Finite Group Databasebeta

← C139×#20063 #48014659

Subgroups — C139×#20063 #48014659

Order 35584.

688 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3391×C139C211yesmaximal, characteristic, complemented
2#3332×C139C211yesmaximal, characteristic, complemented
3#3330×C139C211yesmaximal, characteristic, complemented
4#3284×C139C211yesmaximal, characteristic, complemented
5#1717×C139C211yesmaximal, characteristic, complemented
6#1687×C139C211yesmaximal, characteristic, complemented
7#1685×C139C211yesmaximal, characteristic, complemented
8#1681×C139C211yesmaximal, characteristic, complemented
9#1680×C139C211yesmaximal, characteristic, complemented
10#1642×C139C211yesmaximal, characteristic, complemented
11#1641×C139C211yesmaximal, characteristic, complemented
12#1625×C139C211yesmaximal, characteristic, complemented
13#1625×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1586×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#550×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19#547×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#493×C139—21no—
22#493×C139C2211yescharacteristic
23#492×C139C2211yescharacteristic
24#487×C139C2211yescharacteristic
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#484×C139—21no—
29#481×C139—21no—
30#475×C139C2211yescharacteristic
31#474×C139C2211yescharacteristic
32#469×C139—21no—
33#468×C139—21no—
34#465×C139—21no—
35#462×C139C2211yescharacteristic
36#461×C139C2211yescharacteristic
37#459×C139—21no—
38#459×C139—21no—
39#459×C139C2211yescharacteristic
40#459×C139C2211yescharacteristic
41#459×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#452×C139—21no—
44#449×C139—21no—
45#449×C139—21no—
46#449×C139—21no—
47C8×Q8×C139C2211yescharacteristic
48C4×SD16×C139C2211yescharacteristic
49C4×D8×C139—21no—
50C4×D8×C139C2211yescharacteristic
51#436×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#417×C139—21no—
55#417×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C2×#41×C139—21no—
70C2×#41×C139—21no—
71#135×C139—44no—
72C2×Q16×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×C139D411yescharacteristic
84C2×M16×C139—21no—
85C2×M16×C139—21no—
86C22×C8×C139—21no—
87C4⋊Q8×C139C2311yescharacteristic
88C4⋊Q8×C139C2311yescharacteristic
89#127×C139—21no—
90#127×C139—21no—
91#127×C139C2311yescharacteristic
92#127×C139C2311yescharacteristic
93#123×C139—41no—
94#123×C139—41no—
95C22⋊Q8×C139—21no—
96C22⋊Q8×C139—21no—
97#121×C139—21no—
98#121×C139—21no—
99#121×C139—21no—
100#121×C139—21no—
101#121×C139—41no—
102#121×C139—41no—
103C4×Q8×C139C2311yescharacteristic
104C4×D4×C139—21no—
105C4×D4×C139—21no—
106C4×D4×C139C2311yescharacteristic
107C4×D4×C139C2311yescharacteristic
108C4×D4×C139C2311yescharacteristic
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111#107×C139—21no—
112#107×C139D411yescharacteristic
113#106×C139—21no—
114#106×C139D411yescharacteristic
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×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
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
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C22⋊C8×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—42no—
148#41×C139—42no—
149#41×C139—81no—
150#41×C139—81no—
151#41×C139—81no—
152#41×C139—81no—
153C2×Q8×C139—21no—
154C2×Q8×C139—21no—
155C2×Q8×C139C2×D411yescharacteristic
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×C139—41no—
167C2×D4×C139—41no—
168C2×D4×C139C2×D411yescharacteristic
169C2×D4×C139C2×D411yescharacteristic
170C2×D4×C139C2×D411yescharacteristic
171C22×C4×C139—21no—
172C22×C4×C139—21no—
173C22×C4×C139—21no—
174C22×C4×C139—41no—
175C22×C4×C139—41no—
176C22×C4×C139—41no—
177C22×C4×C139—41no—
178Q16×C139—42no—
179SD16×C139—22no—
180SD16×C139—42no—
181SD16×C139—81no—
182SD16×C139—81no—
183D8×C139—41no—
184D8×C139—42no—
185D8×C139—42no—
186D8×C139—81no—
187D8×C139—81no—
188D8×C139—81no—
189D8×C139—81no—
190M16×C139—81no—
191M16×C139—81no—
192C2×C8×C139—21no—
193C2×C8×C139—21no—
194C2×C8×C139—21no—
195C2×C8×C139—21no—
196C2×C8×C139—21no—
197C2×C8×C139—42no—
198C2×C8×C139C2×D411yescharacteristic
199C2×C8×C139C2×D411yescharacteristic
200C2×C8×C139C2×D411yescharacteristic
201C2×C8×C139C2×D411yescharacteristic
202C4⋊C4×C139—21no—
203C4⋊C4×C139—21no—
204C4⋊C4×C139—21no—
205C4⋊C4×C139—21no—
206C4⋊C4×C139—21no—
207C4⋊C4×C139—41no—
208C4⋊C4×C139—41no—
209C4⋊C4×C139C2×D411yescharacteristic
210C4⋊C4×C139C2×D411yescharacteristic
211C4⋊C4×C139C2×D411yescharacteristic
212C4⋊C4×C139C2×D411yescharacteristic
213C22⋊C4×C139—21no—
214C22⋊C4×C139—21no—
215C22⋊C4×C139—21no—
216C22⋊C4×C139—41no—
217C22⋊C4×C139—41no—
218C22⋊C4×C139—41no—
219C22⋊C4×C139—41no—
220C42×C139—21no—
221C42×C139C2411yescharacteristic
222C23×C139—21no—
223C23×C139—21no—
224C23×C139—21no—
225C23×C139—41no—
226C23×C139—41no—
227Q8×C139—21no—
228Q8×C139—41no—
229Q8×C139—41no—
230Q8×C139—41no—
231Q8×C139—41no—
232Q8×C139AGL(1,ℤ/8)12yes—
233D4×C139—21no—
234D4×C139—21no—
235D4×C139—21no—
236D4×C139—21no—
237D4×C139—21no—
238D4×C139—21no—
239D4×C139—41no—
240D4×C139—41no—
241D4×C139—41no—
242D4×C139—41no—
243D4×C139—41no—
244D4×C139—41no—
245D4×C139—41no—
246D4×C139—41no—
247D4×C139—82no—
248D4×C139—82no—
249D4×C139—81no—
250D4×C139—81no—
251D4×C139—82no—
252D4×C139—82no—
253D4×C139—161no—
254D4×C139—161no—
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—41no—
264C2×C4×C139—41no—
265C2×C4×C139—41no—
266C2×C4×C139—41no—
267C2×C4×C139—41no—
268C2×C4×C139—82no—
269C2×C4×C139—82no—
270C2×C4×C139—82no—
271C2×C4×C139—82no—
272C2×C4×C139C22×D411yescharacteristic
273C2×C4×C139C22×D411yescharacteristic
274C2×C4×C139H(5,𝔽2)11yescharacteristic
275C8×C139—21no—
276C8×C139—21no—
277C8×C139—21no—
278C8×C139—21no—
279C8×C139—41no—
280C8×C139—41no—
281C8×C139—41no—
282C8×C139—41no—
283C8×C139—41no—
284C22×C139—41no—
285C22×C139—41no—
286C22×C139—41no—
287C22×C139—41no—
288C22×C139—41no—
289C22×C139—41no—
290C22×C139—41no—
291C22×C139—41no—
292C22×C139—41no—
293C22×C139—81no—
294C22×C139—81no—
295C22×C139—81no—
296C22×C139—81no—
297C22×C139—81no—
298C22×C139—81no—
299C22×C139D4211yescharacteristic
300C4×C139—22no—
301C4×C139—21no—
302C4×C139—41no—
303C4×C139—41no—
304C4×C139—41no—
305C4×C139—41no—
306C4×C139—81no—
307C4×C139—81no—
308C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C139#57511yescharacteristic
310C4×C139#57611yescharacteristic
311C4×C139#57611yescharacteristic
312C2×C139—81no—
313C2×C139—81no—
314C2×C139—81no—
315C2×C139—161no—
316C2×C139—161no—
317C2×C139#326411yescharacteristic
318C2×C139#326811yescharacteristic
319C2×C139#329011yescharacteristic
320#20063C13911yesmaximal, characteristic, direct product factor, Sylow
321C139#2006311yescharacteristic, direct product factor, Sylow
322#3391C2×C13911yescharacteristic, complemented
323#3332C2×C13911yescharacteristic, complemented
324#3330C2×C13911yescharacteristic, complemented
325#3284C2×C13911yescharacteristic, complemented
326#1717C2×C13911yescharacteristic, complemented
327#1687C2×C13911yescharacteristic, complemented
328#1685C2×C13911yescharacteristic, complemented
329#1681C2×C13911yescharacteristic, complemented
330#1680C2×C13911yescharacteristic, complemented
331#1642C2×C13911yescharacteristic, complemented
332#1641C2×C13911yescharacteristic, complemented
333#1625C2×C13911yescharacteristic, complemented
334#1625C2×C13911yescharacteristic, complemented
335#1588C2×C13911yescharacteristic, complemented
336#1586C2×C13911yescharacteristic, complemented
337C2×#135—21no—
338#550C22×C13911yescharacteristic
339#550C22×C13911yescharacteristic
340#547C22×C13911yescharacteristic
341#547C22×C13911yescharacteristic
342#493—21no—
343#493C22×C13911yescharacteristic
344#492C22×C13911yescharacteristic
345#487C22×C13911yescharacteristic
346#486C22×C13911yescharacteristic
347#486C22×C13911yescharacteristic
348#486C22×C13911yescharacteristic
349#484—21no—
350#481—21no—
351#475C22×C13911yescharacteristic
352#474C22×C13911yescharacteristic
353#469—21no—
354#468—21no—
355#465—21no—
356#462C22×C13911yescharacteristic
357#461C22×C13911yescharacteristic
358#459—21no—
359#459—21no—
360#459C22×C13911yescharacteristic
361#459C22×C13911yescharacteristic
362#459C22×C13911yescharacteristic
363#459C22×C13911yescharacteristic
364#452—21no—
365#449—21no—
366#449—21no—
367#449—21no—
368C8×Q8C22×C13911yescharacteristic
369C4×SD16C22×C13911yescharacteristic
370C4×D8—21no—
371C4×D8C22×C13911yescharacteristic
372#436C22×C13911yescharacteristic
373#436C22×C13911yescharacteristic
374C8×D4C22×C13911yescharacteristic
375#417—21no—
376#417—21no—
377#335C22×C13911yescharacteristic
378#334C22×C13911yescharacteristic
379#332C22×C13911yescharacteristic
380#332C22×C13911yescharacteristic
381#331C22×C13911yescharacteristic
382#331C22×C13911yescharacteristic
383Q8⋊C8C22×C13911yescharacteristic
384D4⋊C8C22×C13911yescharacteristic
385D4⋊C8C22×C13911yescharacteristic
386D4⋊C8C22×C13911yescharacteristic
387#322C22×C13911yescharacteristic
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392#135—44no—
393C2×Q16—21no—
394C2×SD16—21no—
395C2×SD16—21no—
396C2×SD16—21no—
397C2×SD16D4×C13911yescharacteristic
398C2×D8—21no—
399C2×D8—21no—
400C2×D8—21no—
401C2×D8—21no—
402C2×D8—21no—
403C2×D8—21no—
404C2×D8D4×C13911yescharacteristic
405C2×M16—21no—
406C2×M16—21no—
407C22×C8—21no—
408C4⋊Q8C23×C13911yescharacteristic
409C4⋊Q8C23×C13911yescharacteristic
410#127—21no—
411#127—21no—
412#127C23×C13911yescharacteristic
413#127C23×C13911yescharacteristic
414#123—41no—
415#123—41no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—41no—
423#121—41no—
424C4×Q8C23×C13911yescharacteristic
425C4×D4—21no—
426C4×D4—21no—
427C4×D4C23×C13911yescharacteristic
428C4×D4C23×C13911yescharacteristic
429C4×D4C23×C13911yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432#107—21no—
433#107D4×C13911yescharacteristic
434#106—21no—
435#106D4×C13911yescharacteristic
436C4⋊C8—21no—
437C4⋊C8C23×C13911yescharacteristic
438C4⋊C8C23×C13911yescharacteristic
439C4⋊C8C23×C13911yescharacteristic
440C4⋊C8C23×C13911yescharacteristic
441#103—21no—
442#103—21no—
443#103—21no—
444#103—21no—
445#103—21no—
446#103D4×C13911yescharacteristic
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—41no—
455#102—41no—
456#102D4×C13911yescharacteristic
457#102D4×C13911yescharacteristic
458#102D4×C13911yescharacteristic
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8—21no—
462C4×C8—21no—
463C4×C8C23×C13911yescharacteristic
464C4×C8C23×C13911yescharacteristic
465C4×C8C23×C13911yescharacteristic
466#41—42no—
467#41—42no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—81no—
473#41—81no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8C2×D4×C13911yescharacteristic
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4C2×D4×C13911yescharacteristic
490C2×D4C2×D4×C13911yescharacteristic
491C2×D4C2×D4×C13911yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499Q16—42no—
500SD16—22no—
501SD16—42no—
502SD16—81no—
503SD16—81no—
504D8—41no—
505D8—42no—
506D8—42no—
507D8—81no—
508D8—81no—
509D8—81no—
510D8—81no—
511M16—81no—
512M16—81no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—42no—
519C2×C8C2×D4×C13911yescharacteristic
520C2×C8C2×D4×C13911yescharacteristic
521C2×C8C2×D4×C13911yescharacteristic
522C2×C8C2×D4×C13911yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C13911yescharacteristic
531C4⋊C4C2×D4×C13911yescharacteristic
532C4⋊C4C2×D4×C13911yescharacteristic
533C4⋊C4C2×D4×C13911yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—21no—
542C42C24×C13911yescharacteristic
543C23—21no—
544C23—21no—
545C23—21no—
546C23—41no—
547C23—41no—
548Q8—21no—
549Q8—41no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8AGL(1,ℤ/8)×C13912yes—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—82no—
569D4—82no—
570D4—81no—
571D4—81no—
572D4—82no—
573D4—82no—
574D4—161no—
575D4—161no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—82no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4C22×D4×C13911yescharacteristic
594C2×C4C22×D4×C13911yescharacteristic
595C2×C4H(5,𝔽2)×C13911yescharacteristic
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—41no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22D42×C13911yescharacteristic
621C4—21no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
630C4#575×C13911yescharacteristic
631C4#576×C13911yescharacteristic
632C4#576×C13911yescharacteristic
633C2—81no—
634C2—81no—
635C2—81no—
636C2—161no—
637C2—161no—
638C2#3264×C13911yescharacteristic
639C2#3268×C13911yescharacteristic
640C2#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. #3391×C139C2semidirect
2. #3332×C139C2semidirect
3. #3330×C139C2semidirect
4. #3284×C139C2semidirect
5. #1717×C139C2semidirect
6. #1687×C139C2semidirect
7. #1685×C139C2semidirect
8. #1681×C139C2semidirect
9. #1680×C139C2semidirect
10. #1642×C139C2semidirect
11. #1641×C139C2semidirect
12. #1625×C139C2semidirect
13. #1625×C139C2semidirect
14. #1588×C139C2semidirect
15. #1586×C139C2semidirect
320. #20063C139direct (N × H)
321. C139#20063direct (N × H)
322. #3391C2×C139semidirect
323. #3332C2×C139semidirect
324. #3330C2×C139semidirect
325. #3284C2×C139semidirect
326. #1717C2×C139semidirect
327. #1687C2×C139semidirect
328. #1685C2×C139semidirect
329. #1681C2×C139semidirect
330. #1680C2×C139semidirect
331. #1642C2×C139semidirect
332. #1641C2×C139semidirect
333. #1625C2×C139semidirect
334. #1625C2×C139semidirect
335. #1588C2×C139semidirect
336. #1586C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3391×C1392
#3332×C1392
#3330×C1392
#3284×C1392
#1717×C1392
#1687×C1392
#1685×C1392
#1681×C1392
#1680×C1392
#1642×C1392
#1641×C1392
#1625×C1392
#1588×C1392
#1586×C1392
#20063139