Finite Group Databasebeta

← C139×#19899 #48014495

Subgroups — C139×#19899 #48014495

Order 35584.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3330×C139C211yesmaximal, characteristic, complemented
2#3325×C139C211yesmaximal, characteristic, complemented
3#3303×C139C211yesmaximal, characteristic, complemented
4#3294×C139C211yesmaximal, characteristic, complemented
5#1711×C139C211yesmaximal, characteristic, complemented
6#1699×C139C211yesmaximal, characteristic, complemented
7#1697×C139C211yesmaximal, characteristic, complemented
8#1683×C139C211yesmaximal, characteristic, complemented
9#1681×C139C211yesmaximal, characteristic, complemented
10#1646×C139C211yesmaximal, characteristic, complemented
11#1639×C139C211yesmaximal, characteristic, complemented
12#1635×C139C211yesmaximal, characteristic, complemented
13#1625×C139C211yesmaximal, characteristic, complemented
14#1589×C139C211yesmaximal, characteristic, complemented
15C8×D8×C139C211yesmaximal, characteristic, complemented
16#555×C139C2211yescharacteristic
17#547×C139C2211yescharacteristic
18#547×C139C2211yescharacteristic, complemented
19D42×C139C2211yescharacteristic
20#487×C139C2211yescharacteristic, complemented
21#487×C139C2211yescharacteristic, complemented
22#487×C139C2211yescharacteristic, complemented
23#486×C139C2211yescharacteristic
24#486×C139C2211yescharacteristic
25#486×C139C2211yescharacteristic
26#485×C139—21no—
27#484×C139—21no—
28#482×C139—21no—
29#480×C139—21no—
30#476×C139C2211yescharacteristic
31#476×C139C2211yescharacteristic, complemented
32#474×C139C2211yescharacteristic
33#474×C139C2211yescharacteristic
34#469×C139—21no—
35#468×C139—21no—
36#466×C139—21no—
37#465×C139—21no—
38#461×C139C2211yescharacteristic
39#461×C139C2211yescharacteristic, complemented
40#459×C139C2211yescharacteristic
41#459×C139C2211yescharacteristic
42#449×C139—21no—
43#449×C139—21no—
44#447×C139—21no—
45#447×C139—21no—
46C4×D8×C139C2211yescharacteristic
47C4×D8×C139C2211yescharacteristic
48#436×C139C2211yescharacteristic
49#436×C139C2211yescharacteristic, complemented
50C8×D4×C139C2211yescharacteristic
51C8×D4×C139C2211yescharacteristic, complemented
52#418×C139—21no—
53#417×C139—21no—
54#416×C139—21no—
55C2×#102×C139—21no—
56#335×C139C2211yescharacteristic, complemented
57#335×C139C2211yescharacteristic, complemented
58#333×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#332×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic
62D4⋊C8×C139C2211yescharacteristic
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic, complemented
65D4⋊C8×C139C2211yescharacteristic, complemented
66C82×C139C2211yescharacteristic, complemented
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×D8×C139—21no—
74C2×D8×C139—21no—
75C2×D8×C139D411yescharacteristic
76C2×D8×C139D411yescharacteristic
77C2×M16×C139—21no—
78C2×M16×C139—21no—
79C22×C8×C139—21no—
80C22×C8×C139—21no—
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83C4⋊Q8×C139C2311yescharacteristic
84#127×C139C2311yescharacteristic
85#124×C139—41no—
86#123×C139—41no—
87#123×C139—41no—
88C22⋊Q8×C139—21no—
89C22⋊Q8×C139—21no—
90#121×C139—21no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—21no—
94#121×C139—21no—
95#121×C139—21no—
96#120×C139—41no—
97C4×D4×C139C2311yescharacteristic
98C4×D4×C139C2311yescharacteristic
99C4×D4×C139C2311yescharacteristic
100C4×D4×C139C2311yescharacteristic
101#117×C139—21no—
102#117×C139—21no—
103C2×C4⋊C4×C139—21no—
104C2×C4⋊C4×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139D411yescharacteristic
108#107×C139D411yescharacteristic
109#106×C139—21no—
110#106×C139—21no—
111C4⋊C8×C139C2311yescharacteristic
112C4⋊C8×C139C2311yescharacteristic
113C4⋊C8×C139C2311yescharacteristic
114C4⋊C8×C139C2311yescharacteristic
115#103×C139—21no—
116#103×C139—21no—
117#103×C139—21no—
118#103×C139—21no—
119#103×C139—21no—
120#103×C139—21no—
121#103×C139—41no—
122#102×C139—21no—
123#102×C139—21no—
124#102×C139—21no—
125#102×C139—21no—
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—41no—
133#102×C139D411yescharacteristic
134#102×C139D411yescharacteristic
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C22⋊C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C24×C139—41no—
145#41×C139—42no—
146#41×C139—42no—
147#41×C139—81no—
148#41×C139—81no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—41no—
156C2×D4×C139—41no—
157C2×D4×C139—42no—
158C2×D4×C139—42no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139—41no—
162C2×D4×C139—81no—
163C2×D4×C139—81no—
164C2×D4×C139C2×D411yescharacteristic
165C2×D4×C139C2×D411yescharacteristic
166C2×D4×C139C2×D411yescharacteristic
167C2×D4×C139C2×D411yescharacteristic
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—41no—
173C22×C4×C139—41no—
174SD16×C139—81no—
175SD16×C139—81no—
176D8×C139—22no—
177D8×C139—41no—
178D8×C139—81no—
179D8×C139—81no—
180M16×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×C139—81no—
188C2×C8×C139—81no—
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
191C2×C8×C139C2×D411yescharacteristic
192C2×C8×C139C2×D411yescharacteristic
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139—41no—
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C4⋊C4×C139C2×D411yescharacteristic
204C4⋊C4×C139C2×D411yescharacteristic
205C22⋊C4×C139—21no—
206C22⋊C4×C139—21no—
207C22⋊C4×C139—21no—
208C22⋊C4×C139—21no—
209C22⋊C4×C139—41no—
210C22⋊C4×C139—41no—
211C22⋊C4×C139—41no—
212C22⋊C4×C139—41no—
213C22⋊C4×C139—41no—
214C42×C139—41no—
215C42×C139C2411yescharacteristic
216C23×C139—21no—
217C23×C139—21no—
218C23×C139—21no—
219C23×C139—21no—
220C23×C139—41no—
221C23×C139—82no—
222C23×C139—82no—
223C23×C139—161no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—41no—
228Q8×C139—81no—
229D4×C139—21no—
230D4×C139—21no—
231D4×C139—21no—
232D4×C139—21no—
233D4×C139—21no—
234D4×C139—21no—
235D4×C139—21no—
236D4×C139—41no—
237D4×C139—41no—
238D4×C139—41no—
239D4×C139—41no—
240D4×C139—81no—
241D4×C139—82no—
242D4×C139—82no—
243D4×C139—82no—
244D4×C139—82no—
245D4×C139—161no—
246D4×C139#13512yes—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—82no—
263C2×C4×C139—82no—
264C2×C4×C139C22×D411yescharacteristic
265C2×C4×C139C22×D411yescharacteristic
266C2×C4×C139H(5,𝔽2)11yescharacteristic
267C8×C139—21no—
268C8×C139—21no—
269C8×C139—21no—
270C8×C139—21no—
271C8×C139—41no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C8×C139—41no—
276C22×C139—22no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—41no—
282C22×C139—41no—
283C22×C139—41no—
284C22×C139—41no—
285C22×C139—41no—
286C22×C139—41no—
287C22×C139—41no—
288C22×C139—81no—
289C22×C139—81no—
290C22×C139—81no—
291C22×C139—164no—
292C22×C139D4211yescharacteristic
293C4×C139—21no—
294C4×C139—41no—
295C4×C139—41no—
296C4×C139—41no—
297C4×C139—41no—
298C4×C139—81no—
299C4×C139—81no—
300C4×C139—81no—
301C4×C139C2×#13511yescharacteristic
302C4×C139#57511yescharacteristic
303C4×C139#57611yescharacteristic
304C4×C139#57611yescharacteristic
305C2×C139—42no—
306C2×C139—81no—
307C2×C139—81no—
308C2×C139—81no—
309C2×C139—161no—
310C2×C139#327311yescharacteristic
311C2×C139#328011yescharacteristic
312C2×C139#329011yescharacteristic
313#19899C13911yesmaximal, characteristic, direct product factor, Sylow
314C139#1989911yescharacteristic, direct product factor, Sylow
315#3330C2×C13911yescharacteristic, complemented
316#3325C2×C13911yescharacteristic, complemented
317#3303C2×C13911yescharacteristic, complemented
318#3294C2×C13911yescharacteristic, complemented
319#1711C2×C13911yescharacteristic, complemented
320#1699C2×C13911yescharacteristic, complemented
321#1697C2×C13911yescharacteristic, complemented
322#1683C2×C13911yescharacteristic, complemented
323#1681C2×C13911yescharacteristic, complemented
324#1646C2×C13911yescharacteristic, complemented
325#1639C2×C13911yescharacteristic, complemented
326#1635C2×C13911yescharacteristic, complemented
327#1625C2×C13911yescharacteristic, complemented
328#1589C2×C13911yescharacteristic, complemented
329C8×D8C2×C13911yescharacteristic, complemented
330#555C22×C13911yescharacteristic
331#547C22×C13911yescharacteristic
332#547C22×C13911yescharacteristic, complemented
333D42C22×C13911yescharacteristic
334#487C22×C13911yescharacteristic, complemented
335#487C22×C13911yescharacteristic, complemented
336#487C22×C13911yescharacteristic, complemented
337#486C22×C13911yescharacteristic
338#486C22×C13911yescharacteristic
339#486C22×C13911yescharacteristic
340#485—21no—
341#484—21no—
342#482—21no—
343#480—21no—
344#476C22×C13911yescharacteristic
345#476C22×C13911yescharacteristic, complemented
346#474C22×C13911yescharacteristic
347#474C22×C13911yescharacteristic
348#469—21no—
349#468—21no—
350#466—21no—
351#465—21no—
352#461C22×C13911yescharacteristic
353#461C22×C13911yescharacteristic, complemented
354#459C22×C13911yescharacteristic
355#459C22×C13911yescharacteristic
356#449—21no—
357#449—21no—
358#447—21no—
359#447—21no—
360C4×D8C22×C13911yescharacteristic
361C4×D8C22×C13911yescharacteristic
362#436C22×C13911yescharacteristic
363#436C22×C13911yescharacteristic, complemented
364C8×D4C22×C13911yescharacteristic
365C8×D4C22×C13911yescharacteristic, complemented
366#418—21no—
367#417—21no—
368#416—21no—
369C2×#102—21no—
370#335C22×C13911yescharacteristic, complemented
371#335C22×C13911yescharacteristic, complemented
372#333C22×C13911yescharacteristic, complemented
373#332C22×C13911yescharacteristic, complemented
374#332C22×C13911yescharacteristic, complemented
375#331C22×C13911yescharacteristic
376D4⋊C8C22×C13911yescharacteristic
377D4⋊C8C22×C13911yescharacteristic
378D4⋊C8C22×C13911yescharacteristic, complemented
379D4⋊C8C22×C13911yescharacteristic, complemented
380C82C22×C13911yescharacteristic, complemented
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C13911yescharacteristic
390C2×D8D4×C13911yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C13911yescharacteristic
396C4⋊Q8C23×C13911yescharacteristic
397C4⋊Q8C23×C13911yescharacteristic
398#127C23×C13911yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C13911yescharacteristic
412C4×D4C23×C13911yescharacteristic
413C4×D4C23×C13911yescharacteristic
414C4×D4C23×C13911yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C13911yescharacteristic
422#107D4×C13911yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C13911yescharacteristic
426C4⋊C8C23×C13911yescharacteristic
427C4⋊C8C23×C13911yescharacteristic
428C4⋊C8C23×C13911yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—41no—
447#102D4×C13911yescharacteristic
448#102D4×C13911yescharacteristic
449#102D4×C13911yescharacteristic
450#102D4×C13911yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C13911yescharacteristic
456C4×C8C23×C13911yescharacteristic
457C4×C8C23×C13911yescharacteristic
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C13911yescharacteristic
479C2×D4C2×D4×C13911yescharacteristic
480C2×D4C2×D4×C13911yescharacteristic
481C2×D4C2×D4×C13911yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C13911yescharacteristic
504C2×C8C2×D4×C13911yescharacteristic
505C2×C8C2×D4×C13911yescharacteristic
506C2×C8C2×D4×C13911yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C13911yescharacteristic
516C4⋊C4C2×D4×C13911yescharacteristic
517C4⋊C4C2×D4×C13911yescharacteristic
518C4⋊C4C2×D4×C13911yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C13911yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4#135×C13912yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C13911yescharacteristic
579C2×C4C22×D4×C13911yescharacteristic
580C2×C4H(5,𝔽2)×C13911yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C13911yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C13911yescharacteristic
616C4#575×C13911yescharacteristic
617C4#576×C13911yescharacteristic
618C4#576×C13911yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2#3273×C13911yescharacteristic
625C2#3280×C13911yescharacteristic
626C2#3290×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. #3330×C139C2semidirect
2. #3325×C139C2semidirect
3. #3303×C139C2semidirect
4. #3294×C139C2semidirect
5. #1711×C139C2semidirect
6. #1699×C139C2semidirect
7. #1697×C139C2semidirect
8. #1683×C139C2semidirect
9. #1681×C139C2semidirect
10. #1646×C139C2semidirect
11. #1639×C139C2semidirect
12. #1635×C139C2semidirect
13. #1625×C139C2semidirect
14. #1589×C139C2semidirect
15. C8×D8×C139C2semidirect
18. #547×C139C22semidirect
20. #487×C139C22semidirect
21. #487×C139C22semidirect
22. #487×C139C22semidirect
31. #476×C139C22semidirect
39. #461×C139C22semidirect
49. #436×C139C22semidirect
51. C8×D4×C139C22semidirect
56. #335×C139C22semidirect
57. #335×C139C22semidirect
58. #333×C139C22semidirect
59. #332×C139C22semidirect
60. #332×C139C22semidirect
64. D4⋊C8×C139C22semidirect
65. D4⋊C8×C139C22semidirect
66. C82×C139C22semidirect
313. #19899C139direct (N × H)
314. C139#19899direct (N × H)
315. #3330C2×C139semidirect
316. #3325C2×C139semidirect
317. #3303C2×C139semidirect
318. #3294C2×C139semidirect
319. #1711C2×C139semidirect
320. #1699C2×C139semidirect
321. #1697C2×C139semidirect
322. #1683C2×C139semidirect
323. #1681C2×C139semidirect
324. #1646C2×C139semidirect
325. #1639C2×C139semidirect
326. #1635C2×C139semidirect
327. #1625C2×C139semidirect
328. #1589C2×C139semidirect
329. C8×D8C2×C139semidirect
332. #547C22×C139semidirect
334. #487C22×C139semidirect
335. #487C22×C139semidirect
336. #487C22×C139semidirect
345. #476C22×C139semidirect
353. #461C22×C139semidirect
363. #436C22×C139semidirect
365. C8×D4C22×C139semidirect
370. #335C22×C139semidirect
371. #335C22×C139semidirect
372. #333C22×C139semidirect
373. #332C22×C139semidirect
374. #332C22×C139semidirect
378. D4⋊C8C22×C139semidirect
379. D4⋊C8C22×C139semidirect
380. C82C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3330×C1392
#3325×C1392
#3303×C1392
#3294×C1392
#1711×C1392
#1699×C1392
#1697×C1392
#1683×C1392
#1681×C1392
#1646×C1392
#1639×C1392
#1635×C1392
#1625×C1392
#1589×C1392
C8×D8×C1392
#19899139