Finite Group Databasebeta

← C139×#20256 #48014852

Subgroups — C139×#20256 #48014852

Order 35584.

686 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3399×C139C211yesmaximal, characteristic, complemented
2#3399×C139C211yesmaximal, characteristic, complemented
3#3332×C139C211yesmaximal, characteristic, complemented
4#3284×C139C211yesmaximal, characteristic, complemented
5#1721×C139C211yesmaximal, characteristic, complemented
6#1702×C139C211yesmaximal, characteristic, complemented
7#1687×C139C211yesmaximal, characteristic, complemented
8#1686×C139C211yesmaximal, characteristic, complemented
9#1667×C139C211yesmaximal, characteristic, complemented
10#1640×C139C211yesmaximal, characteristic, complemented
11#1625×C139C211yesmaximal, characteristic, complemented
12#1621×C139C211yesmaximal, characteristic, complemented
13#1621×C139C211yesmaximal, characteristic, complemented
14#1592×C139C211yesmaximal, characteristic, complemented
15#1582×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139—21no—
17#559×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#496×C139—21no—
22#496×C139—21no—
23#493×C139C2211yescharacteristic
24#493×C139C2211yescharacteristic
25#493×C139C2211yescharacteristic
26#492×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#481×C139—21no—
30#475×C139C2211yescharacteristic
31#469×C139—21no—
32#465×C139—21no—
33#463×C139—21no—
34#463×C139—21no—
35#462×C139C2211yescharacteristic
36#460×C139C2211yescharacteristic
37#460×C139C2211yescharacteristic
38#459×C139—21no—
39#459×C139—21no—
40#459×C139C2211yescharacteristic
41#459×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#452×C139—21no—
45#449×C139—21no—
46#449×C139—21no—
47#446×C139C2211yescharacteristic
48#446×C139C2211yescharacteristic
49#442×C139—21no—
50#442×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55#417×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#331×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—
68C2×#41×C139—21no—
69C2×#41×C139—21no—
70#135×C139—44no—
71C2×Q16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139D411yescharacteristic
77C2×SD16×C139D411yescharacteristic
78C2×D8×C139—21no—
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139—21no—
83C2×D8×C139—21no—
84C2×D8×C139—21no—
85C2×D8×C139—21no—
86C2×D8×C139—41no—
87C2×M16×C139—21no—
88C22×C8×C139—21no—
89C4⋊Q8×C139C2311yescharacteristic
90#127×C139—21no—
91#127×C139—21no—
92#127×C139C2311yescharacteristic
93#127×C139C2311yescharacteristic
94#127×C139C2311yescharacteristic
95#124×C139—21no—
96#124×C139—21no—
97#123×C139—41no—
98#123×C139—41no—
99C22⋊Q8×C139—21no—
100#121×C139—21no—
101#121×C139—21no—
102#121×C139—21no—
103#121×C139—41no—
104#121×C139—41no—
105C4×Q8×C139C2311yescharacteristic
106C4×Q8×C139C2311yescharacteristic
107C4×D4×C139—21no—
108C4×D4×C139—21no—
109C4×D4×C139—21no—
110C4×D4×C139—21no—
111C4×D4×C139C2311yescharacteristic
112C4×D4×C139C2311yescharacteristic
113C2×C4⋊C4×C139—21no—
114#106×C139—21no—
115#106×C139D411yescharacteristic
116#106×C139D411yescharacteristic
117C4⋊C8×C139—21no—
118C4⋊C8×C139—21no—
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122C4⋊C8×C139C2311yescharacteristic
123#103×C139—21no—
124#103×C139—21no—
125#103×C139D411yescharacteristic
126#103×C139D411yescharacteristic
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—41no—
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—42no—
148#41×C139—81no—
149#41×C139—81no—
150#41×C139—81no—
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—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—41no—
164C2×D4×C139—41no—
165C2×D4×C139—41no—
166C2×D4×C139—41no—
167C2×D4×C139—41no—
168C2×D4×C139C2×D411yescharacteristic
169C2×D4×C139C2×D411yescharacteristic
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—41no—
173C22×C4×C139—41no—
174C22×C4×C139—41no—
175C22×C4×C139—41no—
176Q16×C139—42no—
177SD16×C139—22no—
178SD16×C139—41no—
179SD16×C139—42no—
180SD16×C139—81no—
181SD16×C139—81no—
182SD16×C139—81no—
183D8×C139—42no—
184D8×C139—42no—
185D8×C139—42no—
186D8×C139—81no—
187D8×C139—81no—
188D8×C139—81no—
189D8×C139—81no—
190D8×C139—81no—
191D8×C139—82no—
192M16×C139—81no—
193C2×C8×C139—21no—
194C2×C8×C139—21no—
195C2×C8×C139—21no—
196C2×C8×C139—21no—
197C2×C8×C139—21no—
198C2×C8×C139—42no—
199C2×C8×C139C2×D411yescharacteristic
200C2×C8×C139C2×D411yescharacteristic
201C2×C8×C139C2×D411yescharacteristic
202C2×C8×C139C2×D411yescharacteristic
203C4⋊C4×C139—21no—
204C4⋊C4×C139—21no—
205C4⋊C4×C139—21no—
206C4⋊C4×C139—21no—
207C4⋊C4×C139—41no—
208C4⋊C4×C139C2×D411yescharacteristic
209C4⋊C4×C139C2×D411yescharacteristic
210C4⋊C4×C139C2×D411yescharacteristic
211C4⋊C4×C139C2×D411yescharacteristic
212C22⋊C4×C139—21no—
213C22⋊C4×C139—21no—
214C22⋊C4×C139—41no—
215C22⋊C4×C139—41no—
216C22⋊C4×C139—41no—
217C22⋊C4×C139—41no—
218C22⋊C4×C139—41no—
219C22⋊C4×C139—41no—
220C42×C139—21no—
221C42×C139—21no—
222C42×C139C2411yescharacteristic
223C23×C139—21no—
224C23×C139—21no—
225C23×C139—41no—
226C23×C139—41no—
227C23×C139—41no—
228Q8×C139—21no—
229Q8×C139—21no—
230Q8×C139—21no—
231Q8×C139—21no—
232Q8×C139—41no—
233Q8×C139—41no—
234D4×C139—21no—
235D4×C139—21no—
236D4×C139—21no—
237D4×C139—21no—
238D4×C139—41no—
239D4×C139—41no—
240D4×C139—41no—
241D4×C139—41no—
242D4×C139—41no—
243D4×C139—41no—
244D4×C139—41no—
245D4×C139—41no—
246D4×C139—41no—
247D4×C139—41no—
248D4×C139—41no—
249D4×C139—41no—
250D4×C139—81no—
251D4×C139—81no—
252D4×C139—81no—
253D4×C139—82no—
254D4×C139—82no—
255D4×C139—82no—
256D4×C139—161no—
257D4×C139—161no—
258C2×C4×C139—21no—
259C2×C4×C139—21no—
260C2×C4×C139—21no—
261C2×C4×C139—21no—
262C2×C4×C139—21no—
263C2×C4×C139—21no—
264C2×C4×C139—41no—
265C2×C4×C139—41no—
266C2×C4×C139—41no—
267C2×C4×C139—41no—
268C2×C4×C139—41no—
269C2×C4×C139—82no—
270C2×C4×C139—82no—
271C2×C4×C139—82no—
272C2×C4×C139—161no—
273C2×C4×C139C22×D411yescharacteristic
274C2×C4×C139C22×D411yescharacteristic
275C2×C4×C139H(5,𝔽2)11yescharacteristic
276C8×C139—21no—
277C8×C139—21no—
278C8×C139—21no—
279C8×C139—41no—
280C8×C139—41no—
281C8×C139—41no—
282C8×C139—41no—
283C8×C139—41no—
284C8×C139AGL(1,ℤ/8)12yes—
285C22×C139—41no—
286C22×C139—41no—
287C22×C139—41no—
288C22×C139—41no—
289C22×C139—41no—
290C22×C139—41no—
291C22×C139—81no—
292C22×C139—81no—
293C22×C139—81no—
294C22×C139—81no—
295C22×C139—81no—
296C22×C139—81no—
297C22×C139—81no—
298C22×C139—81no—
299C22×C139—81no—
300C22×C139D4211yescharacteristic
301C4×C139—21no—
302C4×C139—41no—
303C4×C139—41no—
304C4×C139—41no—
305C4×C139—41no—
306C4×C139—41no—
307C4×C139—41no—
308C4×C139—81no—
309C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C139#57511yescharacteristic
311C4×C139#57611yescharacteristic
312C4×C139#57611yescharacteristic
313C2×C139—81no—
314C2×C139—81no—
315C2×C139—161no—
316C2×C139—161no—
317C2×C139—161no—
318C2×C139#326811yescharacteristic
319C2×C139#327411yescharacteristic
320C2×C139#328811yescharacteristic
321#20256C13911yesmaximal, characteristic, direct product factor, Sylow
322C139#2025611yescharacteristic, direct product factor, Sylow
323#3399C2×C13911yescharacteristic, complemented
324#3399C2×C13911yescharacteristic, complemented
325#3332C2×C13911yescharacteristic, complemented
326#3284C2×C13911yescharacteristic, complemented
327#1721C2×C13911yescharacteristic, complemented
328#1702C2×C13911yescharacteristic, complemented
329#1687C2×C13911yescharacteristic, complemented
330#1686C2×C13911yescharacteristic, complemented
331#1667C2×C13911yescharacteristic, complemented
332#1640C2×C13911yescharacteristic, complemented
333#1625C2×C13911yescharacteristic, complemented
334#1621C2×C13911yescharacteristic, complemented
335#1621C2×C13911yescharacteristic, complemented
336#1592C2×C13911yescharacteristic, complemented
337#1582C2×C13911yescharacteristic, complemented
338C2×#135—21no—
339#559C22×C13911yescharacteristic
340#550C22×C13911yescharacteristic
341#550C22×C13911yescharacteristic
342#547C22×C13911yescharacteristic
343#496—21no—
344#496—21no—
345#493C22×C13911yescharacteristic
346#493C22×C13911yescharacteristic
347#493C22×C13911yescharacteristic
348#492C22×C13911yescharacteristic
349#486C22×C13911yescharacteristic
350#486C22×C13911yescharacteristic
351#481—21no—
352#475C22×C13911yescharacteristic
353#469—21no—
354#465—21no—
355#463—21no—
356#463—21no—
357#462C22×C13911yescharacteristic
358#460C22×C13911yescharacteristic
359#460C22×C13911yescharacteristic
360#459—21no—
361#459—21no—
362#459C22×C13911yescharacteristic
363#459C22×C13911yescharacteristic
364#459C22×C13911yescharacteristic
365#459C22×C13911yescharacteristic
366#452—21no—
367#449—21no—
368#449—21no—
369#446C22×C13911yescharacteristic
370#446C22×C13911yescharacteristic
371#442—21no—
372#442—21no—
373C4×SD16C22×C13911yescharacteristic
374C4×SD16C22×C13911yescharacteristic
375#436C22×C13911yescharacteristic
376C8×D4C22×C13911yescharacteristic
377#417—21no—
378#335C22×C13911yescharacteristic
379#334C22×C13911yescharacteristic
380#332C22×C13911yescharacteristic
381#331C22×C13911yescharacteristic
382#331C22×C13911yescharacteristic
383#331C22×C13911yescharacteristic
384Q8⋊C8C22×C13911yescharacteristic
385Q8⋊C8C22×C13911yescharacteristic
386D4⋊C8C22×C13911yescharacteristic
387D4⋊C8C22×C13911yescharacteristic
388#322C22×C13911yescharacteristic
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392#135—44no—
393C2×Q16—21no—
394C2×SD16—21no—
395C2×SD16—21no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16D4×C13911yescharacteristic
399C2×SD16D4×C13911yescharacteristic
400C2×D8—21no—
401C2×D8—21no—
402C2×D8—21no—
403C2×D8—21no—
404C2×D8—21no—
405C2×D8—21no—
406C2×D8—21no—
407C2×D8—21no—
408C2×D8—41no—
409C2×M16—21no—
410C22×C8—21no—
411C4⋊Q8C23×C13911yescharacteristic
412#127—21no—
413#127—21no—
414#127C23×C13911yescharacteristic
415#127C23×C13911yescharacteristic
416#127C23×C13911yescharacteristic
417#124—21no—
418#124—21no—
419#123—41no—
420#123—41no—
421C22⋊Q8—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—41no—
426#121—41no—
427C4×Q8C23×C13911yescharacteristic
428C4×Q8C23×C13911yescharacteristic
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4C23×C13911yescharacteristic
434C4×D4C23×C13911yescharacteristic
435C2×C4⋊C4—21no—
436#106—21no—
437#106D4×C13911yescharacteristic
438#106D4×C13911yescharacteristic
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8C23×C13911yescharacteristic
442C4⋊C8C23×C13911yescharacteristic
443C4⋊C8C23×C13911yescharacteristic
444C4⋊C8C23×C13911yescharacteristic
445#103—21no—
446#103—21no—
447#103D4×C13911yescharacteristic
448#103D4×C13911yescharacteristic
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—21no—
456#102—21no—
457#102—41no—
458#102D4×C13911yescharacteristic
459#102D4×C13911yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—21no—
462#97—21no—
463#97—21no—
464C4×C8C23×C13911yescharacteristic
465C4×C8C23×C13911yescharacteristic
466C4×C8C23×C13911yescharacteristic
467#41—42no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—81no—
473C2×Q8—21no—
474C2×Q8C2×D4×C13911yescharacteristic
475C2×Q8C2×D4×C13911yescharacteristic
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4C2×D4×C13911yescharacteristic
491C2×D4C2×D4×C13911yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498Q16—42no—
499SD16—22no—
500SD16—41no—
501SD16—42no—
502SD16—81no—
503SD16—81no—
504SD16—81no—
505D8—42no—
506D8—42no—
507D8—42no—
508D8—81no—
509D8—81no—
510D8—81no—
511D8—81no—
512D8—81no—
513D8—82no—
514M16—81no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—42no—
521C2×C8C2×D4×C13911yescharacteristic
522C2×C8C2×D4×C13911yescharacteristic
523C2×C8C2×D4×C13911yescharacteristic
524C2×C8C2×D4×C13911yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C13911yescharacteristic
531C4⋊C4C2×D4×C13911yescharacteristic
532C4⋊C4C2×D4×C13911yescharacteristic
533C4⋊C4C2×D4×C13911yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C42—21no—
543C42—21no—
544C42C24×C13911yescharacteristic
545C23—21no—
546C23—21no—
547C23—41no—
548C23—41no—
549C23—41no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—21no—
554Q8—41no—
555Q8—41no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—81no—
574D4—81no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—161no—
579D4—161no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—161no—
595C2×C4C22×D4×C13911yescharacteristic
596C2×C4C22×D4×C13911yescharacteristic
597C2×C4H(5,𝔽2)×C13911yescharacteristic
598C8—21no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C8—41no—
606C8AGL(1,ℤ/8)×C13912yes—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22D42×C13911yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
632C4#575×C13911yescharacteristic
633C4#576×C13911yescharacteristic
634C4#576×C13911yescharacteristic
635C2—81no—
636C2—81no—
637C2—161no—
638C2—161no—
639C2—161no—
640C2#3268×C13911yescharacteristic
641C2#3274×C13911yescharacteristic
642C2#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. #3399×C139C2semidirect
3. #3332×C139C2semidirect
4. #3284×C139C2semidirect
5. #1721×C139C2semidirect
6. #1702×C139C2semidirect
7. #1687×C139C2semidirect
8. #1686×C139C2semidirect
9. #1667×C139C2semidirect
10. #1640×C139C2semidirect
11. #1625×C139C2semidirect
12. #1621×C139C2semidirect
13. #1621×C139C2semidirect
14. #1592×C139C2semidirect
15. #1582×C139C2semidirect
321. #20256C139direct (N × H)
322. C139#20256direct (N × H)
323. #3399C2×C139semidirect
324. #3399C2×C139semidirect
325. #3332C2×C139semidirect
326. #3284C2×C139semidirect
327. #1721C2×C139semidirect
328. #1702C2×C139semidirect
329. #1687C2×C139semidirect
330. #1686C2×C139semidirect
331. #1667C2×C139semidirect
332. #1640C2×C139semidirect
333. #1625C2×C139semidirect
334. #1621C2×C139semidirect
335. #1621C2×C139semidirect
336. #1592C2×C139semidirect
337. #1582C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3399×C1392
#3332×C1392
#3284×C1392
#1721×C1392
#1702×C1392
#1687×C1392
#1686×C1392
#1667×C1392
#1640×C1392
#1625×C1392
#1621×C1392
#1592×C1392
#1582×C1392
#20256139