Finite Group Databasebeta

← C139×#20056 #48014652

Subgroups — C139×#20056 #48014652

Order 35584.

668 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#3334×C139C211yesmaximal, characteristic, complemented
2#3330×C139C211yesmaximal, characteristic, complemented
3#3330×C139C211yesmaximal, characteristic, complemented
4#3283×C139C211yesmaximal, characteristic, complemented
5#1723×C139C211yesmaximal, characteristic, complemented
6#1693×C139C211yesmaximal, characteristic, complemented
7#1689×C139C211yesmaximal, characteristic, complemented
8#1679×C139C211yesmaximal, characteristic, complemented
9#1679×C139C211yesmaximal, characteristic, complemented
10#1654×C139C211yesmaximal, characteristic, complemented
11#1654×C139C211yesmaximal, characteristic, complemented
12#1647×C139C211yesmaximal, characteristic, complemented
13#1647×C139C211yesmaximal, characteristic, complemented
14#1586×C139C211yesmaximal, characteristic, complemented
15#1586×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#547×C139C2211yescharacteristic
18#547×C139C2211yescharacteristic
19#547×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#500×C139C2211yescharacteristic
23#498×C139C2211yescharacteristic
24#494×C139C2211yescharacteristic
25#487×C139C2211yescharacteristic
26#487×C139C2211yescharacteristic
27#484×C139—21no—
28#484×C139—21no—
29#480×C139—21no—
30#480×C139—21no—
31#474×C139C2211yescharacteristic
32#474×C139C2211yescharacteristic
33#474×C139C2211yescharacteristic
34#474×C139C2211yescharacteristic
35#468×C139—21no—
36#468×C139—21no—
37#467×C139—21no—
38#466×C139—21no—
39#461×C139C2211yescharacteristic
40#461×C139C2211yescharacteristic
41#461×C139C2211yescharacteristic
42#461×C139C2211yescharacteristic
43#452×C139—21no—
44#452×C139—21no—
45#449×C139—21no—
46#449×C139—21no—
47C4×D8×C139C2211yescharacteristic
48C4×D8×C139C2211yescharacteristic
49#436×C139C2211yescharacteristic
50#436×C139C2211yescharacteristic
51C8×D4×C139C2211yescharacteristic
52C8×D4×C139C2211yescharacteristic
53C2×#107×C139—21no—
54#417×C139—21no—
55#417×C139—21no—
56#334×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62D4⋊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×Q16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139—21no—
78C2×D8×C139D411yescharacteristic
79C2×D8×C139D411yescharacteristic
80C2×M16×C139—21no—
81C2×M16×C139—21no—
82C22×C8×C139—21no—
83C22×C8×C139—21no—
84C4⋊Q8×C139C2311yescharacteristic
85C4⋊Q8×C139C2311yescharacteristic
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88#123×C139—41no—
89#123×C139—41no—
90#123×C139—41no—
91#123×C139—41no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—21no—
94C22⋊Q8×C139—21no—
95C22⋊Q8×C139—21no—
96#121×C139—21no—
97#121×C139—21no—
98#121×C139—21no—
99#121×C139—21no—
100C4×D4×C139C2311yescharacteristic
101C4×D4×C139C2311yescharacteristic
102C4×D4×C139C2311yescharacteristic
103C4×D4×C139C2311yescharacteristic
104C2×C4⋊C4×C139—21no—
105C2×C4⋊C4×C139—21no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—21no—
108#107×C139—21no—
109#107×C139—21no—
110#107×C139—21no—
111#107×C139—21no—
112#107×C139—21no—
113#107×C139—21no—
114#107×C139—41no—
115#107×C139D411yescharacteristic
116#107×C139D411yescharacteristic
117#106×C139—41no—
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122#103×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#103×C139—21no—
126#103×C139—21no—
127#103×C139—21no—
128#103×C139—21no—
129#103×C139—21no—
130#102×C139—21no—
131#102×C139—21no—
132#102×C139—21no—
133#102×C139—21no—
134#102×C139D411yescharacteristic
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C22⋊C8×C139—21no—
141C22⋊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×C139—21no—
156C2×Q8×C139—21no—
157C2×D4×C139—41no—
158C2×D4×C139—41no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139C2×D411yescharacteristic
162C2×D4×C139C2×D411yescharacteristic
163C2×D4×C139C2×D411yescharacteristic
164C2×D4×C139C2×D411yescharacteristic
165C22×C4×C139—21no—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—41no—
170C22×C4×C139—41no—
171C22×C4×C139—41no—
172C22×C4×C139—41no—
173Q16×C139—42no—
174Q16×C139—81no—
175SD16×C139—42no—
176SD16×C139—42no—
177SD16×C139—81no—
178SD16×C139—81no—
179D8×C139—22no—
180D8×C139—41no—
181M16×C139—81no—
182M16×C139—81no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—42no—
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—21no—
201C4⋊C4×C139—21no—
202C4⋊C4×C139—41no—
203C4⋊C4×C139—41no—
204C4⋊C4×C139—41no—
205C4⋊C4×C139—41no—
206C4⋊C4×C139C2×D411yescharacteristic
207C4⋊C4×C139C2×D411yescharacteristic
208C4⋊C4×C139C2×D411yescharacteristic
209C4⋊C4×C139C2×D411yescharacteristic
210C22⋊C4×C139—21no—
211C22⋊C4×C139—21no—
212C22⋊C4×C139—21no—
213C22⋊C4×C139—21no—
214C22⋊C4×C139—41no—
215C22⋊C4×C139—41no—
216C22⋊C4×C139—41no—
217C22⋊C4×C139—41no—
218C42×C139C2411yescharacteristic
219C23×C139—21no—
220C23×C139—21no—
221C23×C139—21no—
222C23×C139—21no—
223Q8×C139—41no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—41no—
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—21no—
236D4×C139—21no—
237D4×C139—21no—
238D4×C139—82no—
239D4×C139—82no—
240D4×C139—82no—
241D4×C139—82no—
242D4×C139AGL(1,ℤ/8)12yes—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—82no—
260C2×C4×C139—82no—
261C2×C4×C139—82no—
262C2×C4×C139—82no—
263C2×C4×C139C22×D411yescharacteristic
264C2×C4×C139C22×D411yescharacteristic
265C2×C4×C139H(5,𝔽2)11yescharacteristic
266C8×C139—22no—
267C8×C139—21no—
268C8×C139—21no—
269C8×C139—21no—
270C8×C139—21no—
271C8×C139—41no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C22×C139—22no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—41no—
282C22×C139—41no—
283C22×C139—41no—
284C22×C139—41no—
285C22×C139—41no—
286C22×C139—41no—
287C22×C139D4211yescharacteristic
288C4×C139—21no—
289C4×C139—41no—
290C4×C139—41no—
291C4×C139—41no—
292C4×C139—41no—
293C4×C139—81no—
294C4×C139—81no—
295C4×C139—81no—
296C4×C139—81no—
297C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C139#57511yescharacteristic
299C4×C139#57611yescharacteristic
300C4×C139#57711yescharacteristic
301C2×C139—42no—
302C2×C139—81no—
303C2×C139—81no—
304C2×C139—81no—
305C2×C139#326411yescharacteristic
306C2×C139#326711yescharacteristic
307C2×C139#329311yescharacteristic
308#20056C13911yesmaximal, characteristic, direct product factor, Sylow
309C139#2005611yescharacteristic, direct product factor, Sylow
310#3334C2×C13911yescharacteristic, complemented
311#3330C2×C13911yescharacteristic, complemented
312#3330C2×C13911yescharacteristic, complemented
313#3283C2×C13911yescharacteristic, complemented
314#1723C2×C13911yescharacteristic, complemented
315#1693C2×C13911yescharacteristic, complemented
316#1689C2×C13911yescharacteristic, complemented
317#1679C2×C13911yescharacteristic, complemented
318#1679C2×C13911yescharacteristic, complemented
319#1654C2×C13911yescharacteristic, complemented
320#1654C2×C13911yescharacteristic, complemented
321#1647C2×C13911yescharacteristic, complemented
322#1647C2×C13911yescharacteristic, complemented
323#1586C2×C13911yescharacteristic, complemented
324#1586C2×C13911yescharacteristic, complemented
325C2×#135—21no—
326#547C22×C13911yescharacteristic
327#547C22×C13911yescharacteristic
328#547C22×C13911yescharacteristic
329#547C22×C13911yescharacteristic
330#500C22×C13911yescharacteristic
331#500C22×C13911yescharacteristic
332#498C22×C13911yescharacteristic
333#494C22×C13911yescharacteristic
334#487C22×C13911yescharacteristic
335#487C22×C13911yescharacteristic
336#484—21no—
337#484—21no—
338#480—21no—
339#480—21no—
340#474C22×C13911yescharacteristic
341#474C22×C13911yescharacteristic
342#474C22×C13911yescharacteristic
343#474C22×C13911yescharacteristic
344#468—21no—
345#468—21no—
346#467—21no—
347#466—21no—
348#461C22×C13911yescharacteristic
349#461C22×C13911yescharacteristic
350#461C22×C13911yescharacteristic
351#461C22×C13911yescharacteristic
352#452—21no—
353#452—21no—
354#449—21no—
355#449—21no—
356C4×D8C22×C13911yescharacteristic
357C4×D8C22×C13911yescharacteristic
358#436C22×C13911yescharacteristic
359#436C22×C13911yescharacteristic
360C8×D4C22×C13911yescharacteristic
361C8×D4C22×C13911yescharacteristic
362C2×#107—21no—
363#417—21no—
364#417—21no—
365#334C22×C13911yescharacteristic
366#334C22×C13911yescharacteristic
367#332C22×C13911yescharacteristic
368#332C22×C13911yescharacteristic
369#332C22×C13911yescharacteristic
370#332C22×C13911yescharacteristic
371D4⋊C8C22×C13911yescharacteristic
372D4⋊C8C22×C13911yescharacteristic
373D4⋊C8C22×C13911yescharacteristic
374D4⋊C8C22×C13911yescharacteristic
375#322C22×C13911yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380#135—44no—
381C2×Q16—21no—
382C2×Q16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8D4×C13911yescharacteristic
388C2×D8D4×C13911yescharacteristic
389C2×M16—21no—
390C2×M16—21no—
391C22×C8—21no—
392C22×C8—21no—
393C4⋊Q8C23×C13911yescharacteristic
394C4⋊Q8C23×C13911yescharacteristic
395C4⋊Q8C23×C13911yescharacteristic
396C4⋊Q8C23×C13911yescharacteristic
397#123—41no—
398#123—41no—
399#123—41no—
400#123—41no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409C4×D4C23×C13911yescharacteristic
410C4×D4C23×C13911yescharacteristic
411C4×D4C23×C13911yescharacteristic
412C4×D4C23×C13911yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417#107—21no—
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—41no—
424#107D4×C13911yescharacteristic
425#107D4×C13911yescharacteristic
426#106—41no—
427C4⋊C8C23×C13911yescharacteristic
428C4⋊C8C23×C13911yescharacteristic
429C4⋊C8C23×C13911yescharacteristic
430C4⋊C8C23×C13911yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#103—21no—
438#103—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102D4×C13911yescharacteristic
444#102D4×C13911yescharacteristic
445#102D4×C13911yescharacteristic
446#102D4×C13911yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8C23×C13911yescharacteristic
452C4×C8C23×C13911yescharacteristic
453C4×C8C23×C13911yescharacteristic
454#41—42no—
455#41—42no—
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4C2×D4×C13911yescharacteristic
471C2×D4C2×D4×C13911yescharacteristic
472C2×D4C2×D4×C13911yescharacteristic
473C2×D4C2×D4×C13911yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482Q16—42no—
483Q16—81no—
484SD16—42no—
485SD16—42no—
486SD16—81no—
487SD16—81no—
488D8—22no—
489D8—41no—
490M16—81no—
491M16—81no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—42no—
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—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C13911yescharacteristic
516C4⋊C4C2×D4×C13911yescharacteristic
517C4⋊C4C2×D4×C13911yescharacteristic
518C4⋊C4C2×D4×C13911yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42C24×C13911yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—82no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4AGL(1,ℤ/8)×C13912yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4C22×D4×C13911yescharacteristic
573C2×C4C22×D4×C13911yescharacteristic
574C2×C4H(5,𝔽2)×C13911yescharacteristic
575C8—22no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22D42×C13911yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
607C4#575×C13911yescharacteristic
608C4#576×C13911yescharacteristic
609C4#577×C13911yescharacteristic
610C2—42no—
611C2—81no—
612C2—81no—
613C2—81no—
614C2#3264×C13911yescharacteristic
615C2#3267×C13911yescharacteristic
616C2#3293×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. #3334×C139C2semidirect
2. #3330×C139C2semidirect
3. #3330×C139C2semidirect
4. #3283×C139C2semidirect
5. #1723×C139C2semidirect
6. #1693×C139C2semidirect
7. #1689×C139C2semidirect
8. #1679×C139C2semidirect
9. #1679×C139C2semidirect
10. #1654×C139C2semidirect
11. #1654×C139C2semidirect
12. #1647×C139C2semidirect
13. #1647×C139C2semidirect
14. #1586×C139C2semidirect
15. #1586×C139C2semidirect
308. #20056C139direct (N × H)
309. C139#20056direct (N × H)
310. #3334C2×C139semidirect
311. #3330C2×C139semidirect
312. #3330C2×C139semidirect
313. #3283C2×C139semidirect
314. #1723C2×C139semidirect
315. #1693C2×C139semidirect
316. #1689C2×C139semidirect
317. #1679C2×C139semidirect
318. #1679C2×C139semidirect
319. #1654C2×C139semidirect
320. #1654C2×C139semidirect
321. #1647C2×C139semidirect
322. #1647C2×C139semidirect
323. #1586C2×C139semidirect
324. #1586C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3334×C1392
#3330×C1392
#3283×C1392
#1723×C1392
#1693×C1392
#1689×C1392
#1679×C1392
#1654×C1392
#1647×C1392
#1586×C1392
#20056139