Finite Group Databasebeta

← C139×#20176 #48014772

Subgroups — C139×#20176 #48014772

Order 35584.

660 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#3398×C139C211yesmaximal, characteristic, complemented
2#3386×C139C211yesmaximal, characteristic, complemented
3#3324×C139C211yesmaximal, characteristic
4D4×SD16×C139C211yesmaximal, characteristic
5#1722×C139C211yesmaximal, characteristic, complemented
6#1702×C139C211yesmaximal, characteristic, complemented
7#1693×C139C211yesmaximal, characteristic, complemented
8#1686×C139C211yesmaximal, characteristic, complemented
9#1669×C139C211yesmaximal, characteristic, complemented
10#1650×C139C211yesmaximal, characteristic, complemented
11#1649×C139C211yesmaximal, characteristic, complemented
12#1639×C139C211yesmaximal, characteristic
13#1626×C139C211yesmaximal, characteristic, complemented
14#1592×C139C211yesmaximal, characteristic, complemented
15#1582×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139—21no—
17#557×C139C2211yescharacteristic, complemented
18#556×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20D42×C139C2211yescharacteristic
21#501×C139—21no—
22#500×C139C2211yescharacteristic, complemented
23#500×C139C2211yescharacteristic, complemented
24#497×C139—21no—
25#494×C139C2211yescharacteristic, complemented
26#492×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#482×C139—21no—
30#478×C139—21no—
31#477×C139—21no—
32#475×C139C2211yescharacteristic, complemented
33#474×C139C2211yescharacteristic
34#474×C139C2211yescharacteristic
35#468×C139—21no—
36#465×C139—21no—
37#464×C139—21no—
38#462×C139—21no—
39#462×C139C2211yescharacteristic, complemented
40#461×C139C2211yescharacteristic
41#461×C139C2211yescharacteristic
42#460×C139C2211yescharacteristic
43#460×C139C2211yescharacteristic
44#450×C139—21no—
45#450×C139—21no—
46#448×C139—21no—
47#446×C139C2211yescharacteristic, complemented
48#446×C139C2211yescharacteristic, complemented
49#441×C139—21no—
50#440×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55#418×C139—21no—
56#335×C139C2211yescharacteristic, complemented
57#334×C139C2211yescharacteristic, complemented
58#332×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#332×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic, complemented
63Q8⋊C8×C139C2211yescharacteristic, complemented
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic, complemented
67C22×Q8×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139—21no—
79C2×SD16×C139—44no—
80C2×SD16×C139D411yescharacteristic
81C2×SD16×C139D411yescharacteristic
82C2×M16×C139—21no—
83C22×C8×C139—21no—
84C4⋊Q8×C139—21no—
85C4⋊Q8×C139—21no—
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88C4⋊Q8×C139C2311yescharacteristic
89#127×C139C2311yescharacteristic
90#126×C139—41no—
91#125×C139—21no—
92#125×C139—41no—
93#124×C139—21no—
94C22⋊Q8×C139—21no—
95C22⋊Q8×C139—21no—
96C22⋊Q8×C139—41no—
97#121×C139—21no—
98#121×C139—21no—
99#120×C139—41no—
100C4×Q8×C139—21no—
101C4×Q8×C139—21no—
102C4×Q8×C139—21no—
103C4×Q8×C139C2311yescharacteristic
104C4×Q8×C139C2311yescharacteristic
105C4×D4×C139—21no—
106C4×D4×C139C2311yescharacteristic
107C4×D4×C139C2311yescharacteristic
108#117×C139—21no—
109#107×C139—21no—
110#107×C139—21no—
111#107×C139—21no—
112#107×C139—21no—
113#107×C139—41no—
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×C139—21no—
126#103×C139—21no—
127#103×C139D411yescharacteristic
128#103×C139D411yescharacteristic
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
145C24×C139—41no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—41no—
150C2×Q8×C139—42no—
151C2×Q8×C139—81no—
152C2×Q8×C139C2×D411yescharacteristic
153C2×Q8×C139C2×D411yescharacteristic
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—41no—
158C2×D4×C139—41no—
159C2×D4×C139—42no—
160C2×D4×C139—42no—
161C2×D4×C139—81no—
162C2×D4×C139—81no—
163C2×D4×C139C2×D411yescharacteristic
164C2×D4×C139C2×D411yescharacteristic
165C22×C4×C139—21no—
166C22×C4×C139—21no—
167C22×C4×C139—41no—
168Q16×C139—42no—
169Q16×C139—81no—
170Q16×C139—81no—
171SD16×C139—22no—
172SD16×C139—22no—
173SD16×C139—42no—
174SD16×C139—42no—
175SD16×C139—42no—
176SD16×C139—81no—
177SD16×C139—81no—
178SD16×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—42no—
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—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139—41no—
201C4⋊C4×C139—41no—
202C4⋊C4×C139—41no—
203C4⋊C4×C139C2×D411yescharacteristic
204C4⋊C4×C139C2×D411yescharacteristic
205C4⋊C4×C139C2×D411yescharacteristic
206C4⋊C4×C139C2×D411yescharacteristic
207C22⋊C4×C139—21no—
208C22⋊C4×C139—21no—
209C22⋊C4×C139—41no—
210C22⋊C4×C139—41no—
211C22⋊C4×C139—41no—
212C22⋊C4×C139—41no—
213C42×C139—21no—
214C42×C139—21no—
215C42×C139—41no—
216C42×C139—41no—
217C42×C139C2411yescharacteristic
218C23×C139—21no—
219C23×C139—21no—
220C23×C139—41no—
221C23×C139—82no—
222C23×C139—82no—
223C23×C139—161no—
224Q8×C139—21no—
225Q8×C139—21no—
226Q8×C139—21no—
227Q8×C139—21no—
228Q8×C139—41no—
229Q8×C139—41no—
230Q8×C139—41no—
231Q8×C139—41no—
232Q8×C139—41no—
233Q8×C139—41no—
234Q8×C139—82no—
235D4×C139—21no—
236D4×C139—21no—
237D4×C139—21no—
238D4×C139—41no—
239D4×C139—41no—
240D4×C139—41no—
241D4×C139—41no—
242D4×C139—81no—
243D4×C139—82no—
244D4×C139—82no—
245D4×C139#13712yes—
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—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—82no—
260C2×C4×C139C22×D411yescharacteristic
261C2×C4×C139C22×D411yescharacteristic
262C2×C4×C139H(5,𝔽2)11yescharacteristic
263C8×C139—21no—
264C8×C139—21no—
265C8×C139—21no—
266C8×C139—41no—
267C8×C139—41no—
268C8×C139—41no—
269C8×C139—41no—
270C8×C139—41no—
271C8×C139AGL(1,ℤ/8)12yes—
272C22×C139—22no—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—164no—
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—81no—
293C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C139C2×#13711yescharacteristic
295C4×C139#57611yescharacteristic
296C4×C139#57711yescharacteristic
297C2×C139—42no—
298C2×C139—81no—
299C2×C139—161no—
300C2×C139#326611yescharacteristic
301C2×C139#327411yescharacteristic
302C2×C139#328911yescharacteristic
303#20176C13911yesmaximal, characteristic, direct product factor, Sylow
304C139#2017611yescharacteristic, direct product factor, Sylow
305#3398C2×C13911yescharacteristic, complemented
306#3386C2×C13911yescharacteristic, complemented
307#3324C2×C13911yescharacteristic
308D4×SD16C2×C13911yescharacteristic
309#1722C2×C13911yescharacteristic, complemented
310#1702C2×C13911yescharacteristic, complemented
311#1693C2×C13911yescharacteristic, complemented
312#1686C2×C13911yescharacteristic, complemented
313#1669C2×C13911yescharacteristic, complemented
314#1650C2×C13911yescharacteristic, complemented
315#1649C2×C13911yescharacteristic, complemented
316#1639C2×C13911yescharacteristic
317#1626C2×C13911yescharacteristic, complemented
318#1592C2×C13911yescharacteristic, complemented
319#1582C2×C13911yescharacteristic, complemented
320C22×SD16—21no—
321#557C22×C13911yescharacteristic, complemented
322#556C22×C13911yescharacteristic
323D4×Q8C22×C13911yescharacteristic
324D42C22×C13911yescharacteristic
325#501—21no—
326#500C22×C13911yescharacteristic, complemented
327#500C22×C13911yescharacteristic, complemented
328#497—21no—
329#494C22×C13911yescharacteristic, complemented
330#492C22×C13911yescharacteristic
331#486C22×C13911yescharacteristic
332#486C22×C13911yescharacteristic
333#482—21no—
334#478—21no—
335#477—21no—
336#475C22×C13911yescharacteristic, complemented
337#474C22×C13911yescharacteristic
338#474C22×C13911yescharacteristic
339#468—21no—
340#465—21no—
341#464—21no—
342#462—21no—
343#462C22×C13911yescharacteristic, complemented
344#461C22×C13911yescharacteristic
345#461C22×C13911yescharacteristic
346#460C22×C13911yescharacteristic
347#460C22×C13911yescharacteristic
348#450—21no—
349#450—21no—
350#448—21no—
351#446C22×C13911yescharacteristic, complemented
352#446C22×C13911yescharacteristic, complemented
353#441—21no—
354#440—21no—
355C4×SD16C22×C13911yescharacteristic
356C4×SD16C22×C13911yescharacteristic
357#436C22×C13911yescharacteristic
358C8×D4C22×C13911yescharacteristic
359#418—21no—
360#335C22×C13911yescharacteristic, complemented
361#334C22×C13911yescharacteristic, complemented
362#332C22×C13911yescharacteristic, complemented
363#332C22×C13911yescharacteristic, complemented
364#332C22×C13911yescharacteristic, complemented
365#331C22×C13911yescharacteristic
366Q8⋊C8C22×C13911yescharacteristic, complemented
367Q8⋊C8C22×C13911yescharacteristic, complemented
368D4⋊C8C22×C13911yescharacteristic
369D4⋊C8C22×C13911yescharacteristic
370#322C22×C13911yescharacteristic, complemented
371C22×Q8—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×Q16—21no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—44no—
384C2×SD16D4×C13911yescharacteristic
385C2×SD16D4×C13911yescharacteristic
386C2×M16—21no—
387C22×C8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C23×C13911yescharacteristic
391C4⋊Q8C23×C13911yescharacteristic
392C4⋊Q8C23×C13911yescharacteristic
393#127C23×C13911yescharacteristic
394#126—41no—
395#125—21no—
396#125—41no—
397#124—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—41no—
401#121—21no—
402#121—21no—
403#120—41no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8C23×C13911yescharacteristic
408C4×Q8C23×C13911yescharacteristic
409C4×D4—21no—
410C4×D4C23×C13911yescharacteristic
411C4×D4C23×C13911yescharacteristic
412#117—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#107—21no—
417#107—41no—
418#106—21no—
419#106D4×C13911yescharacteristic
420#106D4×C13911yescharacteristic
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8C23×C13911yescharacteristic
424C4⋊C8C23×C13911yescharacteristic
425C4⋊C8C23×C13911yescharacteristic
426C4⋊C8C23×C13911yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103D4×C13911yescharacteristic
432#103D4×C13911yescharacteristic
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—41no—
440#102D4×C13911yescharacteristic
441#102D4×C13911yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97—21no—
445#97—21no—
446C4×C8C23×C13911yescharacteristic
447C4×C8C23×C13911yescharacteristic
448C4×C8C23×C13911yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—41no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8C2×D4×C13911yescharacteristic
457C2×Q8C2×D4×C13911yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4C2×D4×C13911yescharacteristic
468C2×D4C2×D4×C13911yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472Q16—42no—
473Q16—81no—
474Q16—81no—
475SD16—22no—
476SD16—22no—
477SD16—42no—
478SD16—42no—
479SD16—42no—
480SD16—81no—
481SD16—81no—
482SD16—81no—
483M16—81no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—42no—
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—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C13911yescharacteristic
508C4⋊C4C2×D4×C13911yescharacteristic
509C4⋊C4C2×D4×C13911yescharacteristic
510C4⋊C4C2×D4×C13911yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C42—21no—
518C42—21no—
519C42—41no—
520C42—41no—
521C42C24×C13911yescharacteristic
522C23—21no—
523C23—21no—
524C23—41no—
525C23—82no—
526C23—82no—
527C23—161no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—82no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—81no—
547D4—82no—
548D4—82no—
549D4#137×C13912yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—82no—
564C2×C4C22×D4×C13911yescharacteristic
565C2×C4C22×D4×C13911yescharacteristic
566C2×C4H(5,𝔽2)×C13911yescharacteristic
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8AGL(1,ℤ/8)×C13912yes—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22D42×C13911yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
598C4C2×#137×C13911yescharacteristic
599C4#576×C13911yescharacteristic
600C4#577×C13911yescharacteristic
601C2—42no—
602C2—81no—
603C2—161no—
604C2#3266×C13911yescharacteristic
605C2#3274×C13911yescharacteristic
606C2#3289×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radicalD42×C139C22
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. #3398×C139C2semidirect
2. #3386×C139C2semidirect
5. #1722×C139C2semidirect
6. #1702×C139C2semidirect
7. #1693×C139C2semidirect
8. #1686×C139C2semidirect
9. #1669×C139C2semidirect
10. #1650×C139C2semidirect
11. #1649×C139C2semidirect
13. #1626×C139C2semidirect
14. #1592×C139C2semidirect
15. #1582×C139C2semidirect
17. #557×C139C22semidirect
22. #500×C139C22semidirect
23. #500×C139C22semidirect
25. #494×C139C22semidirect
32. #475×C139C22semidirect
39. #462×C139C22semidirect
47. #446×C139C22semidirect
48. #446×C139C22semidirect
56. #335×C139C22semidirect
57. #334×C139C22semidirect
58. #332×C139C22semidirect
59. #332×C139C22semidirect
60. #332×C139C22semidirect
62. Q8⋊C8×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
66. #322×C139C22semidirect
303. #20176C139direct (N × H)
304. C139#20176direct (N × H)
305. #3398C2×C139semidirect
306. #3386C2×C139semidirect
309. #1722C2×C139semidirect
310. #1702C2×C139semidirect
311. #1693C2×C139semidirect
312. #1686C2×C139semidirect
313. #1669C2×C139semidirect
314. #1650C2×C139semidirect
315. #1649C2×C139semidirect
317. #1626C2×C139semidirect
318. #1592C2×C139semidirect
319. #1582C2×C139semidirect
321. #557C22×C139semidirect
326. #500C22×C139semidirect
327. #500C22×C139semidirect
329. #494C22×C139semidirect
336. #475C22×C139semidirect
343. #462C22×C139semidirect
351. #446C22×C139semidirect
352. #446C22×C139semidirect
360. #335C22×C139semidirect
361. #334C22×C139semidirect
362. #332C22×C139semidirect
363. #332C22×C139semidirect
364. #332C22×C139semidirect
366. Q8⋊C8C22×C139semidirect
367. Q8⋊C8C22×C139semidirect
370. #322C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3398×C1392
#3386×C1392
#3324×C1392
D4×SD16×C1392
#1722×C1392
#1702×C1392
#1693×C1392
#1686×C1392
#1669×C1392
#1650×C1392
#1649×C1392
#1639×C1392
#1626×C1392
#1592×C1392
#1582×C1392
#20176139