Finite Group Databasebeta

← C139×#20154 #48014750

Subgroups — C139×#20154 #48014750

Order 35584.

628 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C139C211yesmaximal, characteristic, complemented
2#3396×C139C211yesmaximal, characteristic, complemented
3#3361×C139C211yesmaximal, characteristic, complemented
4#3333×C139C211yesmaximal, characteristic, complemented
5#1721×C139C211yesmaximal, characteristic, complemented
6#1698×C139C211yesmaximal, characteristic, complemented
7#1687×C139C211yesmaximal, characteristic, complemented
8#1678×C139C211yesmaximal, characteristic, complemented
9#1668×C139C211yesmaximal, characteristic, complemented
10#1630×C139C211yesmaximal, characteristic, complemented
11#1622×C139C211yesmaximal, characteristic, complemented
12#1621×C139C211yesmaximal, characteristic, complemented
13#1620×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1587×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic
17#559×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#496×C139—21no—
21#495×C139—21no—
22#493×C139C2211yescharacteristic
23#493×C139C2211yescharacteristic
24#493×C139C2211yescharacteristic
25#492×C139C2211yescharacteristic
26#488×C139—21no—
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#480×C139—21no—
30#478×C139—21no—
31#477×C139C2211yescharacteristic
32#477×C139C2211yescharacteristic
33#468×C139—21no—
34#463×C139—21no—
35#463×C139—21no—
36#463×C139—21no—
37#463×C139—21no—
38#460×C139C2211yescharacteristic
39#460×C139C2211yescharacteristic
40#460×C139C2211yescharacteristic
41#460×C139C2211yescharacteristic
42#459×C139—21no—
43#459×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#452×C139—21no—
46#446×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49#442×C139—21no—
50C4×Q16×C139C2211yescharacteristic
51C4×SD16×C139C2211yescharacteristic
52C4×D8×C139—21no—
53C4×D8×C139—21no—
54#436×C139C2211yescharacteristic
55#417×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#331×C139C2211yescharacteristic
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×Q16×C139D411yescharacteristic
69C2×SD16×C139—21no—
70C2×SD16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—41no—
74C2×SD16×C139D411yescharacteristic
75C2×D8×C139—21no—
76C2×D8×C139—21no—
77C2×D8×C139—21no—
78C2×D8×C139—21no—
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×D8×C139—41no—
82C2×M16×C139—21no—
83C4⋊Q8×C139C2311yescharacteristic
84#127×C139—21no—
85#127×C139C2311yescharacteristic
86#127×C139C2311yescharacteristic
87#127×C139C2311yescharacteristic
88#125×C139—21no—
89#124×C139—21no—
90#124×C139—21no—
91#124×C139—21no—
92#124×C139—21no—
93#123×C139—41no—
94#123×C139—41no—
95C22⋊Q8×C139—21no—
96C22⋊Q8×C139—41no—
97#121×C139—21no—
98#121×C139—41no—
99C4×Q8×C139C2311yescharacteristic
100C4×Q8×C139C2311yescharacteristic
101C4×Q8×C139C2311yescharacteristic
102C4×D4×C139—21no—
103C4×D4×C139—21no—
104C4×D4×C139—21no—
105C4×D4×C139—21no—
106C4×D4×C139—21no—
107C4×D4×C139—21no—
108C4×D4×C139C2311yescharacteristic
109C2×C4⋊C4×C139—21no—
110#107×C139—21no—
111#107×C139—21no—
112#107×C139D411yescharacteristic
113#106×C139D411yescharacteristic
114C4⋊C8×C139—21no—
115C4⋊C8×C139—21no—
116C4⋊C8×C139—21no—
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121#103×C139—21no—
122#103×C139—21no—
123#103×C139D411yescharacteristic
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—21no—
135#102×C139—21no—
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138#97×C139—21no—
139C4×C8×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×C139C2×D411yescharacteristic
148C2×Q8×C139C2×D411yescharacteristic
149C2×Q8×C139C2×D411yescharacteristic
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
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×C139C2×D411yescharacteristic
162C22×C4×C139—21no—
163C22×C4×C139—41no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167Q16×C139—41no—
168SD16×C139—41no—
169SD16×C139—82no—
170SD16×C139—81no—
171SD16×C139—81no—
172SD16×C139—81no—
173SD16×C139—81no—
174D8×C139—42no—
175D8×C139—42no—
176D8×C139—42no—
177D8×C139—81no—
178D8×C139—81no—
179D8×C139—82no—
180D8×C139—81no—
181M16×C139—81no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139C2×D411yescharacteristic
188C2×C8×C139C2×D411yescharacteristic
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
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×C139—41no—
198C4⋊C4×C139C2×D411yescharacteristic
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
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—
210C22⋊C4×C139—41no—
211C42×C139—21no—
212C42×C139—21no—
213C42×C139—21no—
214C42×C139C2411yescharacteristic
215C23×C139—21no—
216C23×C139—41no—
217C23×C139—41no—
218C23×C139—41no—
219Q8×C139—21no—
220Q8×C139—21no—
221Q8×C139—21no—
222Q8×C139—21no—
223Q8×C139—21no—
224Q8×C139—21no—
225Q8×C139—81no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—41no—
229D4×C139—41no—
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—41no—
239D4×C139—41no—
240D4×C139—81no—
241D4×C139—81no—
242D4×C139—81no—
243D4×C139—82no—
244D4×C139—161no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—82no—
256C2×C4×C139—161no—
257C2×C4×C139—161no—
258C2×C4×C139—161no—
259C2×C4×C139C22×D411yescharacteristic
260C2×C4×C139C22×D411yescharacteristic
261C2×C4×C139H(5,𝔽2)11yescharacteristic
262C8×C139—22no—
263C8×C139—21no—
264C8×C139—21no—
265C8×C139—21no—
266C8×C139—21no—
267C8×C139—41no—
268C8×C139—41no—
269C8×C139—41no—
270C8×C139—41no—
271C22×C139—41no—
272C22×C139—41no—
273C22×C139—41no—
274C22×C139—81no—
275C22×C139—81no—
276C22×C139—81no—
277C22×C139—81no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139D4211yescharacteristic
284C4×C139—21no—
285C4×C139—41no—
286C4×C139—41no—
287C4×C139—41no—
288C4×C139—41no—
289C4×C139—41no—
290C4×C139—41no—
291C4×C139—41no—
292C4×C139—81no—
293C4×C139#57511yescharacteristic
294C4×C139#57511yescharacteristic
295C4×C139#57611yescharacteristic
296C4×C139#57711yescharacteristic
297C2×C139—81no—
298C2×C139—161no—
299C2×C139—161no—
300C2×C139—161no—
301C2×C139#326811yescharacteristic
302C2×C139#327111yescharacteristic
303C2×C139#329211yescharacteristic
304#20154C13911yesmaximal, characteristic, direct product factor, Sylow
305C139#2015411yescharacteristic, direct product factor, Sylow
306#3399C2×C13911yescharacteristic, complemented
307#3396C2×C13911yescharacteristic, complemented
308#3361C2×C13911yescharacteristic, complemented
309#3333C2×C13911yescharacteristic, complemented
310#1721C2×C13911yescharacteristic, complemented
311#1698C2×C13911yescharacteristic, complemented
312#1687C2×C13911yescharacteristic, complemented
313#1678C2×C13911yescharacteristic, complemented
314#1668C2×C13911yescharacteristic, complemented
315#1630C2×C13911yescharacteristic, complemented
316#1622C2×C13911yescharacteristic, complemented
317#1621C2×C13911yescharacteristic, complemented
318#1620C2×C13911yescharacteristic, complemented
319#1588C2×C13911yescharacteristic, complemented
320#1587C2×C13911yescharacteristic, complemented
321#559C22×C13911yescharacteristic
322#559C22×C13911yescharacteristic
323#554C22×C13911yescharacteristic
324#550C22×C13911yescharacteristic
325#496—21no—
326#495—21no—
327#493C22×C13911yescharacteristic
328#493C22×C13911yescharacteristic
329#493C22×C13911yescharacteristic
330#492C22×C13911yescharacteristic
331#488—21no—
332#486C22×C13911yescharacteristic
333#486C22×C13911yescharacteristic
334#480—21no—
335#478—21no—
336#477C22×C13911yescharacteristic
337#477C22×C13911yescharacteristic
338#468—21no—
339#463—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#460C22×C13911yescharacteristic
344#460C22×C13911yescharacteristic
345#460C22×C13911yescharacteristic
346#460C22×C13911yescharacteristic
347#459—21no—
348#459C22×C13911yescharacteristic
349#459C22×C13911yescharacteristic
350#452—21no—
351#446C22×C13911yescharacteristic
352C8×Q8C22×C13911yescharacteristic
353C8×Q8C22×C13911yescharacteristic
354#442—21no—
355C4×Q16C22×C13911yescharacteristic
356C4×SD16C22×C13911yescharacteristic
357C4×D8—21no—
358C4×D8—21no—
359#436C22×C13911yescharacteristic
360#417—21no—
361#335C22×C13911yescharacteristic
362#334C22×C13911yescharacteristic
363#333C22×C13911yescharacteristic
364#331C22×C13911yescharacteristic
365#331C22×C13911yescharacteristic
366#331C22×C13911yescharacteristic
367Q8⋊C8C22×C13911yescharacteristic
368Q8⋊C8C22×C13911yescharacteristic
369Q8⋊C8C22×C13911yescharacteristic
370D4⋊C8C22×C13911yescharacteristic
371#322C22×C13911yescharacteristic
372C2×#41—21no—
373C2×Q16D4×C13911yescharacteristic
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—41no—
379C2×SD16D4×C13911yescharacteristic
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—41no—
387C2×M16—21no—
388C4⋊Q8C23×C13911yescharacteristic
389#127—21no—
390#127C23×C13911yescharacteristic
391#127C23×C13911yescharacteristic
392#127C23×C13911yescharacteristic
393#125—21no—
394#124—21no—
395#124—21no—
396#124—21no—
397#124—21no—
398#123—41no—
399#123—41no—
400C22⋊Q8—21no—
401C22⋊Q8—41no—
402#121—21no—
403#121—41no—
404C4×Q8C23×C13911yescharacteristic
405C4×Q8C23×C13911yescharacteristic
406C4×Q8C23×C13911yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C13911yescharacteristic
414C2×C4⋊C4—21no—
415#107—21no—
416#107—21no—
417#107D4×C13911yescharacteristic
418#106D4×C13911yescharacteristic
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8C23×C13911yescharacteristic
423C4⋊C8C23×C13911yescharacteristic
424C4⋊C8C23×C13911yescharacteristic
425C4⋊C8C23×C13911yescharacteristic
426#103—21no—
427#103—21no—
428#103D4×C13911yescharacteristic
429#103D4×C13911yescharacteristic
430#103D4×C13911yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102D4×C13911yescharacteristic
442C22⋊C8—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C13911yescharacteristic
447C4×C8C23×C13911yescharacteristic
448C4×C8C23×C13911yescharacteristic
449#41—42no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8C2×D4×C13911yescharacteristic
453C2×Q8C2×D4×C13911yescharacteristic
454C2×Q8C2×D4×C13911yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C13911yescharacteristic
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—41no—
473SD16—41no—
474SD16—82no—
475SD16—81no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—42no—
481D8—42no—
482D8—81no—
483D8—81no—
484D8—82no—
485D8—81no—
486M16—81no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8C2×D4×C13911yescharacteristic
493C2×C8C2×D4×C13911yescharacteristic
494C2×C8C2×D4×C13911yescharacteristic
495C2×C8C2×D4×C13911yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C13911yescharacteristic
504C4⋊C4C2×D4×C13911yescharacteristic
505C4⋊C4C2×D4×C13911yescharacteristic
506C4⋊C4C2×D4×C13911yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42C24×C13911yescharacteristic
520C23—21no—
521C23—41no—
522C23—41no—
523C23—41no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—81no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—81no—
547D4—81no—
548D4—82no—
549D4—161no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4—161no—
564C2×C4C22×D4×C13911yescharacteristic
565C2×C4C22×D4×C13911yescharacteristic
566C2×C4H(5,𝔽2)×C13911yescharacteristic
567C8—22no—
568C8—21no—
569C8—21no—
570C8—21no—
571C8—21no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22D42×C13911yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4#575×C13911yescharacteristic
599C4#575×C13911yescharacteristic
600C4#576×C13911yescharacteristic
601C4#577×C13911yescharacteristic
602C2—81no—
603C2—161no—
604C2—161no—
605C2—161no—
606C2#3268×C13911yescharacteristic
607C2#3271×C13911yescharacteristic
608C2#3292×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. #3396×C139C2semidirect
3. #3361×C139C2semidirect
4. #3333×C139C2semidirect
5. #1721×C139C2semidirect
6. #1698×C139C2semidirect
7. #1687×C139C2semidirect
8. #1678×C139C2semidirect
9. #1668×C139C2semidirect
10. #1630×C139C2semidirect
11. #1622×C139C2semidirect
12. #1621×C139C2semidirect
13. #1620×C139C2semidirect
14. #1588×C139C2semidirect
15. #1587×C139C2semidirect
304. #20154C139direct (N × H)
305. C139#20154direct (N × H)
306. #3399C2×C139semidirect
307. #3396C2×C139semidirect
308. #3361C2×C139semidirect
309. #3333C2×C139semidirect
310. #1721C2×C139semidirect
311. #1698C2×C139semidirect
312. #1687C2×C139semidirect
313. #1678C2×C139semidirect
314. #1668C2×C139semidirect
315. #1630C2×C139semidirect
316. #1622C2×C139semidirect
317. #1621C2×C139semidirect
318. #1620C2×C139semidirect
319. #1588C2×C139semidirect
320. #1587C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3399×C1392
#3396×C1392
#3361×C1392
#3333×C1392
#1721×C1392
#1698×C1392
#1687×C1392
#1678×C1392
#1668×C1392
#1630×C1392
#1622×C1392
#1621×C1392
#1620×C1392
#1588×C1392
#1587×C1392
#20154139