Finite Group Databasebeta

← C139×#19906 #48014502

Subgroups — C139×#19906 #48014502

Order 35584.

608 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3360×C139C211yesmaximal, characteristic, complemented
2#3358×C139C211yesmaximal, characteristic
3#3333×C139C211yesmaximal, characteristic, complemented
4#3328×C139C211yesmaximal, characteristic, complemented
5#1711×C139C211yesmaximal, characteristic, complemented
6#1699×C139C211yesmaximal, characteristic, complemented
7#1697×C139C211yesmaximal, characteristic, complemented
8#1684×C139C211yesmaximal, characteristic, complemented
9#1682×C139C211yesmaximal, characteristic, complemented
10#1644×C139C211yesmaximal, characteristic, complemented
11#1642×C139C211yesmaximal, characteristic, complemented
12#1637×C139C211yesmaximal, characteristic, complemented
13#1628×C139C211yesmaximal, characteristic, complemented
14#1589×C139C211yesmaximal, characteristic, complemented
15C8×Q16×C139C211yesmaximal, characteristic, complemented
16#556×C139C2211yescharacteristic
17#554×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#488×C139—21no—
21#487×C139C2211yescharacteristic
22#487×C139C2211yescharacteristic
23#487×C139C2211yescharacteristic
24#486×C139—21no—
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#485×C139—21no—
29#480×C139—21no—
30#479×C139—21no—
31#477×C139C2211yescharacteristic
32#476×C139C2211yescharacteristic
33#475×C139C2211yescharacteristic
34#474×C139—21no—
35#474×C139C2211yescharacteristic
36#470×C139—21no—
37#468×C139—21no—
38#463×C139—21no—
39#462×C139C2211yescharacteristic
40#461×C139C2211yescharacteristic
41#460×C139C2211yescharacteristic
42#459×C139—21no—
43#459×C139C2211yescharacteristic
44#452×C139—21no—
45#451×C139—21no—
46C8×Q8×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48C4×Q16×C139C2211yescharacteristic
49C4×SD16×C139—21no—
50C4×D8×C139—21no—
51C4×D8×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54#419×C139—21no—
55#417×C139—21no—
56#335×C139C2211yescharacteristic
57#335×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66C82×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C22×Q8×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139D411yescharacteristic
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×D8×C139—21no—
74C2×D8×C139D411yescharacteristic
75C2×M16×C139—21no—
76C2×M16×C139—21no—
77C4⋊Q8×C139—21no—
78C4⋊Q8×C139C2311yescharacteristic
79C4⋊Q8×C139C2311yescharacteristic
80C4⋊Q8×C139C2311yescharacteristic
81#127×C139—21no—
82#127×C139C2311yescharacteristic
83#126×C139—41no—
84#125×C139—21no—
85#124×C139—21no—
86C22⋊Q8×C139—21no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—21no—
89C22⋊Q8×C139—41no—
90C22⋊Q8×C139—41no—
91#121×C139—21no—
92#121×C139—41no—
93C4×Q8×C139—21no—
94C4×Q8×C139C2311yescharacteristic
95C4×Q8×C139C2311yescharacteristic
96C4×D4×C139—21no—
97C4×D4×C139—21no—
98C4×D4×C139—21no—
99C4×D4×C139C2311yescharacteristic
100C4×D4×C139C2311yescharacteristic
101#117×C139—21no—
102C2×C4⋊C4×C139—21no—
103#107×C139—21no—
104#107×C139—21no—
105#107×C139D411yescharacteristic
106#107×C139D411yescharacteristic
107#106×C139—21no—
108#106×C139—21no—
109C4⋊C8×C139—21no—
110C4⋊C8×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—21no—
122#103×C139—21no—
123#103×C139—41no—
124#103×C139D411yescharacteristic
125#103×C139D411yescharacteristic
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—41no—
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
144#41×C139—42no—
145#41×C139—81no—
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×C139C2×D411yescharacteristic
160C2×D4×C139C2×D411yescharacteristic
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—41no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166Q16×C139—22no—
167Q16×C139—81no—
168SD16×C139—42no—
169SD16×C139—81no—
170D8×C139—41no—
171D8×C139—42no—
172M16×C139—81no—
173M16×C139—81no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139C2×D411yescharacteristic
180C2×C8×C139C2×D411yescharacteristic
181C2×C8×C139C2×D411yescharacteristic
182C2×C8×C139C2×D411yescharacteristic
183C4⋊C4×C139—21no—
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—41no—
192C4⋊C4×C139—41no—
193C4⋊C4×C139—41no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139C2×D411yescharacteristic
196C4⋊C4×C139C2×D411yescharacteristic
197C4⋊C4×C139C2×D411yescharacteristic
198C4⋊C4×C139C2×D411yescharacteristic
199C22⋊C4×C139—21no—
200C22⋊C4×C139—21no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C42×C139—21no—
207C42×C139—21no—
208C42×C139—41no—
209C42×C139C2411yescharacteristic
210C23×C139—21no—
211C23×C139—21no—
212C23×C139—41no—
213Q8×C139—21no—
214Q8×C139—21no—
215Q8×C139—21no—
216Q8×C139—41no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—82no—
221Q8×C139—81no—
222Q8×C139#13512yes—
223D4×C139—21no—
224D4×C139—21no—
225D4×C139—21no—
226D4×C139—21no—
227D4×C139—41no—
228D4×C139—41no—
229D4×C139—41no—
230D4×C139—41no—
231D4×C139—82no—
232D4×C139—81no—
233D4×C139—161no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
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—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—81no—
269C22×C139—81no—
270C22×C139—81no—
271C22×C139D4211yescharacteristic
272C4×C139—22no—
273C4×C139—21no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—81no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139C2×#13511yescharacteristic
283C4×C139#57511yescharacteristic
284C4×C139#57611yescharacteristic
285C4×C139#57811yescharacteristic
286C2×C139—81no—
287C2×C139—81no—
288C2×C139—161no—
289C2×C139#327711yescharacteristic
290C2×C139#328011yescharacteristic
291C2×C139#329011yescharacteristic
292#19906C13911yesmaximal, characteristic, direct product factor, Sylow
293C139#1990611yescharacteristic, direct product factor, Sylow
294#3360C2×C13911yescharacteristic, complemented
295#3358C2×C13911yescharacteristic
296#3333C2×C13911yescharacteristic, complemented
297#3328C2×C13911yescharacteristic, complemented
298#1711C2×C13911yescharacteristic, complemented
299#1699C2×C13911yescharacteristic, complemented
300#1697C2×C13911yescharacteristic, complemented
301#1684C2×C13911yescharacteristic, complemented
302#1682C2×C13911yescharacteristic, complemented
303#1644C2×C13911yescharacteristic, complemented
304#1642C2×C13911yescharacteristic, complemented
305#1637C2×C13911yescharacteristic, complemented
306#1628C2×C13911yescharacteristic, complemented
307#1589C2×C13911yescharacteristic, complemented
308C8×Q16C2×C13911yescharacteristic, complemented
309#556C22×C13911yescharacteristic
310#554C22×C13911yescharacteristic
311#550C22×C13911yescharacteristic
312D4×Q8C22×C13911yescharacteristic
313#488—21no—
314#487C22×C13911yescharacteristic
315#487C22×C13911yescharacteristic
316#487C22×C13911yescharacteristic
317#486—21no—
318#486C22×C13911yescharacteristic
319#486C22×C13911yescharacteristic
320#486C22×C13911yescharacteristic
321#485—21no—
322#480—21no—
323#479—21no—
324#477C22×C13911yescharacteristic
325#476C22×C13911yescharacteristic
326#475C22×C13911yescharacteristic
327#474—21no—
328#474C22×C13911yescharacteristic
329#470—21no—
330#468—21no—
331#463—21no—
332#462C22×C13911yescharacteristic
333#461C22×C13911yescharacteristic
334#460C22×C13911yescharacteristic
335#459—21no—
336#459C22×C13911yescharacteristic
337#452—21no—
338#451—21no—
339C8×Q8C22×C13911yescharacteristic
340C8×Q8C22×C13911yescharacteristic
341C4×Q16C22×C13911yescharacteristic
342C4×SD16—21no—
343C4×D8—21no—
344C4×D8C22×C13911yescharacteristic
345#436C22×C13911yescharacteristic
346#436C22×C13911yescharacteristic
347#419—21no—
348#417—21no—
349#335C22×C13911yescharacteristic
350#335C22×C13911yescharacteristic
351#333C22×C13911yescharacteristic
352#332C22×C13911yescharacteristic
353#332C22×C13911yescharacteristic
354#331C22×C13911yescharacteristic
355Q8⋊C8C22×C13911yescharacteristic
356Q8⋊C8C22×C13911yescharacteristic
357D4⋊C8C22×C13911yescharacteristic
358D4⋊C8C22×C13911yescharacteristic
359C82C22×C13911yescharacteristic
360C2×#41—21no—
361C22×Q8—21no—
362C2×Q16—21no—
363C2×Q16D4×C13911yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×D8D4×C13911yescharacteristic
368C2×M16—21no—
369C2×M16—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C13911yescharacteristic
372C4⋊Q8C23×C13911yescharacteristic
373C4⋊Q8C23×C13911yescharacteristic
374#127—21no—
375#127C23×C13911yescharacteristic
376#126—41no—
377#125—21no—
378#124—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384#121—21no—
385#121—41no—
386C4×Q8—21no—
387C4×Q8C23×C13911yescharacteristic
388C4×Q8C23×C13911yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C13911yescharacteristic
393C4×D4C23×C13911yescharacteristic
394#117—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#107—21no—
398#107D4×C13911yescharacteristic
399#107D4×C13911yescharacteristic
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C13911yescharacteristic
405C4⋊C8C23×C13911yescharacteristic
406C4⋊C8C23×C13911yescharacteristic
407C4⋊C8C23×C13911yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
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—21no—
427#102—41no—
428#102D4×C13911yescharacteristic
429#102D4×C13911yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432C4×C8—21no—
433C4×C8—21no—
434C4×C8C23×C13911yescharacteristic
435C4×C8C23×C13911yescharacteristic
436C4×C8C23×C13911yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C13911yescharacteristic
446C2×Q8C2×D4×C13911yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C13911yescharacteristic
453C2×D4C2×D4×C13911yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—22no—
460Q16—81no—
461SD16—42no—
462SD16—81no—
463D8—41no—
464D8—42no—
465M16—81no—
466M16—81no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8C2×D4×C13911yescharacteristic
473C2×C8C2×D4×C13911yescharacteristic
474C2×C8C2×D4×C13911yescharacteristic
475C2×C8C2×D4×C13911yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C13911yescharacteristic
489C4⋊C4C2×D4×C13911yescharacteristic
490C4⋊C4C2×D4×C13911yescharacteristic
491C4⋊C4C2×D4×C13911yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C24×C13911yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—81no—
515Q8#135×C13912yes—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—82no—
525D4—81no—
526D4—161no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—161no—
543C2×C4C22×D4×C13911yescharacteristic
544C2×C4C22×D4×C13911yescharacteristic
545C2×C4H(5,𝔽2)×C13911yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C13911yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C13911yescharacteristic
576C4#575×C13911yescharacteristic
577C4#576×C13911yescharacteristic
578C4#578×C13911yescharacteristic
579C2—81no—
580C2—81no—
581C2—161no—
582C2#3277×C13911yescharacteristic
583C2#3280×C13911yescharacteristic
584C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3358×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. #3360×C139C2semidirect
3. #3333×C139C2semidirect
4. #3328×C139C2semidirect
5. #1711×C139C2semidirect
6. #1699×C139C2semidirect
7. #1697×C139C2semidirect
8. #1684×C139C2semidirect
9. #1682×C139C2semidirect
10. #1644×C139C2semidirect
11. #1642×C139C2semidirect
12. #1637×C139C2semidirect
13. #1628×C139C2semidirect
14. #1589×C139C2semidirect
15. C8×Q16×C139C2semidirect
292. #19906C139direct (N × H)
293. C139#19906direct (N × H)
294. #3360C2×C139semidirect
296. #3333C2×C139semidirect
297. #3328C2×C139semidirect
298. #1711C2×C139semidirect
299. #1699C2×C139semidirect
300. #1697C2×C139semidirect
301. #1684C2×C139semidirect
302. #1682C2×C139semidirect
303. #1644C2×C139semidirect
304. #1642C2×C139semidirect
305. #1637C2×C139semidirect
306. #1628C2×C139semidirect
307. #1589C2×C139semidirect
308. C8×Q16C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3360×C1392
#3358×C1392
#3333×C1392
#3328×C1392
#1711×C1392
#1699×C1392
#1697×C1392
#1684×C1392
#1682×C1392
#1644×C1392
#1642×C1392
#1637×C1392
#1628×C1392
#1589×C1392
C8×Q16×C1392
#19906139