Finite Group Databasebeta

← C139×#20049 #48014645

Subgroups — C139×#20049 #48014645

Order 35584.

610 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#3392×C139C211yesmaximal, characteristic, complemented
2#3386×C139C211yesmaximal, characteristic, complemented
3#3329×C139C211yesmaximal, characteristic, complemented
4#3305×C139C211yesmaximal, characteristic
5#1719×C139C211yesmaximal, characteristic, complemented
6#1698×C139C211yesmaximal, characteristic, complemented
7#1685×C139C211yesmaximal, characteristic, complemented
8#1684×C139C211yesmaximal, characteristic, complemented
9#1673×C139C211yesmaximal, characteristic, complemented
10#1646×C139C211yesmaximal, characteristic, complemented
11#1642×C139C211yesmaximal, characteristic, complemented
12#1636×C139C211yesmaximal, characteristic, complemented
13#1627×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16#557×C139C2211yescharacteristic
17#555×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#501×C139—21no—
21#500×C139C2211yescharacteristic
22#492×C139—21no—
23#492×C139C2211yescharacteristic
24#487×C139C2211yescharacteristic
25#487×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#485×C139—21no—
29#482×C139—21no—
30#478×C139—21no—
31#477×C139—21no—
32#477×C139C2211yescharacteristic
33#477×C139C2211yescharacteristic
34#475×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#468×C139—21no—
37#466×C139—21no—
38#461×C139—21no—
39#461×C139C2211yescharacteristic
40#461×C139C2211yescharacteristic
41#460×C139—21no—
42#460×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#449×C139—21no—
45#448×C139—21no—
46#446×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48#440×C139—21no—
49C4×SD16×C139—21no—
50C4×SD16×C139C2211yescharacteristic
51C4×SD16×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#419×C139—21no—
55#416×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—
68C22×Q8×C139—21no—
69C2×SD16×C139—21no—
70C2×SD16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139D411yescharacteristic
75C2×SD16×C139D411yescharacteristic
76C2×D8×C139—21no—
77C2×M16×C139—21no—
78C22×C8×C139—21no—
79C4⋊Q8×C139—21no—
80C4⋊Q8×C139—21no—
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83C4⋊Q8×C139C2311yescharacteristic
84#127×C139—21no—
85#127×C139C2311yescharacteristic
86#125×C139—21no—
87#125×C139—41no—
88#124×C139—41no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—41no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—21no—
94#121×C139—41no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139C2311yescharacteristic
98C4×Q8×C139C2311yescharacteristic
99C4×D4×C139—21no—
100C4×D4×C139—21no—
101C4×D4×C139C2311yescharacteristic
102C4×D4×C139C2311yescharacteristic
103#117×C139—21no—
104#117×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—21no—
110#106×C139—21no—
111#106×C139D411yescharacteristic
112#106×C139D411yescharacteristic
113C4⋊C8×C139—21no—
114C4⋊C8×C139—21no—
115C4⋊C8×C139C2311yescharacteristic
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
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—41no—
127#103×C139D411yescharacteristic
128#103×C139D411yescharacteristic
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×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139#97×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144#41×C139—42no—
145#41×C139—81no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—41no—
150C2×Q8×C139—42no—
151C2×Q8×C139—81no—
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—
166SD16×C139—22no—
167SD16×C139—41no—
168SD16×C139—42no—
169SD16×C139—81no—
170SD16×C139—81no—
171SD16×C139—81no—
172SD16×C139—81no—
173D8×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—41no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139C2×D411yescharacteristic
198C4⋊C4×C139C2×D411yescharacteristic
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C22⋊C4×C139—21no—
202C22⋊C4×C139—21no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C42×C139—21no—
208C42×C139—21no—
209C42×C139—41no—
210C42×C139—41no—
211C42×C139C2411yescharacteristic
212C23×C139—21no—
213C23×C139—21no—
214C23×C139—41no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—21no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—81no—
223Q8×C139—82no—
224Q8×C139#13712yes—
225D4×C139—21no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—21no—
229D4×C139—41no—
230D4×C139—41no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—82no—
234D4×C139—81no—
235D4×C139—161no—
236D4×C139—161no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—21no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—41no—
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—82no—
251C2×C4×C139—82no—
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—41no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—81no—
271C22×C139—81no—
272C22×C139—81no—
273C22×C139D4211yescharacteristic
274C4×C139—22no—
275C4×C139—21no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—41no—
281C4×C139—81no—
282C4×C139—81no—
283C4×C139—81no—
284C4×C139C2×#13711yescharacteristic
285C4×C139#57511yescharacteristic
286C4×C139#57611yescharacteristic
287C4×C139#57711yescharacteristic
288C2×C139—81no—
289C2×C139—81no—
290C2×C139—161no—
291C2×C139#326611yescharacteristic
292C2×C139#326811yescharacteristic
293C2×C139#329011yescharacteristic
294#20049C13911yesmaximal, characteristic, direct product factor, Sylow
295C139#2004911yescharacteristic, direct product factor, Sylow
296#3392C2×C13911yescharacteristic, complemented
297#3386C2×C13911yescharacteristic, complemented
298#3329C2×C13911yescharacteristic, complemented
299#3305C2×C13911yescharacteristic
300#1719C2×C13911yescharacteristic, complemented
301#1698C2×C13911yescharacteristic, complemented
302#1685C2×C13911yescharacteristic, complemented
303#1684C2×C13911yescharacteristic, complemented
304#1673C2×C13911yescharacteristic, complemented
305#1646C2×C13911yescharacteristic, complemented
306#1642C2×C13911yescharacteristic, complemented
307#1636C2×C13911yescharacteristic, complemented
308#1627C2×C13911yescharacteristic, complemented
309#1588C2×C13911yescharacteristic, complemented
310#1585C2×C13911yescharacteristic, complemented
311#557C22×C13911yescharacteristic
312#555C22×C13911yescharacteristic
313#550C22×C13911yescharacteristic
314D4×Q8C22×C13911yescharacteristic
315#501—21no—
316#500C22×C13911yescharacteristic
317#492—21no—
318#492C22×C13911yescharacteristic
319#487C22×C13911yescharacteristic
320#487C22×C13911yescharacteristic
321#486C22×C13911yescharacteristic
322#486C22×C13911yescharacteristic
323#485—21no—
324#482—21no—
325#478—21no—
326#477—21no—
327#477C22×C13911yescharacteristic
328#477C22×C13911yescharacteristic
329#475C22×C13911yescharacteristic
330#474C22×C13911yescharacteristic
331#468—21no—
332#466—21no—
333#461—21no—
334#461C22×C13911yescharacteristic
335#461C22×C13911yescharacteristic
336#460—21no—
337#460C22×C13911yescharacteristic
338#459C22×C13911yescharacteristic
339#449—21no—
340#448—21no—
341#446C22×C13911yescharacteristic
342C8×Q8C22×C13911yescharacteristic
343#440—21no—
344C4×SD16—21no—
345C4×SD16C22×C13911yescharacteristic
346C4×SD16C22×C13911yescharacteristic
347#436C22×C13911yescharacteristic
348C8×D4C22×C13911yescharacteristic
349#419—21no—
350#416—21no—
351#335C22×C13911yescharacteristic
352#335C22×C13911yescharacteristic
353#333C22×C13911yescharacteristic
354#332C22×C13911yescharacteristic
355#332C22×C13911yescharacteristic
356#331C22×C13911yescharacteristic
357Q8⋊C8C22×C13911yescharacteristic
358Q8⋊C8C22×C13911yescharacteristic
359D4⋊C8C22×C13911yescharacteristic
360D4⋊C8C22×C13911yescharacteristic
361#322C22×C13911yescharacteristic
362C2×#41—21no—
363C22×Q8—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C13911yescharacteristic
370C2×SD16D4×C13911yescharacteristic
371C2×D8—21no—
372C2×M16—21no—
373C22×C8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8C23×C13911yescharacteristic
377C4⋊Q8C23×C13911yescharacteristic
378C4⋊Q8C23×C13911yescharacteristic
379#127—21no—
380#127C23×C13911yescharacteristic
381#125—21no—
382#125—41no—
383#124—41no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—41no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C13911yescharacteristic
393C4×Q8C23×C13911yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C13911yescharacteristic
397C4×D4C23×C13911yescharacteristic
398#117—21no—
399#117—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#107—21no—
405#106—21no—
406#106D4×C13911yescharacteristic
407#106D4×C13911yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C13911yescharacteristic
411C4⋊C8C23×C13911yescharacteristic
412C4⋊C8C23×C13911yescharacteristic
413C4⋊C8C23×C13911yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—41no—
422#103D4×C13911yescharacteristic
423#103D4×C13911yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—41no—
430#102D4×C13911yescharacteristic
431#102D4×C13911yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434#97—21no—
435C4×C8—21no—
436C4×C8C23×C13911yescharacteristic
437C4×C8C23×C13911yescharacteristic
438C4×C8C23×C13911yescharacteristic
439#41—42no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—42no—
446C2×Q8—81no—
447C2×Q8C2×D4×C13911yescharacteristic
448C2×Q8C2×D4×C13911yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C13911yescharacteristic
456C2×D4C2×D4×C13911yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461SD16—22no—
462SD16—41no—
463SD16—42no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468D8—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—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C13911yescharacteristic
493C4⋊C4C2×D4×C13911yescharacteristic
494C4⋊C4C2×D4×C13911yescharacteristic
495C4⋊C4C2×D4×C13911yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42—41no—
505C42—41no—
506C42C24×C13911yescharacteristic
507C23—21no—
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—82no—
519Q8#137×C13912yes—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—82no—
529D4—81no—
530D4—161no—
531D4—161no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—82no—
546C2×C4—82no—
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—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22D42×C13911yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#137×C13911yescharacteristic
580C4#575×C13911yescharacteristic
581C4#576×C13911yescharacteristic
582C4#577×C13911yescharacteristic
583C2—81no—
584C2—81no—
585C2—161no—
586C2#3266×C13911yescharacteristic
587C2#3268×C13911yescharacteristic
588C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3305×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. #3392×C139C2semidirect
2. #3386×C139C2semidirect
3. #3329×C139C2semidirect
5. #1719×C139C2semidirect
6. #1698×C139C2semidirect
7. #1685×C139C2semidirect
8. #1684×C139C2semidirect
9. #1673×C139C2semidirect
10. #1646×C139C2semidirect
11. #1642×C139C2semidirect
12. #1636×C139C2semidirect
13. #1627×C139C2semidirect
14. #1588×C139C2semidirect
15. #1585×C139C2semidirect
294. #20049C139direct (N × H)
295. C139#20049direct (N × H)
296. #3392C2×C139semidirect
297. #3386C2×C139semidirect
298. #3329C2×C139semidirect
300. #1719C2×C139semidirect
301. #1698C2×C139semidirect
302. #1685C2×C139semidirect
303. #1684C2×C139semidirect
304. #1673C2×C139semidirect
305. #1646C2×C139semidirect
306. #1642C2×C139semidirect
307. #1636C2×C139semidirect
308. #1627C2×C139semidirect
309. #1588C2×C139semidirect
310. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3392×C1392
#3386×C1392
#3329×C1392
#3305×C1392
#1719×C1392
#1698×C1392
#1685×C1392
#1684×C1392
#1673×C1392
#1646×C1392
#1642×C1392
#1636×C1392
#1627×C1392
#1588×C1392
#1585×C1392
#20049139