Finite Group Databasebeta

← C139×#19825 #48014421

Subgroups — C139×#19825 #48014421

Order 35584.

642 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#3394×C139C211yesmaximal, characteristic, complemented
2#3361×C139C211yesmaximal, characteristic, complemented
3#3324×C139C211yesmaximal, characteristic, complemented
4#3295×C139C211yesmaximal, characteristic, complemented
5#1717×C139C211yesmaximal, characteristic, complemented
6#1697×C139C211yesmaximal, characteristic, complemented
7#1682×C139C211yesmaximal, characteristic, complemented
8#1678×C139C211yesmaximal, characteristic, complemented
9#1665×C139C211yesmaximal, characteristic, complemented
10#1644×C139C211yesmaximal, characteristic, complemented
11#1638×C139C211yesmaximal, characteristic, complemented
12#1620×C139C211yesmaximal, characteristic, complemented
13#1619×C139C211yesmaximal, characteristic
14#1583×C139C211yesmaximal, characteristic, complemented
15SD16⋊C8×C139C211yesmaximal, characteristic, complemented
16#559×C139C2211yescharacteristic, complemented
17#556×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19D42×C139C2211yescharacteristic
20#495×C139—21no—
21#493×C139C2211yescharacteristic
22#492×C139C2211yescharacteristic, complemented
23#488×C139—21no—
24#487×C139C2211yescharacteristic, complemented
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic, complemented
28#482×C139—21no—
29#481×C139—21no—
30#478×C139—21no—
31#477×C139C2211yescharacteristic, complemented
32#476×C139C2211yescharacteristic
33#474×C139C2211yescharacteristic
34#468×C139—21no—
35#465×C139—21no—
36#464×C139—21no—
37#463×C139—21no—
38#463×C139—21no—
39#462×C139C2211yescharacteristic, complemented
40#460×C139C2211yescharacteristic
41#460×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#450×C139—21no—
45#450×C139—21no—
46C8×Q8×C139C2211yescharacteristic, complemented
47C8×Q8×C139C2211yescharacteristic, complemented
48C4×SD16×C139—21no—
49C4×SD16×C139C2211yescharacteristic
50C4×SD16×C139C2211yescharacteristic
51C4×D8×C139—21no—
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#418×C139—21no—
55C2×#102×C139—21no—
56#335×C139C2211yescharacteristic, complemented
57#334×C139C2211yescharacteristic, complemented
58#333×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic, complemented
62Q8⋊C8×C139C2211yescharacteristic, complemented
63Q8⋊C8×C139C2211yescharacteristic, complemented
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic, complemented
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C2×Q16×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×D8×C139—21no—
78C2×D8×C139—41no—
79C2×M16×C139—21no—
80C22×C8×C139—21no—
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83#127×C139C2311yescharacteristic
84#127×C139C2311yescharacteristic
85#126×C139—41no—
86#125×C139—21no—
87#124×C139—21no—
88#124×C139—21no—
89#124×C139—21no—
90#123×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—41no—
94#121×C139—21no—
95#121×C139—21no—
96#120×C139—41no—
97C4×Q8×C139—21no—
98C4×Q8×C139C2311yescharacteristic
99C4×Q8×C139C2311yescharacteristic
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139C2311yescharacteristic
104C4×D4×C139C2311yescharacteristic
105#117×C139—21no—
106C2×C4⋊C4×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—41no—
121#103×C139D411yescharacteristic
122#103×C139D411yescharacteristic
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—21no—
133#102×C139—21no—
134#102×C139—21no—
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139C4×C8×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C24×C139—41no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139C2×D411yescharacteristic
148C2×Q8×C139C2×D411yescharacteristic
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×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—81no—
160C2×D4×C139—81no—
161C2×D4×C139C2×D411yescharacteristic
162C2×D4×C139C2×D411yescharacteristic
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167Q16×C139—81no—
168SD16×C139—22no—
169SD16×C139—41no—
170SD16×C139—42no—
171SD16×C139—81no—
172SD16×C139—81no—
173SD16×C139—81no—
174D8×C139—42no—
175D8×C139—81no—
176D8×C139—82no—
177M16×C139—81no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139—21no—
182C2×C8×C139—21no—
183C2×C8×C139—81no—
184C2×C8×C139C2×D411yescharacteristic
185C2×C8×C139C2×D411yescharacteristic
186C2×C8×C139C2×D411yescharacteristic
187C2×C8×C139C2×D411yescharacteristic
188C4⋊C4×C139—21no—
189C4⋊C4×C139—21no—
190C4⋊C4×C139—21no—
191C4⋊C4×C139—21no—
192C4⋊C4×C139—21no—
193C4⋊C4×C139—21no—
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—
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—
218C23×C139—82no—
219C23×C139—82no—
220C23×C139—161no—
221Q8×C139—21no—
222Q8×C139—21no—
223Q8×C139—21no—
224Q8×C139—21no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—81no—
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—21no—
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—81no—
240D4×C139—81no—
241D4×C139—82no—
242D4×C139—82no—
243D4×C139#13512yes—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—161no—
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—22no—
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×C139—164no—
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—81no—
292C4×C139—81no—
293C4×C139C2×#13511yescharacteristic
294C4×C139#57511yescharacteristic
295C4×C139#57611yescharacteristic
296C4×C139#57711yescharacteristic
297C2×C139—42no—
298C2×C139—81no—
299C2×C139—161no—
300C2×C139—161no—
301C2×C139#326811yescharacteristic
302C2×C139#328211yescharacteristic
303C2×C139#328811yescharacteristic
304#19825C13911yesmaximal, characteristic, direct product factor, Sylow
305C139#1982511yescharacteristic, direct product factor, Sylow
306#3394C2×C13911yescharacteristic, complemented
307#3361C2×C13911yescharacteristic, complemented
308#3324C2×C13911yescharacteristic, complemented
309#3295C2×C13911yescharacteristic, complemented
310#1717C2×C13911yescharacteristic, complemented
311#1697C2×C13911yescharacteristic, complemented
312#1682C2×C13911yescharacteristic, complemented
313#1678C2×C13911yescharacteristic, complemented
314#1665C2×C13911yescharacteristic, complemented
315#1644C2×C13911yescharacteristic, complemented
316#1638C2×C13911yescharacteristic, complemented
317#1620C2×C13911yescharacteristic, complemented
318#1619C2×C13911yescharacteristic
319#1583C2×C13911yescharacteristic, complemented
320SD16⋊C8C2×C13911yescharacteristic, complemented
321#559C22×C13911yescharacteristic, complemented
322#556C22×C13911yescharacteristic
323#554C22×C13911yescharacteristic
324D42C22×C13911yescharacteristic
325#495—21no—
326#493C22×C13911yescharacteristic
327#492C22×C13911yescharacteristic, complemented
328#488—21no—
329#487C22×C13911yescharacteristic, complemented
330#486C22×C13911yescharacteristic
331#486C22×C13911yescharacteristic
332#486C22×C13911yescharacteristic, complemented
333#482—21no—
334#481—21no—
335#478—21no—
336#477C22×C13911yescharacteristic, complemented
337#476C22×C13911yescharacteristic
338#474C22×C13911yescharacteristic
339#468—21no—
340#465—21no—
341#464—21no—
342#463—21no—
343#463—21no—
344#462C22×C13911yescharacteristic, complemented
345#460C22×C13911yescharacteristic
346#460C22×C13911yescharacteristic
347#459C22×C13911yescharacteristic
348#459C22×C13911yescharacteristic
349#450—21no—
350#450—21no—
351C8×Q8C22×C13911yescharacteristic, complemented
352C8×Q8C22×C13911yescharacteristic, complemented
353C4×SD16—21no—
354C4×SD16C22×C13911yescharacteristic
355C4×SD16C22×C13911yescharacteristic
356C4×D8—21no—
357#436C22×C13911yescharacteristic
358C8×D4C22×C13911yescharacteristic
359#418—21no—
360C2×#102—21no—
361#335C22×C13911yescharacteristic, complemented
362#334C22×C13911yescharacteristic, complemented
363#333C22×C13911yescharacteristic, complemented
364#332C22×C13911yescharacteristic, complemented
365#331C22×C13911yescharacteristic
366#331C22×C13911yescharacteristic, complemented
367Q8⋊C8C22×C13911yescharacteristic, complemented
368Q8⋊C8C22×C13911yescharacteristic, complemented
369D4⋊C8C22×C13911yescharacteristic
370D4⋊C8C22×C13911yescharacteristic
371#322C22×C13911yescharacteristic, complemented
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C13911yescharacteristic
380C2×SD16D4×C13911yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C13911yescharacteristic
387C4⋊Q8C23×C13911yescharacteristic
388#127C23×C13911yescharacteristic
389#127C23×C13911yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C13911yescharacteristic
404C4×Q8C23×C13911yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C13911yescharacteristic
409C4×D4C23×C13911yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C13911yescharacteristic
416#106D4×C13911yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C13911yescharacteristic
420C4⋊C8C23×C13911yescharacteristic
421C4⋊C8C23×C13911yescharacteristic
422C4⋊C8C23×C13911yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C13911yescharacteristic
427#103D4×C13911yescharacteristic
428#102—21no—
429#102—21no—
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—21no—
439#102—21no—
440#102D4×C13911yescharacteristic
441#102D4×C13911yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C13911yescharacteristic
447C4×C8C23×C13911yescharacteristic
448C4×C8C23×C13911yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C13911yescharacteristic
453C2×Q8C2×D4×C13911yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C13911yescharacteristic
467C2×D4C2×D4×C13911yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C13911yescharacteristic
490C2×C8C2×D4×C13911yescharacteristic
491C2×C8C2×D4×C13911yescharacteristic
492C2×C8C2×D4×C13911yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C13911yescharacteristic
503C4⋊C4C2×D4×C13911yescharacteristic
504C4⋊C4C2×D4×C13911yescharacteristic
505C4⋊C4C2×D4×C13911yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C13911yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C13912yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C13911yescharacteristic
564C2×C4C22×D4×C13911yescharacteristic
565C2×C4H(5,𝔽2)×C13911yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C13911yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C13911yescharacteristic
599C4#575×C13911yescharacteristic
600C4#576×C13911yescharacteristic
601C4#577×C13911yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2#3268×C13911yescharacteristic
607C2#3282×C13911yescharacteristic
608C2#3288×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#1619×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. #3394×C139C2semidirect
2. #3361×C139C2semidirect
3. #3324×C139C2semidirect
4. #3295×C139C2semidirect
5. #1717×C139C2semidirect
6. #1697×C139C2semidirect
7. #1682×C139C2semidirect
8. #1678×C139C2semidirect
9. #1665×C139C2semidirect
10. #1644×C139C2semidirect
11. #1638×C139C2semidirect
12. #1620×C139C2semidirect
14. #1583×C139C2semidirect
15. SD16⋊C8×C139C2semidirect
16. #559×C139C22semidirect
22. #492×C139C22semidirect
24. #487×C139C22semidirect
27. #486×C139C22semidirect
31. #477×C139C22semidirect
39. #462×C139C22semidirect
46. C8×Q8×C139C22semidirect
47. C8×Q8×C139C22semidirect
56. #335×C139C22semidirect
57. #334×C139C22semidirect
58. #333×C139C22semidirect
59. #332×C139C22semidirect
61. #331×C139C22semidirect
62. Q8⋊C8×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
66. #322×C139C22semidirect
304. #19825C139direct (N × H)
305. C139#19825direct (N × H)
306. #3394C2×C139semidirect
307. #3361C2×C139semidirect
308. #3324C2×C139semidirect
309. #3295C2×C139semidirect
310. #1717C2×C139semidirect
311. #1697C2×C139semidirect
312. #1682C2×C139semidirect
313. #1678C2×C139semidirect
314. #1665C2×C139semidirect
315. #1644C2×C139semidirect
316. #1638C2×C139semidirect
317. #1620C2×C139semidirect
319. #1583C2×C139semidirect
320. SD16⋊C8C2×C139semidirect
321. #559C22×C139semidirect
327. #492C22×C139semidirect
329. #487C22×C139semidirect
332. #486C22×C139semidirect
336. #477C22×C139semidirect
344. #462C22×C139semidirect
351. C8×Q8C22×C139semidirect
352. C8×Q8C22×C139semidirect
361. #335C22×C139semidirect
362. #334C22×C139semidirect
363. #333C22×C139semidirect
364. #332C22×C139semidirect
366. #331C22×C139semidirect
367. Q8⋊C8C22×C139semidirect
368. Q8⋊C8C22×C139semidirect
371. #322C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3394×C1392
#3361×C1392
#3324×C1392
#3295×C1392
#1717×C1392
#1697×C1392
#1682×C1392
#1678×C1392
#1665×C1392
#1644×C1392
#1638×C1392
#1620×C1392
#1619×C1392
#1583×C1392
SD16⋊C8×C1392
#19825139