Finite Group Databasebeta

← C139×#20178 #48014774

Subgroups — C139×#20178 #48014774

Order 35584.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3384×C139C211yesmaximal, characteristic, complemented
2#3331×C139C211yesmaximal, characteristic, complemented
3#3330×C139C211yesmaximal, characteristic
4#3298×C139C211yesmaximal, characteristic, complemented
5#1718×C139C211yesmaximal, characteristic, complemented
6#1700×C139C211yesmaximal, characteristic, complemented
7#1699×C139C211yesmaximal, characteristic, complemented
8#1691×C139C211yesmaximal, characteristic, complemented
9#1683×C139C211yesmaximal, characteristic, complemented
10#1649×C139C211yesmaximal, characteristic, complemented
11#1647×C139C211yesmaximal, characteristic, complemented
12#1643×C139C211yesmaximal, characteristic, complemented
13#1635×C139C211yesmaximal, characteristic, complemented
14#1592×C139C211yesmaximal, characteristic, complemented
15#1581×C139C211yesmaximal, characteristic, complemented
16#554×C139C2211yescharacteristic
17D4×Q8×C139C2211yescharacteristic
18#547×C139C2211yescharacteristic
19#547×C139C2211yescharacteristic
20#501×C139—21no—
21#500×C139C2211yescharacteristic
22#498×C139C2211yescharacteristic
23#487×C139C2211yescharacteristic
24#487×C139C2211yescharacteristic
25#487×C139C2211yescharacteristic
26#487×C139C2211yescharacteristic
27#484×C139—21no—
28#483×C139—21no—
29#483×C139—21no—
30#478×C139—21no—
31#476×C139—21no—
32#476×C139C2211yescharacteristic
33#476×C139C2211yescharacteristic
34#475×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#470×C139—21no—
38#468×C139—21no—
39#465×C139—21no—
40#462×C139C2211yescharacteristic
41#461×C139C2211yescharacteristic
42#461×C139C2211yescharacteristic
43#452×C139—21no—
44#449×C139—21no—
45#448×C139—21no—
46#446×C139C2211yescharacteristic
47#442×C139—21no—
48C4×SD16×C139C2211yescharacteristic
49C4×D8×C139C2211yescharacteristic
50#436×C139C2211yescharacteristic
51#436×C139C2211yescharacteristic
52C8×D4×C139C2211yescharacteristic
53#417×C139—21no—
54#417×C139—21no—
55C2×#103×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C22×Q8×C139—21no—
70C2×Q16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139D411yescharacteristic
74C2×D8×C139D411yescharacteristic
75C2×M16×C139—21no—
76C2×M16×C139—21no—
77C22×C8×C139—21no—
78C4⋊Q8×C139—21no—
79C4⋊Q8×C139C2311yescharacteristic
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83#125×C139—21no—
84#123×C139—41no—
85#123×C139—41no—
86C22⋊Q8×C139—21no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—21no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—41no—
91C22⋊Q8×C139—41no—
92#121×C139—21no—
93#121×C139—21no—
94C4×Q8×C139C2311yescharacteristic
95C4×D4×C139—21no—
96C4×D4×C139—21no—
97C4×D4×C139C2311yescharacteristic
98C4×D4×C139C2311yescharacteristic
99C4×D4×C139C2311yescharacteristic
100C2×C4⋊C4×C139—21no—
101C2×C4⋊C4×C139—21no—
102C2×C4⋊C4×C139—21no—
103#107×C139—21no—
104#107×C139—21no—
105#107×C139—41no—
106#107×C139D411yescharacteristic
107#106×C139—21no—
108#106×C139—21no—
109#106×C139—21no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139D411yescharacteristic
113C4⋊C8×C139—21no—
114C4⋊C8×C139C2311yescharacteristic
115C4⋊C8×C139C2311yescharacteristic
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118#103×C139—21no—
119#103×C139—21no—
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×C139—21no—
127#103×C139—21no—
128#103×C139—41no—
129#103×C139D411yescharacteristic
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
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140#97×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144#41×C139—42no—
145#41×C139—42no—
146#41×C139—81no—
147#41×C139—81no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—21no—
152C2×Q8×C139—41no—
153C2×Q8×C139—42no—
154C2×Q8×C139—81no—
155C2×Q8×C139C2×D411yescharacteristic
156C2×D4×C139—41no—
157C2×D4×C139—41no—
158C2×D4×C139C2×D411yescharacteristic
159C2×D4×C139C2×D411yescharacteristic
160C2×D4×C139C2×D411yescharacteristic
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167C22×C4×C139—41no—
168Q16×C139—81no—
169SD16×C139—41no—
170SD16×C139—81no—
171SD16×C139—81no—
172D8×C139—22no—
173M16×C139—81no—
174M16×C139—81no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—81no—
181C2×C8×C139C2×D411yescharacteristic
182C2×C8×C139C2×D411yescharacteristic
183C2×C8×C139C2×D411yescharacteristic
184C2×C8×C139C2×D411yescharacteristic
185C4⋊C4×C139—21no—
186C4⋊C4×C139—21no—
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—41no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C22⋊C4×C139—21no—
204C22⋊C4×C139—21no—
205C22⋊C4×C139—21no—
206C22⋊C4×C139—41no—
207C22⋊C4×C139—41no—
208C22⋊C4×C139—41no—
209C22⋊C4×C139—41no—
210C42×C139—21no—
211C42×C139C2411yescharacteristic
212C23×C139—21no—
213C23×C139—21no—
214C23×C139—21no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—41no—
223Q8×C139—81no—
224Q8×C139—82no—
225D4×C139—21no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—82no—
231D4×C139—82no—
232D4×C139#13712yes—
233C2×C4×C139—21no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—82no—
249C2×C4×C139—82no—
250C2×C4×C139—82no—
251C2×C4×C139—161no—
252C2×C4×C139C22×D411yescharacteristic
253C2×C4×C139C22×D411yescharacteristic
254C2×C4×C139H(5,𝔽2)11yescharacteristic
255C8×C139—21no—
256C8×C139—21no—
257C8×C139—21no—
258C8×C139—21no—
259C8×C139—41no—
260C8×C139—41no—
261C8×C139—41no—
262C8×C139—41no—
263C8×C139—41no—
264C22×C139—22no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—41no—
273C22×C139D4211yescharacteristic
274C4×C139—21no—
275C4×C139—41no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139—81no—
283C4×C139—81no—
284C4×C139C2×#13711yescharacteristic
285C4×C139#57511yescharacteristic
286C4×C139#57611yescharacteristic
287C4×C139#57711yescharacteristic
288C2×C139—42no—
289C2×C139—81no—
290C2×C139—81no—
291C2×C139#326611yescharacteristic
292C2×C139#327311yescharacteristic
293C2×C139#328911yescharacteristic
294#20178C13911yesmaximal, characteristic, direct product factor, Sylow
295C139#2017811yescharacteristic, direct product factor, Sylow
296#3384C2×C13911yescharacteristic, complemented
297#3331C2×C13911yescharacteristic, complemented
298#3330C2×C13911yescharacteristic
299#3298C2×C13911yescharacteristic, complemented
300#1718C2×C13911yescharacteristic, complemented
301#1700C2×C13911yescharacteristic, complemented
302#1699C2×C13911yescharacteristic, complemented
303#1691C2×C13911yescharacteristic, complemented
304#1683C2×C13911yescharacteristic, complemented
305#1649C2×C13911yescharacteristic, complemented
306#1647C2×C13911yescharacteristic, complemented
307#1643C2×C13911yescharacteristic, complemented
308#1635C2×C13911yescharacteristic, complemented
309#1592C2×C13911yescharacteristic, complemented
310#1581C2×C13911yescharacteristic, complemented
311#554C22×C13911yescharacteristic
312D4×Q8C22×C13911yescharacteristic
313#547C22×C13911yescharacteristic
314#547C22×C13911yescharacteristic
315#501—21no—
316#500C22×C13911yescharacteristic
317#498C22×C13911yescharacteristic
318#487C22×C13911yescharacteristic
319#487C22×C13911yescharacteristic
320#487C22×C13911yescharacteristic
321#487C22×C13911yescharacteristic
322#484—21no—
323#483—21no—
324#483—21no—
325#478—21no—
326#476—21no—
327#476C22×C13911yescharacteristic
328#476C22×C13911yescharacteristic
329#475C22×C13911yescharacteristic
330#474C22×C13911yescharacteristic
331#474C22×C13911yescharacteristic
332#470—21no—
333#468—21no—
334#465—21no—
335#462C22×C13911yescharacteristic
336#461C22×C13911yescharacteristic
337#461C22×C13911yescharacteristic
338#452—21no—
339#449—21no—
340#448—21no—
341#446C22×C13911yescharacteristic
342#442—21no—
343C4×SD16C22×C13911yescharacteristic
344C4×D8C22×C13911yescharacteristic
345#436C22×C13911yescharacteristic
346#436C22×C13911yescharacteristic
347C8×D4C22×C13911yescharacteristic
348#417—21no—
349#417—21no—
350C2×#103—21no—
351#335C22×C13911yescharacteristic
352#335C22×C13911yescharacteristic
353#333C22×C13911yescharacteristic
354#332C22×C13911yescharacteristic
355#332C22×C13911yescharacteristic
356#332C22×C13911yescharacteristic
357Q8⋊C8C22×C13911yescharacteristic
358D4⋊C8C22×C13911yescharacteristic
359D4⋊C8C22×C13911yescharacteristic
360D4⋊C8C22×C13911yescharacteristic
361#322C22×C13911yescharacteristic
362C2×#41—21no—
363C2×#41—21no—
364C22×Q8—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16D4×C13911yescharacteristic
369C2×D8D4×C13911yescharacteristic
370C2×M16—21no—
371C2×M16—21no—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C13911yescharacteristic
375C4⋊Q8C23×C13911yescharacteristic
376C4⋊Q8C23×C13911yescharacteristic
377C4⋊Q8C23×C13911yescharacteristic
378#125—21no—
379#123—41no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386C22⋊Q8—41no—
387#121—21no—
388#121—21no—
389C4×Q8C23×C13911yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C13911yescharacteristic
393C4×D4C23×C13911yescharacteristic
394C4×D4C23×C13911yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398#107—21no—
399#107—21no—
400#107—41no—
401#107D4×C13911yescharacteristic
402#106—21no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106D4×C13911yescharacteristic
408C4⋊C8—21no—
409C4⋊C8C23×C13911yescharacteristic
410C4⋊C8C23×C13911yescharacteristic
411C4⋊C8C23×C13911yescharacteristic
412C4⋊C8C23×C13911yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—41no—
424#103D4×C13911yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C13911yescharacteristic
430#102D4×C13911yescharacteristic
431#102D4×C13911yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436C4×C8C23×C13911yescharacteristic
437C4×C8C23×C13911yescharacteristic
438C4×C8C23×C13911yescharacteristic
439#41—42no—
440#41—42no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—41no—
448C2×Q8—42no—
449C2×Q8—81no—
450C2×Q8C2×D4×C13911yescharacteristic
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C13911yescharacteristic
454C2×D4C2×D4×C13911yescharacteristic
455C2×D4C2×D4×C13911yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463Q16—81no—
464SD16—41no—
465SD16—81no—
466SD16—81no—
467D8—22no—
468M16—81no—
469M16—81no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8C2×D4×C13911yescharacteristic
477C2×C8C2×D4×C13911yescharacteristic
478C2×C8C2×D4×C13911yescharacteristic
479C2×C8C2×D4×C13911yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C13911yescharacteristic
495C4⋊C4C2×D4×C13911yescharacteristic
496C4⋊C4C2×D4×C13911yescharacteristic
497C4⋊C4C2×D4×C13911yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42C24×C13911yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—82no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—82no—
526D4—82no—
527D4#137×C13912yes—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—161no—
547C2×C4C22×D4×C13911yescharacteristic
548C2×C4C22×D4×C13911yescharacteristic
549C2×C4H(5,𝔽2)×C13911yescharacteristic
550C8—21no—
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22D42×C13911yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#137×C13911yescharacteristic
580C4#575×C13911yescharacteristic
581C4#576×C13911yescharacteristic
582C4#577×C13911yescharacteristic
583C2—42no—
584C2—81no—
585C2—81no—
586C2#3266×C13911yescharacteristic
587C2#3273×C13911yescharacteristic
588C2#3289×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3330×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. #3384×C139C2semidirect
2. #3331×C139C2semidirect
4. #3298×C139C2semidirect
5. #1718×C139C2semidirect
6. #1700×C139C2semidirect
7. #1699×C139C2semidirect
8. #1691×C139C2semidirect
9. #1683×C139C2semidirect
10. #1649×C139C2semidirect
11. #1647×C139C2semidirect
12. #1643×C139C2semidirect
13. #1635×C139C2semidirect
14. #1592×C139C2semidirect
15. #1581×C139C2semidirect
294. #20178C139direct (N × H)
295. C139#20178direct (N × H)
296. #3384C2×C139semidirect
297. #3331C2×C139semidirect
299. #3298C2×C139semidirect
300. #1718C2×C139semidirect
301. #1700C2×C139semidirect
302. #1699C2×C139semidirect
303. #1691C2×C139semidirect
304. #1683C2×C139semidirect
305. #1649C2×C139semidirect
306. #1647C2×C139semidirect
307. #1643C2×C139semidirect
308. #1635C2×C139semidirect
309. #1592C2×C139semidirect
310. #1581C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3384×C1392
#3331×C1392
#3330×C1392
#3298×C1392
#1718×C1392
#1700×C1392
#1699×C1392
#1691×C1392
#1683×C1392
#1649×C1392
#1647×C1392
#1643×C1392
#1635×C1392
#1592×C1392
#1581×C1392
#20178139