Finite Group Databasebeta

← C139×#20288 #48014884

Subgroups — C139×#20288 #48014884

Order 35584.

670 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#3398×C139C211yesmaximal, characteristic, complemented
2#3368×C139C211yesmaximal, characteristic, complemented
3#3324×C139C211yesmaximal, characteristic, complemented
4#3274×C139C211yesmaximal, characteristic
5#1709×C139C211yesmaximal, characteristic, complemented
6#1702×C139C211yesmaximal, characteristic, complemented
7#1701×C139C211yesmaximal, characteristic, complemented
8#1689×C139C211yesmaximal, characteristic, complemented
9#1688×C139C211yesmaximal, characteristic, complemented
10#1641×C139C211yesmaximal, characteristic, complemented
11#1639×C139C211yesmaximal, characteristic, complemented
12#1628×C139C211yesmaximal, characteristic, complemented
13#1626×C139C211yesmaximal, characteristic, complemented
14#1590×C139C211yesmaximal, characteristic, complemented
15#1590×C139C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C139—21no—
17#557×C139C2211yescharacteristic, complemented
18#556×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20D42×C139C2211yescharacteristic
21#497×C139—21no—
22#494×C139C2211yescharacteristic, complemented
23#493×C139C2211yescharacteristic
24#490×C139—21no—
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic, complemented
28#486×C139C2211yescharacteristic, complemented
29#482×C139—21no—
30#478×C139—21no—
31#474×C139C2211yescharacteristic
32#474×C139C2211yescharacteristic
33#469×C139—21no—
34#468×C139—21no—
35#464×C139—21no—
36#462×C139—21no—
37#462×C139C2211yescharacteristic, complemented
38#461×C139C2211yescharacteristic
39#460×C139—21no—
40#460×C139C2211yescharacteristic
41#460×C139C2211yescharacteristic
42#460×C139C2211yescharacteristic, complemented
43#459×C139C2211yescharacteristic
44#450×C139—21no—
45#449×C139—21no—
46#447×C139—21no—
47#446×C139C2211yescharacteristic, complemented
48#446×C139C2211yescharacteristic, complemented
49#441×C139—21no—
50#440×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54#436×C139C2211yescharacteristic
55#418×C139—21no—
56#334×C139C2211yescharacteristic, complemented
57#334×C139C2211yescharacteristic, complemented
58#332×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic, complemented
62Q8⋊C8×C139C2211yescharacteristic, complemented
63Q8⋊C8×C139C2211yescharacteristic, complemented
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66C82×C139C2211yescharacteristic, complemented
67C2×#41×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70AGL(1,ℤ/8)×C139—44no—
71C2×Q16×C139—21no—
72C2×Q16×C139—21no—
73C2×Q16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139D411yescharacteristic
79C2×SD16×C139D411yescharacteristic
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139—21no—
83C2×M16×C139—21no—
84C2×M16×C139—21no—
85C4⋊Q8×C139—21no—
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88#127×C139—21no—
89#127×C139C2311yescharacteristic
90#127×C139C2311yescharacteristic
91#126×C139—41no—
92#125×C139—21no—
93#125×C139—41no—
94#124×C139—21no—
95C22⋊Q8×C139—21no—
96#121×C139—21no—
97#121×C139—21no—
98#121×C139—21no—
99#121×C139—41no—
100#120×C139—41no—
101C4×Q8×C139—21no—
102C4×Q8×C139—21no—
103C4×Q8×C139—21no—
104C4×Q8×C139C2311yescharacteristic
105C4×Q8×C139C2311yescharacteristic
106C4×D4×C139—21no—
107C4×D4×C139C2311yescharacteristic
108C4×D4×C139C2311yescharacteristic
109#117×C139—21no—
110#107×C139—21no—
111#107×C139—21no—
112#106×C139D411yescharacteristic
113#106×C139D411yescharacteristic
114C4⋊C8×C139—21no—
115C4⋊C8×C139—21no—
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120#103×C139—21no—
121#103×C139—21no—
122#103×C139D411yescharacteristic
123#103×C139D411yescharacteristic
124#102×C139—21no—
125#102×C139—21no—
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—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—
141#97×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145C24×C139—41no—
146#41×C139—42no—
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×C139—41no—
162C2×D4×C139—42no—
163C2×D4×C139—42no—
164C2×D4×C139—81no—
165C2×D4×C139—81no—
166C2×D4×C139C2×D411yescharacteristic
167C2×D4×C139C2×D411yescharacteristic
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—41no—
171Q16×C139—42no—
172Q16×C139—81no—
173Q16×C139—81no—
174SD16×C139—22no—
175SD16×C139—41no—
176SD16×C139—42no—
177SD16×C139—42no—
178SD16×C139—81no—
179SD16×C139—81no—
180D8×C139—42no—
181D8×C139—42no—
182D8×C139—81no—
183M16×C139—42no—
184M16×C139—81no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—21no—
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×C139—41no—
203C4⋊C4×C139—41no—
204C4⋊C4×C139C2×D411yescharacteristic
205C4⋊C4×C139C2×D411yescharacteristic
206C4⋊C4×C139C2×D411yescharacteristic
207C4⋊C4×C139C2×D411yescharacteristic
208C22⋊C4×C139—21no—
209C22⋊C4×C139—21no—
210C22⋊C4×C139—41no—
211C22⋊C4×C139—41no—
212C22⋊C4×C139—41no—
213C22⋊C4×C139—41no—
214C42×C139—21no—
215C42×C139—21no—
216C42×C139—41no—
217C42×C139—41no—
218C42×C139C2411yescharacteristic
219C23×C139—21no—
220C23×C139—21no—
221C23×C139—41no—
222C23×C139—41no—
223C23×C139—82no—
224C23×C139—82no—
225C23×C139—161no—
226Q8×C139—21no—
227Q8×C139—21no—
228Q8×C139—21no—
229Q8×C139—21no—
230Q8×C139—41no—
231Q8×C139—41no—
232Q8×C139—41no—
233Q8×C139—41no—
234D4×C139—21no—
235D4×C139—21no—
236D4×C139—21no—
237D4×C139—21no—
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—82no—
249D4×C139—82no—
250D4×C139—82no—
251D4×C139—161no—
252C2×C4×C139—21no—
253C2×C4×C139—21no—
254C2×C4×C139—21no—
255C2×C4×C139—21no—
256C2×C4×C139—21no—
257C2×C4×C139—21no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—41no—
263C2×C4×C139—41no—
264C2×C4×C139—82no—
265C2×C4×C139C22×D411yescharacteristic
266C2×C4×C139C22×D411yescharacteristic
267C2×C4×C139H(5,𝔽2)11yescharacteristic
268C8×C139—21no—
269C8×C139—21no—
270C8×C139—21no—
271C8×C139—41no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C8×C139—41no—
276C8×C139AGL(1,ℤ/8)12yes—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—41no—
282C22×C139—41no—
283C22×C139—81no—
284C22×C139—81no—
285C22×C139—81no—
286C22×C139—81no—
287C22×C139—81no—
288C22×C139—81no—
289C22×C139—164no—
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—81no—
299C4×C139—81no—
300C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C139#57511yescharacteristic
302C4×C139#57611yescharacteristic
303C4×C139#57711yescharacteristic
304C2×C139—81no—
305C2×C139—81no—
306C2×C139—161no—
307C2×C139—161no—
308C2×C139#327411yescharacteristic
309C2×C139#327511yescharacteristic
310C2×C139#329011yescharacteristic
311#20288C13911yesmaximal, characteristic, direct product factor, Sylow
312C139#2028811yescharacteristic, direct product factor, Sylow
313#3398C2×C13911yescharacteristic, complemented
314#3368C2×C13911yescharacteristic, complemented
315#3324C2×C13911yescharacteristic, complemented
316#3274C2×C13911yescharacteristic
317#1709C2×C13911yescharacteristic, complemented
318#1702C2×C13911yescharacteristic, complemented
319#1701C2×C13911yescharacteristic, complemented
320#1689C2×C13911yescharacteristic, complemented
321#1688C2×C13911yescharacteristic, complemented
322#1641C2×C13911yescharacteristic, complemented
323#1639C2×C13911yescharacteristic, complemented
324#1628C2×C13911yescharacteristic, complemented
325#1626C2×C13911yescharacteristic, complemented
326#1590C2×C13911yescharacteristic, complemented
327#1590C2×C13911yescharacteristic, complemented
328C2×AGL(1,ℤ/8)—21no—
329#557C22×C13911yescharacteristic, complemented
330#556C22×C13911yescharacteristic
331#550C22×C13911yescharacteristic
332D42C22×C13911yescharacteristic
333#497—21no—
334#494C22×C13911yescharacteristic, complemented
335#493C22×C13911yescharacteristic
336#490—21no—
337#486C22×C13911yescharacteristic
338#486C22×C13911yescharacteristic
339#486C22×C13911yescharacteristic, complemented
340#486C22×C13911yescharacteristic, complemented
341#482—21no—
342#478—21no—
343#474C22×C13911yescharacteristic
344#474C22×C13911yescharacteristic
345#469—21no—
346#468—21no—
347#464—21no—
348#462—21no—
349#462C22×C13911yescharacteristic, complemented
350#461C22×C13911yescharacteristic
351#460—21no—
352#460C22×C13911yescharacteristic
353#460C22×C13911yescharacteristic
354#460C22×C13911yescharacteristic, complemented
355#459C22×C13911yescharacteristic
356#450—21no—
357#449—21no—
358#447—21no—
359#446C22×C13911yescharacteristic, complemented
360#446C22×C13911yescharacteristic, complemented
361#441—21no—
362#440—21no—
363C4×SD16C22×C13911yescharacteristic
364C4×SD16C22×C13911yescharacteristic
365#436C22×C13911yescharacteristic
366#436C22×C13911yescharacteristic
367#418—21no—
368#334C22×C13911yescharacteristic, complemented
369#334C22×C13911yescharacteristic, complemented
370#332C22×C13911yescharacteristic, complemented
371#332C22×C13911yescharacteristic, complemented
372#331C22×C13911yescharacteristic
373#331C22×C13911yescharacteristic, complemented
374Q8⋊C8C22×C13911yescharacteristic, complemented
375Q8⋊C8C22×C13911yescharacteristic, complemented
376D4⋊C8C22×C13911yescharacteristic
377D4⋊C8C22×C13911yescharacteristic
378C82C22×C13911yescharacteristic, complemented
379C2×#41—21no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—44no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×Q16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16D4×C13911yescharacteristic
391C2×SD16D4×C13911yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×M16—21no—
396C2×M16—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C13911yescharacteristic
399C4⋊Q8C23×C13911yescharacteristic
400#127—21no—
401#127C23×C13911yescharacteristic
402#127C23×C13911yescharacteristic
403#126—41no—
404#125—21no—
405#125—41no—
406#124—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
412#120—41no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C23×C13911yescharacteristic
417C4×Q8C23×C13911yescharacteristic
418C4×D4—21no—
419C4×D4C23×C13911yescharacteristic
420C4×D4C23×C13911yescharacteristic
421#117—21no—
422#107—21no—
423#107—21no—
424#106D4×C13911yescharacteristic
425#106D4×C13911yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8C23×C13911yescharacteristic
429C4⋊C8C23×C13911yescharacteristic
430C4⋊C8C23×C13911yescharacteristic
431C4⋊C8C23×C13911yescharacteristic
432#103—21no—
433#103—21no—
434#103D4×C13911yescharacteristic
435#103D4×C13911yescharacteristic
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—41no—
447#102—41no—
448#102D4×C13911yescharacteristic
449#102D4×C13911yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453#97—21no—
454C4×C8C23×C13911yescharacteristic
455C4×C8C23×C13911yescharacteristic
456C4×C8C23×C13911yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C13911yescharacteristic
463C2×Q8C2×D4×C13911yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C13911yescharacteristic
479C2×D4C2×D4×C13911yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483Q16—42no—
484Q16—81no—
485Q16—81no—
486SD16—22no—
487SD16—41no—
488SD16—42no—
489SD16—42no—
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—81no—
495M16—42no—
496M16—81no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8C2×D4×C13911yescharacteristic
503C2×C8C2×D4×C13911yescharacteristic
504C2×C8C2×D4×C13911yescharacteristic
505C2×C8C2×D4×C13911yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4C2×D4×C13911yescharacteristic
517C4⋊C4C2×D4×C13911yescharacteristic
518C4⋊C4C2×D4×C13911yescharacteristic
519C4⋊C4C2×D4×C13911yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—21no—
527C42—21no—
528C42—41no—
529C42—41no—
530C42C24×C13911yescharacteristic
531C23—21no—
532C23—21no—
533C23—41no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—81no—
559D4—81no—
560D4—82no—
561D4—82no—
562D4—82no—
563D4—161no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4C22×D4×C13911yescharacteristic
578C2×C4C22×D4×C13911yescharacteristic
579C2×C4H(5,𝔽2)×C13911yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8AGL(1,ℤ/8)×C13912yes—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D42×C13911yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
613C4#575×C13911yescharacteristic
614C4#576×C13911yescharacteristic
615C4#577×C13911yescharacteristic
616C2—81no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2#3274×C13911yescharacteristic
621C2#3275×C13911yescharacteristic
622C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3274×C139C2
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. #3398×C139C2semidirect
2. #3368×C139C2semidirect
3. #3324×C139C2semidirect
5. #1709×C139C2semidirect
6. #1702×C139C2semidirect
7. #1701×C139C2semidirect
8. #1689×C139C2semidirect
9. #1688×C139C2semidirect
10. #1641×C139C2semidirect
11. #1639×C139C2semidirect
12. #1628×C139C2semidirect
13. #1626×C139C2semidirect
14. #1590×C139C2semidirect
15. #1590×C139C2semidirect
17. #557×C139C22semidirect
22. #494×C139C22semidirect
27. #486×C139C22semidirect
28. #486×C139C22semidirect
37. #462×C139C22semidirect
42. #460×C139C22semidirect
47. #446×C139C22semidirect
48. #446×C139C22semidirect
56. #334×C139C22semidirect
57. #334×C139C22semidirect
58. #332×C139C22semidirect
59. #332×C139C22semidirect
61. #331×C139C22semidirect
62. Q8⋊C8×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
66. C82×C139C22semidirect
311. #20288C139direct (N × H)
312. C139#20288direct (N × H)
313. #3398C2×C139semidirect
314. #3368C2×C139semidirect
315. #3324C2×C139semidirect
317. #1709C2×C139semidirect
318. #1702C2×C139semidirect
319. #1701C2×C139semidirect
320. #1689C2×C139semidirect
321. #1688C2×C139semidirect
322. #1641C2×C139semidirect
323. #1639C2×C139semidirect
324. #1628C2×C139semidirect
325. #1626C2×C139semidirect
326. #1590C2×C139semidirect
327. #1590C2×C139semidirect
329. #557C22×C139semidirect
334. #494C22×C139semidirect
339. #486C22×C139semidirect
340. #486C22×C139semidirect
349. #462C22×C139semidirect
354. #460C22×C139semidirect
359. #446C22×C139semidirect
360. #446C22×C139semidirect
368. #334C22×C139semidirect
369. #334C22×C139semidirect
370. #332C22×C139semidirect
371. #332C22×C139semidirect
373. #331C22×C139semidirect
374. Q8⋊C8C22×C139semidirect
375. Q8⋊C8C22×C139semidirect
378. C82C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3398×C1392
#3368×C1392
#3324×C1392
#3274×C1392
#1709×C1392
#1702×C1392
#1701×C1392
#1689×C1392
#1688×C1392
#1641×C1392
#1639×C1392
#1628×C1392
#1626×C1392
#1590×C1392
#20288139