Finite Group Databasebeta

← C139×#20070 #48014666

Subgroups — C139×#20070 #48014666

Order 35584.

666 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C139C211yesmaximal, characteristic, complemented
2#3373×C139C211yesmaximal, characteristic, complemented
3#3298×C139C211yesmaximal, characteristic, complemented
4#3284×C139C211yesmaximal, characteristic, complemented
5#1717×C139C211yesmaximal, characteristic, complemented
6#1700×C139C211yesmaximal, characteristic, complemented
7#1686×C139C211yesmaximal, characteristic, complemented
8#1681×C139C211yesmaximal, characteristic, complemented
9#1667×C139C211yesmaximal, characteristic, complemented
10#1642×C139C211yesmaximal, characteristic, complemented
11#1640×C139C211yesmaximal, characteristic, complemented
12#1627×C139C211yesmaximal, characteristic, complemented
13#1625×C139C211yesmaximal, characteristic, complemented
14#1585×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#559×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#496×C139—21no—
22#493×C139C2211yescharacteristic
23#492×C139C2211yescharacteristic
24#489×C139—21no—
25#487×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#483×C139—21no—
30#476×C139—21no—
31#475×C139C2211yescharacteristic
32#475×C139C2211yescharacteristic
33#465×C139—21no—
34#465×C139—21no—
35#463×C139—21no—
36#463×C139—21no—
37#462×C139C2211yescharacteristic
38#461×C139C2211yescharacteristic
39#460×C139C2211yescharacteristic
40#459×C139—21no—
41#459×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#452×C139—21no—
45#449×C139—21no—
46#448×C139—21no—
47#446×C139C2211yescharacteristic
48#446×C139C2211yescharacteristic
49#442×C139—21no—
50#442×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55C2×#103×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C22×Q8×C139—21no—
70#135×C139—44no—
71C2×Q16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139D411yescharacteristic
77C2×SD16×C139D411yescharacteristic
78C2×D8×C139—21no—
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139—21no—
83C22×C8×C139—21no—
84C22×C8×C139—21no—
85C4⋊Q8×C139—21no—
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88#127×C139—21no—
89#127×C139C2311yescharacteristic
90#127×C139C2311yescharacteristic
91#124×C139—21no—
92#124×C139—21no—
93#123×C139—41no—
94#123×C139—41no—
95C22⋊Q8×C139—21no—
96C22⋊Q8×C139—21no—
97C22⋊Q8×C139—41no—
98#121×C139—21no—
99#121×C139—21no—
100#121×C139—41no—
101C4×Q8×C139C2311yescharacteristic
102C4×Q8×C139C2311yescharacteristic
103C4×D4×C139—21no—
104C4×D4×C139—21no—
105C4×D4×C139—21no—
106C4×D4×C139—21no—
107C4×D4×C139C2311yescharacteristic
108C4×D4×C139C2311yescharacteristic
109C2×C4⋊C4×C139—21no—
110#106×C139—21no—
111#106×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×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#103×C139—21no—
126#103×C139D411yescharacteristic
127#103×C139D411yescharacteristic
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
145#41×C139—42no—
146#41×C139—42no—
147#41×C139—81no—
148#41×C139—81no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—41no—
152C2×Q8×C139—42no—
153C2×Q8×C139—81no—
154C2×Q8×C139C2×D411yescharacteristic
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×C139C2×D411yescharacteristic
166C2×D4×C139C2×D411yescharacteristic
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—
174SD16×C139—22no—
175SD16×C139—41no—
176SD16×C139—42no—
177SD16×C139—81no—
178SD16×C139—81no—
179SD16×C139—81no—
180D8×C139—42no—
181D8×C139—42no—
182D8×C139—42no—
183D8×C139—81no—
184D8×C139—81no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—21no—
190C2×C8×C139—42no—
191C2×C8×C139—81no—
192C2×C8×C139C2×D411yescharacteristic
193C2×C8×C139C2×D411yescharacteristic
194C2×C8×C139C2×D411yescharacteristic
195C2×C8×C139C2×D411yescharacteristic
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×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—
214C22⋊C4×C139—41no—
215C22⋊C4×C139—41no—
216C42×C139—21no—
217C42×C139—21no—
218C42×C139C2411yescharacteristic
219C23×C139—21no—
220C23×C139—21no—
221C23×C139—41no—
222C23×C139—41no—
223Q8×C139—21no—
224Q8×C139—21no—
225Q8×C139—21no—
226Q8×C139—21no—
227Q8×C139—41no—
228Q8×C139—41no—
229Q8×C139—41no—
230Q8×C139—41no—
231Q8×C139—82no—
232D4×C139—21no—
233D4×C139—21no—
234D4×C139—21no—
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—82no—
246D4×C139—82no—
247D4×C139—161no—
248D4×C139AGL(1,ℤ/8)12yes—
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—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—82no—
262C2×C4×C139—82no—
263C2×C4×C139—82no—
264C2×C4×C139—161no—
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—21no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C8×C139—41no—
276C8×C139—41no—
277C22×C139—22no—
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×C139D4211yescharacteristic
290C4×C139—21no—
291C4×C139—41no—
292C4×C139—41no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—41no—
296C4×C139—41no—
297C4×C139—81no—
298C4×C139—81no—
299C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C139#57511yescharacteristic
301C4×C139#57611yescharacteristic
302C4×C139#57711yescharacteristic
303C2×C139—42no—
304C2×C139—81no—
305C2×C139—161no—
306C2×C139—161no—
307C2×C139#326511yescharacteristic
308C2×C139#326811yescharacteristic
309C2×C139#329011yescharacteristic
310#20070C13911yesmaximal, characteristic, direct product factor, Sylow
311C139#2007011yescharacteristic, direct product factor, Sylow
312#3399C2×C13911yescharacteristic, complemented
313#3373C2×C13911yescharacteristic, complemented
314#3298C2×C13911yescharacteristic, complemented
315#3284C2×C13911yescharacteristic, complemented
316#1717C2×C13911yescharacteristic, complemented
317#1700C2×C13911yescharacteristic, complemented
318#1686C2×C13911yescharacteristic, complemented
319#1681C2×C13911yescharacteristic, complemented
320#1667C2×C13911yescharacteristic, complemented
321#1642C2×C13911yescharacteristic, complemented
322#1640C2×C13911yescharacteristic, complemented
323#1627C2×C13911yescharacteristic, complemented
324#1625C2×C13911yescharacteristic, complemented
325#1585C2×C13911yescharacteristic, complemented
326#1585C2×C13911yescharacteristic, complemented
327C2×#135—21no—
328#559C22×C13911yescharacteristic
329#550C22×C13911yescharacteristic
330D4×Q8C22×C13911yescharacteristic
331#547C22×C13911yescharacteristic
332#496—21no—
333#493C22×C13911yescharacteristic
334#492C22×C13911yescharacteristic
335#489—21no—
336#487C22×C13911yescharacteristic
337#486C22×C13911yescharacteristic
338#486C22×C13911yescharacteristic
339#486C22×C13911yescharacteristic
340#483—21no—
341#476—21no—
342#475C22×C13911yescharacteristic
343#475C22×C13911yescharacteristic
344#465—21no—
345#465—21no—
346#463—21no—
347#463—21no—
348#462C22×C13911yescharacteristic
349#461C22×C13911yescharacteristic
350#460C22×C13911yescharacteristic
351#459—21no—
352#459C22×C13911yescharacteristic
353#459C22×C13911yescharacteristic
354#459C22×C13911yescharacteristic
355#452—21no—
356#449—21no—
357#448—21no—
358#446C22×C13911yescharacteristic
359#446C22×C13911yescharacteristic
360#442—21no—
361#442—21no—
362C4×SD16C22×C13911yescharacteristic
363C4×SD16C22×C13911yescharacteristic
364C8×D4C22×C13911yescharacteristic
365C8×D4C22×C13911yescharacteristic
366C2×#103—21no—
367#335C22×C13911yescharacteristic
368#335C22×C13911yescharacteristic
369#332C22×C13911yescharacteristic
370#332C22×C13911yescharacteristic
371#331C22×C13911yescharacteristic
372#331C22×C13911yescharacteristic
373Q8⋊C8C22×C13911yescharacteristic
374Q8⋊C8C22×C13911yescharacteristic
375D4⋊C8C22×C13911yescharacteristic
376D4⋊C8C22×C13911yescharacteristic
377#322C22×C13911yescharacteristic
378C2×#41—21no—
379C2×#41—21no—
380C22×Q8—21no—
381#135—44no—
382C2×Q16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16D4×C13911yescharacteristic
388C2×SD16D4×C13911yescharacteristic
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C22×C8—21no—
395C22×C8—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C13911yescharacteristic
398C4⋊Q8C23×C13911yescharacteristic
399#127—21no—
400#127C23×C13911yescharacteristic
401#127C23×C13911yescharacteristic
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—41no—
409#121—21no—
410#121—21no—
411#121—41no—
412C4×Q8C23×C13911yescharacteristic
413C4×Q8C23×C13911yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4C23×C13911yescharacteristic
419C4×D4C23×C13911yescharacteristic
420C2×C4⋊C4—21no—
421#106—21no—
422#106—21no—
423#106D4×C13911yescharacteristic
424#106D4×C13911yescharacteristic
425C4⋊C8—21no—
426C4⋊C8—21no—
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#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—41no—
446#102—41no—
447#102D4×C13911yescharacteristic
448#102D4×C13911yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453C4×C8C23×C13911yescharacteristic
454C4×C8C23×C13911yescharacteristic
455C4×C8C23×C13911yescharacteristic
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8C2×D4×C13911yescharacteristic
466C2×Q8C2×D4×C13911yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C13911yescharacteristic
477C2×D4C2×D4×C13911yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484Q16—42no—
485SD16—22no—
486SD16—41no—
487SD16—42no—
488SD16—81no—
489SD16—81no—
490SD16—81no—
491D8—42no—
492D8—42no—
493D8—42no—
494D8—81no—
495D8—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—42no—
502C2×C8—81no—
503C2×C8C2×D4×C13911yescharacteristic
504C2×C8C2×D4×C13911yescharacteristic
505C2×C8C2×D4×C13911yescharacteristic
506C2×C8C2×D4×C13911yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
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—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42C24×C13911yescharacteristic
530C23—21no—
531C23—21no—
532C23—41no—
533C23—41no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—81no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4AGL(1,ℤ/8)×C13912yes—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—161no—
576C2×C4C22×D4×C13911yescharacteristic
577C2×C4C22×D4×C13911yescharacteristic
578C2×C4H(5,𝔽2)×C13911yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22D42×C13911yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
611C4#575×C13911yescharacteristic
612C4#576×C13911yescharacteristic
613C4#577×C13911yescharacteristic
614C2—42no—
615C2—81no—
616C2—161no—
617C2—161no—
618C2#3265×C13911yescharacteristic
619C2#3268×C13911yescharacteristic
620C2#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. #3399×C139C2semidirect
2. #3373×C139C2semidirect
3. #3298×C139C2semidirect
4. #3284×C139C2semidirect
5. #1717×C139C2semidirect
6. #1700×C139C2semidirect
7. #1686×C139C2semidirect
8. #1681×C139C2semidirect
9. #1667×C139C2semidirect
10. #1642×C139C2semidirect
11. #1640×C139C2semidirect
12. #1627×C139C2semidirect
13. #1625×C139C2semidirect
14. #1585×C139C2semidirect
15. #1585×C139C2semidirect
310. #20070C139direct (N × H)
311. C139#20070direct (N × H)
312. #3399C2×C139semidirect
313. #3373C2×C139semidirect
314. #3298C2×C139semidirect
315. #3284C2×C139semidirect
316. #1717C2×C139semidirect
317. #1700C2×C139semidirect
318. #1686C2×C139semidirect
319. #1681C2×C139semidirect
320. #1667C2×C139semidirect
321. #1642C2×C139semidirect
322. #1640C2×C139semidirect
323. #1627C2×C139semidirect
324. #1625C2×C139semidirect
325. #1585C2×C139semidirect
326. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3399×C1392
#3373×C1392
#3298×C1392
#3284×C1392
#1717×C1392
#1700×C1392
#1686×C1392
#1681×C1392
#1667×C1392
#1642×C1392
#1640×C1392
#1627×C1392
#1625×C1392
#1585×C1392
#20070139