
316#3287C2×C13911yescharacteristic, complemented
317#1721C2×C13911yescharacteristic, complemented
318#1702C2×C13911yescharacteristic, complemented
319#1688C2×C13911yescharacteristic, complemented
320#1688C2×C13911yescharacteristic, complemented
321#1665C2×C13911yescharacteristic, complemented
322#1641C2×C13911yescharacteristic, complemented
323#1626C2×C13911yescharacteristic, complemented
324#1621C2×C13911yescharacteristic, complemented
325#1620C2×C13911yescharacteristic, complemented
326#1593C2×C13911yescharacteristic, complemented
327#1582C2×C13911yescharacteristic, complemented
328C2×#135—21no—
329#559C22×C13911yescharacteristic
330#557C22×C13911yescharacteristic
331#550C22×C13911yescharacteristic
332#550C22×C13911yescharacteristic
333#497—21no—
334#496—21no—
335#493C22×C13911yescharacteristic
336#493C22×C13911yescharacteristic
337#493C22×C13911yescharacteristic
338#492C22×C13911yescharacteristic
339#490—21no—
340#486C22×C13911yescharacteristic
341#486C22×C13911yescharacteristic
342#478—21no—
343#474C22×C13911yescharacteristic
344#466—21no—
345#464—21no—
346#463—21no—
347#462C22×C13911yescharacteristic
348#461—21no—
349#460—21no—
350#460C22×C13911yescharacteristic
351#460C22×C13911yescharacteristic
352#460C22×C13911yescharacteristic
353#460C22×C13911yescharacteristic
354#460C22×C13911yescharacteristic
355#459—21no—
356#459C22×C13911yescharacteristic
357#449—21no—
358#449—21no—
359#446C22×C13911yescharacteristic
360#446C22×C13911yescharacteristic
361#446C22×C13911yescharacteristic
362#442—21no—
363#440—21no—
364#440—21no—
365C4×Q16C22×C13911yescharacteristic
366C4×SD16C22×C13911yescharacteristic
367C8×D4C22×C13911yescharacteristic
368#334C22×C13911yescharacteristic
369#334C22×C13911yescharacteristic
370#332C22×C13911yescharacteristic
371#331C22×C13911yescharacteristic
372#331C22×C13911yescharacteristic
373#331C22×C13911yescharacteristic
374Q8⋊C8C22×C13911yescharacteristic
375Q8⋊C8C22×C13911yescharacteristic
376Q8⋊C8C22×C13911yescharacteristic
377D4⋊C8C22×C13911yescharacteristic
378#322C22×C13911yescharacteristic
379C2×#41—21no—
380C2×#41—21no—
381#135—44no—
382C2×Q16—21no—
383C2×Q16D4×C13911yescharacteristic
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16D4×C13911yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×D8—21no—
397C2×D8—41no—
398C22×C8—21no—
399C4⋊Q8—21no—
400C4⋊Q8C23×C13911yescharacteristic
401#127—21no—
402#127—21no—
403#127C23×C13911yescharacteristic
404#127C23×C13911yescharacteristic
405#127C23×C13911yescharacteristic
406#125—21no—
407#125—41no—
408#124—21no—
409#124—21no—
410#123—41no—
411#121—21no—
412#121—21no—
413#121—41no—
414#121—41no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8C23×C13911yescharacteristic
418C4×Q8C23×C13911yescharacteristic
419C4×Q8C23×C13911yescharacteristic
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C13911yescharacteristic
425#107—21no—
426#107D4×C13911yescharacteristic
427#106D4×C13911yescharacteristic
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8C23×C13911yescharacteristic
432C4⋊C8C23×C13911yescharacteristic
433C4⋊C8C23×C13911yescharacteristic
434C4⋊C8C23×C13911yescharacteristic
435#103—21no—
436#103D4×C13911yescharacteristic
437#103D4×C13911yescharacteristic
438#103D4×C13911yescharacteristic
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—41no—
449#102D4×C13911yescharacteristic
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453#97—21no—
454C4×C8C23×C13911yescharacteristic
455C4×C8C23×C13911yescharacteristic
456C4×C8C23×C13911yescharacteristic
457#41—42no—
458#41—42no—
459#41—81no—
460#41—81no—
461C2×Q8—21no—
462C2×Q8C2×D4×C13911yescharacteristic
463C2×Q8C2×D4×C13911yescharacteristic
464C2×Q8C2×D4×C13911yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4C2×D4×C13911yescharacteristic
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—22no—
484Q16—81no—
485SD16—41no—
486SD16—42no—
487SD16—42no—
488SD16—42no—
489SD16—42no—
490SD16—81no—
491SD16—81no—
492SD16—81no—
493D8—42no—
494D8—42no—
495D8—81no—
496D8—81no—
497D8—81no—
498D8—82no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8C2×D4×C13911yescharacteristic
506C2×C8C2×D4×C13911yescharacteristic
507C2×C8C2×D4×C13911yescharacteristic
508C2×C8C2×D4×C13911yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4C2×D4×C13911yescharacteristic
518C4⋊C4C2×D4×C13911yescharacteristic
519C4⋊C4C2×D4×C13911yescharacteristic
520C4⋊C4C2×D4×C13911yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—41no—
531C42C24×C13911yescharacteristic
532C23—21no—
533C23—41no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544D4—21no—
545D4—21no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—81no—
559D4—81no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—161no—
564D4—161no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—161no—
578C2×C4C22×D4×C13911yescharacteristic
579C2×C4C22×D4×C13911yescharacteristic
580C2×C4H(5,𝔽2)×C13911yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8AGL(1,ℤ/8)×C13912yes—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22D42×C13911yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
613C4#575×C13911yescharacteristic
614C4#576×C13911yescharacteristic
615C4#577×C13911yescharacteristic
616C2—81no—
617C2—161no—
618C2—161no—
619C2—161no—
620C2#3271×C13911yescharacteristic
621C2#3274×C13911yescharacteristic
622C2#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. #3400×C139C2semidirect
2. #3399×C139C2semidirect
3. #3368×C139C2semidirect
4. #3287×C139C2semidirect
5. #1721×C139C2semidirect
6. #1702×C139C2semidirect
7. #1688×C139C2semidirect
8. #1688×C139C2semidirect
9. #1665×C139C2semidirect
10. #1641×C139C2semidirect
11. #1626×C139C2semidirect
12. #1621×C139C2semidirect
13. #1620×C139C2semidirect
14. #1593×C139C2semidirect
15. #1582×C139C2semidirect
311. #20272C139direct (N × H)
312. C139#20272direct (N × H)
313. #3400C2×C139semidirect
314. #3399C2×C139semidirect
315. #3368C2×C139semidirect
316. #3287C2×C139semidirect
317. #1721C2×C139semidirect
318. #1702C2×C139semidirect
319. #1688C2×C139semidirect
320. #1688C2×C139semidirect
321. #1665C2×C139semidirect
322. #1641C2×C139semidirect
323. #1626C2×C139semidirect
324. #1621C2×C139semidirect
325. #1620C2×C139semidirect
326. #1593C2×C139semidirect
327. #1582C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3400×C1392
#3399×C1392
#3368×C1392
#3287×C1392
#1721×C1392
#1702×C1392
#1688×C1392
#1665×C1392
#1641×C1392
#1626×C1392
#1621×C1392
#1620×C1392
#1593×C1392
#1582×C1392
#20272139