Finite Group Databasebeta

← C139×#20260 #48014856

Subgroups — C139×#20260 #48014856

Order 35584.

626 conjugacy classes of subgroups.

The subgroup lattice has 608 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#3329×C139C211yesmaximal, characteristic, complemented
4#3305×C139C211yesmaximal, characteristic, complemented
5#1717×C139C211yesmaximal, characteristic, complemented
6#1704×C139C211yesmaximal, characteristic, complemented
7#1698×C139C211yesmaximal, characteristic, complemented
8#1687×C139C211yesmaximal, characteristic, complemented
9#1681×C139C211yesmaximal, characteristic, complemented
10#1642×C139C211yesmaximal, characteristic, complemented
11#1630×C139C211yesmaximal, characteristic, complemented
12#1627×C139C211yesmaximal, characteristic, complemented
13#1624×C139C211yesmaximal, characteristic, complemented
14#1592×C139C211yesmaximal, characteristic, complemented
15#1582×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic
17#555×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#496×C139—21no—
21#493×C139C2211yescharacteristic
22#492×C139C2211yescharacteristic
23#489×C139—21no—
24#487×C139C2211yescharacteristic
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#485×C139—21no—
29#482×C139—21no—
30#477×C139C2211yescharacteristic
31#477×C139C2211yescharacteristic
32#476×C139—21no—
33#475×C139C2211yescharacteristic
34#468×C139—21no—
35#466×C139—21no—
36#463×C139—21no—
37#463×C139—21no—
38#461×C139C2211yescharacteristic
39#460×C139C2211yescharacteristic
40#459×C139—21no—
41#459×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#449×C139—21no—
45#448×C139—21no—
46#446×C139C2211yescharacteristic
47#446×C139C2211yescharacteristic
48#442×C139—21no—
49#442×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#334×C139C2211yescharacteristic
58#333×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—
68C22×Q8×C139—21no—
69C2×SD16×C139—21no—
70C2×SD16×C139—21no—
71C2×SD16×C139—41no—
72C2×SD16×C139D411yescharacteristic
73C2×SD16×C139D411yescharacteristic
74C2×D8×C139—21no—
75C2×D8×C139—21no—
76C2×D8×C139—21no—
77C2×D8×C139—21no—
78C2×D8×C139—21no—
79C2×M16×C139—21no—
80C22×C8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139C2311yescharacteristic
83C4⋊Q8×C139C2311yescharacteristic
84#127×C139—21no—
85#127×C139C2311yescharacteristic
86#127×C139C2311yescharacteristic
87#124×C139—21no—
88#124×C139—21no—
89#124×C139—41no—
90#123×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—41no—
93#121×C139—21no—
94#121×C139—21no—
95#121×C139—21no—
96#121×C139—41no—
97C4×Q8×C139C2311yescharacteristic
98C4×Q8×C139C2311yescharacteristic
99C4×D4×C139—21no—
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139C2311yescharacteristic
104C4×D4×C139C2311yescharacteristic
105#117×C139—21no—
106#117×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#106×C139—21no—
110#106×C139D411yescharacteristic
111#106×C139D411yescharacteristic
112C4⋊C8×C139—21no—
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×C139D411yescharacteristic
125#103×C139D411yescharacteristic
126#102×C139—21no—
127#102×C139—21no—
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×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139#97×C139—21no—
140#97×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—41no—
149C2×Q8×C139—42no—
150C2×Q8×C139—81no—
151C2×Q8×C139C2×D411yescharacteristic
152C2×Q8×C139C2×D411yescharacteristic
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139—41no—
162C2×D4×C139C2×D411yescharacteristic
163C2×D4×C139C2×D411yescharacteristic
164C22×C4×C139—21no—
165C22×C4×C139—21no—
166C22×C4×C139—41no—
167C22×C4×C139—41no—
168C22×C4×C139—41no—
169SD16×C139—41no—
170SD16×C139—41no—
171SD16×C139—81no—
172SD16×C139—81no—
173SD16×C139—82no—
174D8×C139—42no—
175D8×C139—42no—
176D8×C139—81no—
177D8×C139—81no—
178D8×C139—81no—
179M16×C139—81no—
180C2×C8×C139—21no—
181C2×C8×C139—21no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—81no—
186C2×C8×C139C2×D411yescharacteristic
187C2×C8×C139C2×D411yescharacteristic
188C2×C8×C139C2×D411yescharacteristic
189C2×C8×C139C2×D411yescharacteristic
190C4⋊C4×C139—21no—
191C4⋊C4×C139—21no—
192C4⋊C4×C139—21no—
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
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—
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—
217C23×C139—41no—
218Q8×C139—21no—
219Q8×C139—21no—
220Q8×C139—21no—
221Q8×C139—21no—
222Q8×C139—41no—
223Q8×C139—41no—
224Q8×C139—81no—
225Q8×C139—82no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—41no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—41no—
234D4×C139—41no—
235D4×C139—41no—
236D4×C139—41no—
237D4×C139—41no—
238D4×C139—81no—
239D4×C139—81no—
240D4×C139—82no—
241D4×C139—161no—
242D4×C139—161no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
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—82no—
256C2×C4×C139—82no—
257C2×C4×C139—161no—
258C2×C4×C139C22×D411yescharacteristic
259C2×C4×C139C22×D411yescharacteristic
260C2×C4×C139H(5,𝔽2)11yescharacteristic
261C8×C139—21no—
262C8×C139—21no—
263C8×C139—21no—
264C8×C139—21no—
265C8×C139—41no—
266C8×C139—41no—
267C8×C139—41no—
268C8×C139—41no—
269C8×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—41no—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—81no—
277C22×C139—81no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139D4211yescharacteristic
283C4×C139—21no—
284C4×C139—41no—
285C4×C139—41no—
286C4×C139—41no—
287C4×C139—41no—
288C4×C139—41no—
289C4×C139—41no—
290C4×C139—81no—
291C4×C139—81no—
292C4×C139#57511yescharacteristic
293C4×C139#57511yescharacteristic
294C4×C139#57611yescharacteristic
295C4×C139#57711yescharacteristic
296C2×C139—81no—
297C2×C139—81no—
298C2×C139—161no—
299C2×C139—161no—
300C2×C139#326811yescharacteristic
301C2×C139#327511yescharacteristic
302C2×C139#328811yescharacteristic
303#20260C13911yesmaximal, characteristic, direct product factor, Sylow
304C139#2026011yescharacteristic, direct product factor, Sylow
305#3399C2×C13911yescharacteristic, complemented
306#3373C2×C13911yescharacteristic, complemented
307#3329C2×C13911yescharacteristic, complemented
308#3305C2×C13911yescharacteristic, complemented
309#1717C2×C13911yescharacteristic, complemented
310#1704C2×C13911yescharacteristic, complemented
311#1698C2×C13911yescharacteristic, complemented
312#1687C2×C13911yescharacteristic, complemented
313#1681C2×C13911yescharacteristic, complemented
314#1642C2×C13911yescharacteristic, complemented
315#1630C2×C13911yescharacteristic, complemented
316#1627C2×C13911yescharacteristic, complemented
317#1624C2×C13911yescharacteristic, complemented
318#1592C2×C13911yescharacteristic, complemented
319#1582C2×C13911yescharacteristic, complemented
320#559C22×C13911yescharacteristic
321#555C22×C13911yescharacteristic
322#550C22×C13911yescharacteristic
323D4×Q8C22×C13911yescharacteristic
324#496—21no—
325#493C22×C13911yescharacteristic
326#492C22×C13911yescharacteristic
327#489—21no—
328#487C22×C13911yescharacteristic
329#486C22×C13911yescharacteristic
330#486C22×C13911yescharacteristic
331#486C22×C13911yescharacteristic
332#485—21no—
333#482—21no—
334#477C22×C13911yescharacteristic
335#477C22×C13911yescharacteristic
336#476—21no—
337#475C22×C13911yescharacteristic
338#468—21no—
339#466—21no—
340#463—21no—
341#463—21no—
342#461C22×C13911yescharacteristic
343#460C22×C13911yescharacteristic
344#459—21no—
345#459C22×C13911yescharacteristic
346#459C22×C13911yescharacteristic
347#459C22×C13911yescharacteristic
348#449—21no—
349#448—21no—
350#446C22×C13911yescharacteristic
351#446C22×C13911yescharacteristic
352#442—21no—
353#442—21no—
354C4×SD16C22×C13911yescharacteristic
355C4×SD16C22×C13911yescharacteristic
356#436C22×C13911yescharacteristic
357C8×D4C22×C13911yescharacteristic
358#419—21no—
359#416—21no—
360#335C22×C13911yescharacteristic
361#334C22×C13911yescharacteristic
362#333C22×C13911yescharacteristic
363#332C22×C13911yescharacteristic
364#331C22×C13911yescharacteristic
365#331C22×C13911yescharacteristic
366Q8⋊C8C22×C13911yescharacteristic
367Q8⋊C8C22×C13911yescharacteristic
368D4⋊C8C22×C13911yescharacteristic
369D4⋊C8C22×C13911yescharacteristic
370#322C22×C13911yescharacteristic
371C2×#41—21no—
372C22×Q8—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—41no—
376C2×SD16D4×C13911yescharacteristic
377C2×SD16D4×C13911yescharacteristic
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×M16—21no—
384C22×C8—21no—
385C4⋊Q8—21no—
386C4⋊Q8C23×C13911yescharacteristic
387C4⋊Q8C23×C13911yescharacteristic
388#127—21no—
389#127C23×C13911yescharacteristic
390#127C23×C13911yescharacteristic
391#124—21no—
392#124—21no—
393#124—41no—
394#123—41no—
395C22⋊Q8—21no—
396C22⋊Q8—41no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—41no—
401C4×Q8C23×C13911yescharacteristic
402C4×Q8C23×C13911yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C13911yescharacteristic
408C4×D4C23×C13911yescharacteristic
409#117—21no—
410#117—21no—
411#107—21no—
412#107—21no—
413#106—21no—
414#106D4×C13911yescharacteristic
415#106D4×C13911yescharacteristic
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C13911yescharacteristic
419C4⋊C8C23×C13911yescharacteristic
420C4⋊C8C23×C13911yescharacteristic
421C4⋊C8C23×C13911yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103D4×C13911yescharacteristic
429#103D4×C13911yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—41no—
439#102D4×C13911yescharacteristic
440#102D4×C13911yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444#97—21no—
445C4×C8C23×C13911yescharacteristic
446C4×C8C23×C13911yescharacteristic
447C4×C8C23×C13911yescharacteristic
448#41—42no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C13911yescharacteristic
456C2×Q8C2×D4×C13911yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C13911yescharacteristic
467C2×D4C2×D4×C13911yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473SD16—41no—
474SD16—41no—
475SD16—81no—
476SD16—81no—
477SD16—82no—
478D8—42no—
479D8—42no—
480D8—81no—
481D8—81no—
482D8—81no—
483M16—81no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8C2×D4×C13911yescharacteristic
491C2×C8C2×D4×C13911yescharacteristic
492C2×C8C2×D4×C13911yescharacteristic
493C2×C8C2×D4×C13911yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4C2×D4×C13911yescharacteristic
502C4⋊C4C2×D4×C13911yescharacteristic
503C4⋊C4C2×D4×C13911yescharacteristic
504C4⋊C4C2×D4×C13911yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—41no—
517C42C24×C13911yescharacteristic
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529Q8—82no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—81no—
544D4—82no—
545D4—161no—
546D4—161no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—161no—
562C2×C4C22×D4×C13911yescharacteristic
563C2×C4C22×D4×C13911yescharacteristic
564C2×C4H(5,𝔽2)×C13911yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22D42×C13911yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#575×C13911yescharacteristic
597C4#575×C13911yescharacteristic
598C4#576×C13911yescharacteristic
599C4#577×C13911yescharacteristic
600C2—81no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2#3268×C13911yescharacteristic
605C2#3275×C13911yescharacteristic
606C2#3288×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. #3329×C139C2semidirect
4. #3305×C139C2semidirect
5. #1717×C139C2semidirect
6. #1704×C139C2semidirect
7. #1698×C139C2semidirect
8. #1687×C139C2semidirect
9. #1681×C139C2semidirect
10. #1642×C139C2semidirect
11. #1630×C139C2semidirect
12. #1627×C139C2semidirect
13. #1624×C139C2semidirect
14. #1592×C139C2semidirect
15. #1582×C139C2semidirect
303. #20260C139direct (N × H)
304. C139#20260direct (N × H)
305. #3399C2×C139semidirect
306. #3373C2×C139semidirect
307. #3329C2×C139semidirect
308. #3305C2×C139semidirect
309. #1717C2×C139semidirect
310. #1704C2×C139semidirect
311. #1698C2×C139semidirect
312. #1687C2×C139semidirect
313. #1681C2×C139semidirect
314. #1642C2×C139semidirect
315. #1630C2×C139semidirect
316. #1627C2×C139semidirect
317. #1624C2×C139semidirect
318. #1592C2×C139semidirect
319. #1582C2×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
#3329×C1392
#3305×C1392
#1717×C1392
#1704×C1392
#1698×C1392
#1687×C1392
#1681×C1392
#1642×C1392
#1630×C1392
#1627×C1392
#1624×C1392
#1592×C1392
#1582×C1392
#20260139