Finite Group Databasebeta

← C139×#20075 #48014671

Subgroups — C139×#20075 #48014671

Order 35584.

624 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C139C211yesmaximal, characteristic, complemented
2#3375×C139C211yesmaximal, characteristic, complemented
3#3373×C139C211yesmaximal, characteristic
4D4×Q16×C139C211yesmaximal, characteristic, complemented
5#1720×C139C211yesmaximal, characteristic, complemented
6#1692×C139C211yesmaximal, characteristic, complemented
7#1690×C139C211yesmaximal, characteristic, complemented
8#1682×C139C211yesmaximal, characteristic, complemented
9#1677×C139C211yesmaximal, characteristic
10#1645×C139C211yesmaximal, characteristic, complemented
11#1640×C139C211yesmaximal, characteristic, complemented
12#1637×C139C211yesmaximal, characteristic, complemented
13#1627×C139C211yesmaximal, characteristic
14#1587×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16C22×Q16×C139—21no—
17#559×C139C2211yescharacteristic
18Q82×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20D4×Q8×C139C2211yescharacteristic
21#498×C139—21no—
22#498×C139C2211yescharacteristic
23#494×C139C2211yescharacteristic
24#489×C139—21no—
25#489×C139—21no—
26#487×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#486×C139C2211yescharacteristic
29#486×C139C2211yescharacteristic
30#477×C139C2211yescharacteristic
31#476×C139—21no—
32#476×C139—21no—
33#476×C139C2211yescharacteristic
34#475×C139—21no—
35#475×C139C2211yescharacteristic
36#475×C139C2211yescharacteristic
37#474×C139—21no—
38#467×C139—21no—
39#464×C139—21no—
40#463×C139—21no—
41#462×C139C2211yescharacteristic
42#462×C139C2211yescharacteristic
43#460×C139C2211yescharacteristic
44#459×C139C2211yescharacteristic
45#451×C139—21no—
46#451×C139—21no—
47#446×C139C2211yescharacteristic
48#446×C139C2211yescharacteristic
49C8×Q8×C139C2211yescharacteristic
50#442×C139—21no—
51#440×C139—21no—
52C4×Q16×C139C2211yescharacteristic
53C4×SD16×C139—21no—
54C4×SD16×C139C2211yescharacteristic
55C8×D4×C139C2211yescharacteristic
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C22×Q8×C139—21no—
68C22×Q8×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139—21no—
73C2×Q16×C139—44no—
74C2×Q16×C139D411yescharacteristic
75C2×SD16×C139—21no—
76C2×SD16×C139D411yescharacteristic
77C2×D8×C139—21no—
78C22×C8×C139—21no—
79C4⋊Q8×C139—21no—
80C4⋊Q8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139—21no—
83C4⋊Q8×C139—41no—
84C4⋊Q8×C139C2311yescharacteristic
85C4⋊Q8×C139C2311yescharacteristic
86C4⋊Q8×C139C2311yescharacteristic
87#127×C139C2311yescharacteristic
88#124×C139—21no—
89#124×C139—21no—
90#123×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—41no—
94C22⋊Q8×C139—41no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139C2311yescharacteristic
98C4×Q8×C139C2311yescharacteristic
99C4×Q8×C139C2311yescharacteristic
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139—21no—
104C4×D4×C139C2311yescharacteristic
105#107×C139—21no—
106#107×C139D411yescharacteristic
107#106×C139—21no—
108#106×C139—21no—
109#106×C139—21no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139D411yescharacteristic
113C4⋊C8×C139—21no—
114C4⋊C8×C139—21no—
115C4⋊C8×C139—21no—
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120#103×C139—21no—
121#103×C139—21no—
122#103×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#103×C139—41no—
126#103×C139D411yescharacteristic
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—21no—
136#102×C139—41no—
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139#97×C139—21no—
140#97×C139—21no—
141C4×C8×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—41no—
149C2×Q8×C139—41no—
150C2×Q8×C139—41no—
151C2×Q8×C139—42no—
152C2×Q8×C139—42no—
153C2×Q8×C139—81no—
154C2×Q8×C139—81no—
155C2×Q8×C139C2×D411yescharacteristic
156C2×Q8×C139C2×D411yescharacteristic
157C2×Q8×C139C2×D411yescharacteristic
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139C2×D411yescharacteristic
162C22×C4×C139—21no—
163C22×C4×C139—41no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166Q16×C139—22no—
167Q16×C139—42no—
168Q16×C139—42no—
169Q16×C139—42no—
170Q16×C139—81no—
171SD16×C139—22no—
172SD16×C139—42no—
173D8×C139—42no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—42no—
180C2×C8×C139C2×D411yescharacteristic
181C2×C8×C139C2×D411yescharacteristic
182C2×C8×C139C2×D411yescharacteristic
183C2×C8×C139C2×D411yescharacteristic
184C4⋊C4×C139—21no—
185C4⋊C4×C139—21no—
186C4⋊C4×C139—21no—
187C4⋊C4×C139—21no—
188C4⋊C4×C139—21no—
189C4⋊C4×C139—21no—
190C4⋊C4×C139—21no—
191C4⋊C4×C139—21no—
192C4⋊C4×C139—21no—
193C4⋊C4×C139—41no—
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—41no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C42×C139—21no—
208C42×C139—21no—
209C42×C139—21no—
210C42×C139—41no—
211C42×C139C2411yescharacteristic
212C23×C139—21no—
213C23×C139—41no—
214Q8×C139—21no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—21no—
218Q8×C139—21no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—41no—
223Q8×C139—82no—
224Q8×C139—81no—
225Q8×C139—82no—
226Q8×C139—161no—
227Q8×C139AGL(1,ℤ/8)12yes—
228D4×C139—21no—
229D4×C139—41no—
230D4×C139—41no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—81no—
234D4×C139#13712yes—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—21no—
241C2×C4×C139—21no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—82no—
248C2×C4×C139—82no—
249C2×C4×C139—161no—
250C2×C4×C139C22×D411yescharacteristic
251C2×C4×C139C22×D411yescharacteristic
252C2×C4×C139H(5,𝔽2)11yescharacteristic
253C8×C139—21no—
254C8×C139—21no—
255C8×C139—21no—
256C8×C139—21no—
257C8×C139—41no—
258C8×C139—41no—
259C8×C139—41no—
260C8×C139—41no—
261C8×C139—41no—
262C22×C139—22no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—81no—
266C22×C139—81no—
267C22×C139—81no—
268C22×C139D4211yescharacteristic
269C4×C139—22no—
270C4×C139—21no—
271C4×C139—41no—
272C4×C139—41no—
273C4×C139—41no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—41no—
277C4×C139—81no—
278C4×C139—81no—
279C4×C139—81no—
280C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C139C2×#13711yescharacteristic
282C4×C139#57711yescharacteristic
283C4×C139#57811yescharacteristic
284C2×C139—42no—
285C2×C139—161no—
286C2×C139#326511yescharacteristic
287C2×C139#327011yescharacteristic
288C2×C139#329011yescharacteristic
289#20075C13911yesmaximal, characteristic, direct product factor, Sylow
290C139#2007511yescharacteristic, direct product factor, Sylow
291Q8×SD16C2×C13911yescharacteristic, complemented
292#3375C2×C13911yescharacteristic, complemented
293#3373C2×C13911yescharacteristic
294D4×Q16C2×C13911yescharacteristic, complemented
295#1720C2×C13911yescharacteristic, complemented
296#1692C2×C13911yescharacteristic, complemented
297#1690C2×C13911yescharacteristic, complemented
298#1682C2×C13911yescharacteristic, complemented
299#1677C2×C13911yescharacteristic
300#1645C2×C13911yescharacteristic, complemented
301#1640C2×C13911yescharacteristic, complemented
302#1637C2×C13911yescharacteristic, complemented
303#1627C2×C13911yescharacteristic
304#1587C2×C13911yescharacteristic, complemented
305#1585C2×C13911yescharacteristic, complemented
306C22×Q16—21no—
307#559C22×C13911yescharacteristic
308Q82C22×C13911yescharacteristic
309D4×Q8C22×C13911yescharacteristic
310D4×Q8C22×C13911yescharacteristic
311#498—21no—
312#498C22×C13911yescharacteristic
313#494C22×C13911yescharacteristic
314#489—21no—
315#489—21no—
316#487C22×C13911yescharacteristic
317#486C22×C13911yescharacteristic
318#486C22×C13911yescharacteristic
319#486C22×C13911yescharacteristic
320#477C22×C13911yescharacteristic
321#476—21no—
322#476—21no—
323#476C22×C13911yescharacteristic
324#475—21no—
325#475C22×C13911yescharacteristic
326#475C22×C13911yescharacteristic
327#474—21no—
328#467—21no—
329#464—21no—
330#463—21no—
331#462C22×C13911yescharacteristic
332#462C22×C13911yescharacteristic
333#460C22×C13911yescharacteristic
334#459C22×C13911yescharacteristic
335#451—21no—
336#451—21no—
337#446C22×C13911yescharacteristic
338#446C22×C13911yescharacteristic
339C8×Q8C22×C13911yescharacteristic
340#442—21no—
341#440—21no—
342C4×Q16C22×C13911yescharacteristic
343C4×SD16—21no—
344C4×SD16C22×C13911yescharacteristic
345C8×D4C22×C13911yescharacteristic
346#335C22×C13911yescharacteristic
347#334C22×C13911yescharacteristic
348#333C22×C13911yescharacteristic
349#332C22×C13911yescharacteristic
350#332C22×C13911yescharacteristic
351#331C22×C13911yescharacteristic
352Q8⋊C8C22×C13911yescharacteristic
353Q8⋊C8C22×C13911yescharacteristic
354Q8⋊C8C22×C13911yescharacteristic
355D4⋊C8C22×C13911yescharacteristic
356#322C22×C13911yescharacteristic
357C22×Q8—21no—
358C22×Q8—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—44no—
364C2×Q16D4×C13911yescharacteristic
365C2×SD16—21no—
366C2×SD16D4×C13911yescharacteristic
367C2×D8—21no—
368C22×C8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—41no—
374C4⋊Q8C23×C13911yescharacteristic
375C4⋊Q8C23×C13911yescharacteristic
376C4⋊Q8C23×C13911yescharacteristic
377#127C23×C13911yescharacteristic
378#124—21no—
379#124—21no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C23×C13911yescharacteristic
388C4×Q8C23×C13911yescharacteristic
389C4×Q8C23×C13911yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C13911yescharacteristic
395#107—21no—
396#107D4×C13911yescharacteristic
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106D4×C13911yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C13911yescharacteristic
407C4⋊C8C23×C13911yescharacteristic
408C4⋊C8C23×C13911yescharacteristic
409C4⋊C8C23×C13911yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—41no—
416#103D4×C13911yescharacteristic
417#103D4×C13911yescharacteristic
418#103D4×C13911yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—41no—
427#102D4×C13911yescharacteristic
428C22⋊C8—21no—
429#97—21no—
430#97—21no—
431C4×C8—21no—
432C4×C8C23×C13911yescharacteristic
433C4×C8C23×C13911yescharacteristic
434C4×C8C23×C13911yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8—81no—
445C2×Q8C2×D4×C13911yescharacteristic
446C2×Q8C2×D4×C13911yescharacteristic
447C2×Q8C2×D4×C13911yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4C2×D4×C13911yescharacteristic
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—22no—
457Q16—42no—
458Q16—42no—
459Q16—42no—
460Q16—81no—
461SD16—22no—
462SD16—42no—
463D8—42no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—42no—
470C2×C8C2×D4×C13911yescharacteristic
471C2×C8C2×D4×C13911yescharacteristic
472C2×C8C2×D4×C13911yescharacteristic
473C2×C8C2×D4×C13911yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4C2×D4×C13911yescharacteristic
488C4⋊C4C2×D4×C13911yescharacteristic
489C4⋊C4C2×D4×C13911yescharacteristic
490C4⋊C4C2×D4×C13911yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—41no—
501C42C24×C13911yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—81no—
515Q8—82no—
516Q8—161no—
517Q8AGL(1,ℤ/8)×C13912yes—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4#137×C13912yes—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—161no—
540C2×C4C22×D4×C13911yescharacteristic
541C2×C4C22×D4×C13911yescharacteristic
542C2×C4H(5,𝔽2)×C13911yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D42×C13911yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
571C4C2×#137×C13911yescharacteristic
572C4#577×C13911yescharacteristic
573C4#578×C13911yescharacteristic
574C2—42no—
575C2—161no—
576C2#3265×C13911yescharacteristic
577C2#3270×C13911yescharacteristic
578C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#459×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. Q8×SD16×C139C2semidirect
2. #3375×C139C2semidirect
4. D4×Q16×C139C2semidirect
5. #1720×C139C2semidirect
6. #1692×C139C2semidirect
7. #1690×C139C2semidirect
8. #1682×C139C2semidirect
10. #1645×C139C2semidirect
11. #1640×C139C2semidirect
12. #1637×C139C2semidirect
14. #1587×C139C2semidirect
15. #1585×C139C2semidirect
289. #20075C139direct (N × H)
290. C139#20075direct (N × H)
291. Q8×SD16C2×C139semidirect
292. #3375C2×C139semidirect
294. D4×Q16C2×C139semidirect
295. #1720C2×C139semidirect
296. #1692C2×C139semidirect
297. #1690C2×C139semidirect
298. #1682C2×C139semidirect
300. #1645C2×C139semidirect
301. #1640C2×C139semidirect
302. #1637C2×C139semidirect
304. #1587C2×C139semidirect
305. #1585C2×C139semidirect

Maximal subgroups

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

subgroupindex
Q8×SD16×C1392
#3375×C1392
#3373×C1392
D4×Q16×C1392
#1720×C1392
#1692×C1392
#1690×C1392
#1682×C1392
#1677×C1392
#1645×C1392
#1640×C1392
#1637×C1392
#1627×C1392
#1587×C1392
#1585×C1392
#20075139