Finite Group Databasebeta

← C139×#20071 #48014667

Subgroups — C139×#20071 #48014667

Order 35584.

638 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3372×C139C211yesmaximal, characteristic, complemented
2#3368×C139C211yesmaximal, characteristic, complemented
3#3335×C139C211yesmaximal, characteristic, complemented
4#3284×C139C211yesmaximal, characteristic
5#1714×C139C211yesmaximal, characteristic, complemented
6#1692×C139C211yesmaximal, characteristic, complemented
7#1686×C139C211yesmaximal, characteristic, complemented
8#1683×C139C211yesmaximal, characteristic, complemented
9#1681×C139C211yesmaximal, characteristic, complemented
10#1648×C139C211yesmaximal, characteristic, complemented
11#1647×C139C211yesmaximal, characteristic, complemented
12#1631×C139C211yesmaximal, characteristic, complemented
13#1622×C139C211yesmaximal, characteristic, complemented
14#1585×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#557×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#498×C139C2211yescharacteristic
23#492×C139C2211yescharacteristic
24#492×C139C2211yescharacteristic
25#491×C139—21no—
26#490×C139—21no—
27#487×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#483×C139—21no—
30#481×C139—21no—
31#479×C139—21no—
32#478×C139—21no—
33#477×C139C2211yescharacteristic
34#476×C139C2211yescharacteristic
35#475×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#465×C139—21no—
38#465×C139—21no—
39#462×C139C2211yescharacteristic
40#461×C139—21no—
41#461×C139C2211yescharacteristic
42#460×C139—21no—
43#460×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#452×C139—21no—
46#449×C139—21no—
47#446×C139C2211yescharacteristic
48#446×C139C2211yescharacteristic
49#440×C139—21no—
50#440×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55C2×#106×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×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—
69#135×C139—44no—
70C2×Q16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—41no—
76C2×SD16×C139D411yescharacteristic
77C2×SD16×C139D411yescharacteristic
78C2×D8×C139—21no—
79C22×C8×C139—21no—
80C22×C8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139C2311yescharacteristic
83C4⋊Q8×C139C2311yescharacteristic
84C4⋊Q8×C139C2311yescharacteristic
85#127×C139—21no—
86#127×C139C2311yescharacteristic
87#125×C139—21no—
88#125×C139—21no—
89#125×C139—41no—
90#123×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—41no—
94#121×C139—21no—
95#121×C139—21no—
96#121×C139—41no—
97C4×Q8×C139—21no—
98C4×Q8×C139—21no—
99C4×Q8×C139C2311yescharacteristic
100C4×Q8×C139C2311yescharacteristic
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139C2311yescharacteristic
104C4×D4×C139C2311yescharacteristic
105C2×C4⋊C4×C139—21no—
106C2×C4⋊C4×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—41no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139—21no—
114#106×C139D411yescharacteristic
115#106×C139D411yescharacteristic
116C4⋊C8×C139—21no—
117C4⋊C8×C139—21no—
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×C139D411yescharacteristic
129#103×C139D411yescharacteristic
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×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—21no—
152C2×Q8×C139C2×D411yescharacteristic
153C2×Q8×C139C2×D411yescharacteristic
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—41no—
158C2×D4×C139—41no—
159C2×D4×C139—41no—
160C2×D4×C139C2×D411yescharacteristic
161C2×D4×C139C2×D411yescharacteristic
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167Q16×C139—42no—
168SD16×C139—22no—
169SD16×C139—41no—
170SD16×C139—42no—
171SD16×C139—42no—
172SD16×C139—42no—
173SD16×C139—81no—
174SD16×C139—82no—
175D8×C139—42no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139—42no—
182C2×C8×C139—42no—
183C2×C8×C139C2×D411yescharacteristic
184C2×C8×C139C2×D411yescharacteristic
185C2×C8×C139C2×D411yescharacteristic
186C2×C8×C139C2×D411yescharacteristic
187C4⋊C4×C139—21no—
188C4⋊C4×C139—21no—
189C4⋊C4×C139—21no—
190C4⋊C4×C139—21no—
191C4⋊C4×C139—21no—
192C4⋊C4×C139—21no—
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139—41no—
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C4⋊C4×C139C2×D411yescharacteristic
204C4⋊C4×C139C2×D411yescharacteristic
205C22⋊C4×C139—21no—
206C22⋊C4×C139—21no—
207C22⋊C4×C139—41no—
208C22⋊C4×C139—41no—
209C22⋊C4×C139—41no—
210C42×C139—21no—
211C42×C139—21no—
212C42×C139—41no—
213C42×C139C2411yescharacteristic
214C23×C139—21no—
215C23×C139—21no—
216C23×C139—41no—
217Q8×C139—21no—
218Q8×C139—21no—
219Q8×C139—21no—
220Q8×C139—21no—
221Q8×C139—41no—
222Q8×C139—41no—
223Q8×C139—41no—
224Q8×C139—41no—
225Q8×C139—81no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—21no—
229D4×C139—41no—
230D4×C139—41no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—81no—
234D4×C139—82no—
235D4×C139—82no—
236D4×C139—161no—
237D4×C139AGL(1,ℤ/8)12yes—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—21no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—82no—
252C2×C4×C139—82no—
253C2×C4×C139—161no—
254C2×C4×C139C22×D411yescharacteristic
255C2×C4×C139C22×D411yescharacteristic
256C2×C4×C139H(5,𝔽2)11yescharacteristic
257C8×C139—22no—
258C8×C139—21no—
259C8×C139—21no—
260C8×C139—21no—
261C8×C139—21no—
262C8×C139—41no—
263C8×C139—41no—
264C8×C139—41no—
265C8×C139—41no—
266C22×C139—22no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—81no—
273C22×C139—81no—
274C22×C139—81no—
275C22×C139D4211yescharacteristic
276C4×C139—21no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—41no—
281C4×C139—41no—
282C4×C139—41no—
283C4×C139—81no—
284C4×C139—81no—
285C4×C139—81no—
286C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C139#57511yescharacteristic
288C4×C139#57711yescharacteristic
289C4×C139#57811yescharacteristic
290C2×C139—42no—
291C2×C139—81no—
292C2×C139—161no—
293C2×C139#326511yescharacteristic
294C2×C139#326911yescharacteristic
295C2×C139#329111yescharacteristic
296#20071C13911yesmaximal, characteristic, direct product factor, Sylow
297C139#2007111yescharacteristic, direct product factor, Sylow
298#3372C2×C13911yescharacteristic, complemented
299#3368C2×C13911yescharacteristic, complemented
300#3335C2×C13911yescharacteristic, complemented
301#3284C2×C13911yescharacteristic
302#1714C2×C13911yescharacteristic, complemented
303#1692C2×C13911yescharacteristic, complemented
304#1686C2×C13911yescharacteristic, complemented
305#1683C2×C13911yescharacteristic, complemented
306#1681C2×C13911yescharacteristic, complemented
307#1648C2×C13911yescharacteristic, complemented
308#1647C2×C13911yescharacteristic, complemented
309#1631C2×C13911yescharacteristic, complemented
310#1622C2×C13911yescharacteristic, complemented
311#1585C2×C13911yescharacteristic, complemented
312#1585C2×C13911yescharacteristic, complemented
313C2×#135—21no—
314#557C22×C13911yescharacteristic
315#554C22×C13911yescharacteristic
316#550C22×C13911yescharacteristic
317#547C22×C13911yescharacteristic
318#500C22×C13911yescharacteristic
319#498C22×C13911yescharacteristic
320#492C22×C13911yescharacteristic
321#492C22×C13911yescharacteristic
322#491—21no—
323#490—21no—
324#487C22×C13911yescharacteristic
325#486C22×C13911yescharacteristic
326#483—21no—
327#481—21no—
328#479—21no—
329#478—21no—
330#477C22×C13911yescharacteristic
331#476C22×C13911yescharacteristic
332#475C22×C13911yescharacteristic
333#474C22×C13911yescharacteristic
334#465—21no—
335#465—21no—
336#462C22×C13911yescharacteristic
337#461—21no—
338#461C22×C13911yescharacteristic
339#460—21no—
340#460C22×C13911yescharacteristic
341#459C22×C13911yescharacteristic
342#452—21no—
343#449—21no—
344#446C22×C13911yescharacteristic
345#446C22×C13911yescharacteristic
346#440—21no—
347#440—21no—
348C4×SD16C22×C13911yescharacteristic
349C4×SD16C22×C13911yescharacteristic
350C8×D4C22×C13911yescharacteristic
351C8×D4C22×C13911yescharacteristic
352C2×#106—21no—
353#335C22×C13911yescharacteristic
354#335C22×C13911yescharacteristic
355#333C22×C13911yescharacteristic
356#332C22×C13911yescharacteristic
357#332C22×C13911yescharacteristic
358#331C22×C13911yescharacteristic
359Q8⋊C8C22×C13911yescharacteristic
360Q8⋊C8C22×C13911yescharacteristic
361D4⋊C8C22×C13911yescharacteristic
362D4⋊C8C22×C13911yescharacteristic
363#322C22×C13911yescharacteristic
364C2×#41—21no—
365C2×#41—21no—
366#135—44no—
367C2×Q16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—41no—
373C2×SD16D4×C13911yescharacteristic
374C2×SD16D4×C13911yescharacteristic
375C2×D8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C4⋊Q8—21no—
379C4⋊Q8C23×C13911yescharacteristic
380C4⋊Q8C23×C13911yescharacteristic
381C4⋊Q8C23×C13911yescharacteristic
382#127—21no—
383#127C23×C13911yescharacteristic
384#125—21no—
385#125—21no—
386#125—41no—
387#123—41no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—41no—
391#121—21no—
392#121—21no—
393#121—41no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8C23×C13911yescharacteristic
397C4×Q8C23×C13911yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4C23×C13911yescharacteristic
401C4×D4C23×C13911yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404#107—21no—
405#107—21no—
406#107—41no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C13911yescharacteristic
412#106D4×C13911yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C13911yescharacteristic
416C4⋊C8C23×C13911yescharacteristic
417C4⋊C8C23×C13911yescharacteristic
418C4⋊C8C23×C13911yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103D4×C13911yescharacteristic
426#103D4×C13911yescharacteristic
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C13911yescharacteristic
434#102D4×C13911yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97—21no—
438#97—21no—
439C4×C8C23×C13911yescharacteristic
440C4×C8C23×C13911yescharacteristic
441C4×C8C23×C13911yescharacteristic
442#41—42no—
443#41—42no—
444#41—81no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×D4×C13911yescharacteristic
450C2×Q8C2×D4×C13911yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C2×D4×C13911yescharacteristic
458C2×D4C2×D4×C13911yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464Q16—42no—
465SD16—22no—
466SD16—41no—
467SD16—42no—
468SD16—42no—
469SD16—42no—
470SD16—81no—
471SD16—82no—
472D8—42no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—42no—
480C2×C8C2×D4×C13911yescharacteristic
481C2×C8C2×D4×C13911yescharacteristic
482C2×C8C2×D4×C13911yescharacteristic
483C2×C8C2×D4×C13911yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4C2×D4×C13911yescharacteristic
499C4⋊C4C2×D4×C13911yescharacteristic
500C4⋊C4C2×D4×C13911yescharacteristic
501C4⋊C4C2×D4×C13911yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—21no—
509C42—41no—
510C42C24×C13911yescharacteristic
511C23—21no—
512C23—21no—
513C23—41no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4—82no—
533D4—161no—
534D4AGL(1,ℤ/8)×C13912yes—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—161no—
551C2×C4C22×D4×C13911yescharacteristic
552C2×C4C22×D4×C13911yescharacteristic
553C2×C4H(5,𝔽2)×C13911yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D42×C13911yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
584C4#575×C13911yescharacteristic
585C4#577×C13911yescharacteristic
586C4#578×C13911yescharacteristic
587C2—42no—
588C2—81no—
589C2—161no—
590C2#3265×C13911yescharacteristic
591C2#3269×C13911yescharacteristic
592C2#3291×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3284×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. #3372×C139C2semidirect
2. #3368×C139C2semidirect
3. #3335×C139C2semidirect
5. #1714×C139C2semidirect
6. #1692×C139C2semidirect
7. #1686×C139C2semidirect
8. #1683×C139C2semidirect
9. #1681×C139C2semidirect
10. #1648×C139C2semidirect
11. #1647×C139C2semidirect
12. #1631×C139C2semidirect
13. #1622×C139C2semidirect
14. #1585×C139C2semidirect
15. #1585×C139C2semidirect
296. #20071C139direct (N × H)
297. C139#20071direct (N × H)
298. #3372C2×C139semidirect
299. #3368C2×C139semidirect
300. #3335C2×C139semidirect
302. #1714C2×C139semidirect
303. #1692C2×C139semidirect
304. #1686C2×C139semidirect
305. #1683C2×C139semidirect
306. #1681C2×C139semidirect
307. #1648C2×C139semidirect
308. #1647C2×C139semidirect
309. #1631C2×C139semidirect
310. #1622C2×C139semidirect
311. #1585C2×C139semidirect
312. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3372×C1392
#3368×C1392
#3335×C1392
#3284×C1392
#1714×C1392
#1692×C1392
#1686×C1392
#1683×C1392
#1681×C1392
#1648×C1392
#1647×C1392
#1631×C1392
#1622×C1392
#1585×C1392
#20071139