Finite Group Databasebeta

← C139×#18680 #48013276

Subgroups — C139×#18680 #48013276

Order 35584.

1000 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C139C211yesmaximal, characteristic, complemented
2#3245×C139C211yesmaximal, characteristic, complemented
3#3167×C139C211yesmaximal, characteristic, complemented
4#3036×C139C211yesmaximal, characteristic, complemented
5#1654×C139C212yesmaximal, complemented
6#1646×C139C212yesmaximal, complemented
7#1625×C139C212yesmaximal, complemented
8#1624×C139C212yesmaximal, complemented
9#1550×C139C211yesmaximal, characteristic, complemented
10#1492×C139C211yesmaximal, characteristic, complemented
11C2×D4⋊C8×C139C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C139—21no—
13#559×C139—22no—
14#556×C139—21no—
15#555×C139C2212yes—
16#553×C139—22no—
17#550×C139—21no—
18#547×C139C2212yes—
19#538×C139—22no—
20#535×C139—21no—
21#533×C139C2211yescharacteristic
22#532×C139C2211yescharacteristic
23#532×C139C2211yescharacteristic
24#525×C139—22no—
25#520×C139—21no—
26C2×C4×D4×C139C2211yescharacteristic
27#498×C139C2211yescharacteristic, complemented
28#492×C139C2211yescharacteristic, complemented
29#487×C139C2211yescharacteristic, complemented
30#486×C139C2211yescharacteristic, complemented
31#474×C139—21no—
32#474×C139C2212yescomplemented
33#466×C139—22no—
34#465×C139—22no—
35#463×C139—22no—
36#461×C139C2212yes—
37#459×C139—21no—
38#459×C139C2212yes—
39#459×C139C2212yescomplemented
40C4×SD16×C139—22no—
41#423×C139C2211yescharacteristic
42C2×C4⋊C8×C139C2211yescharacteristic
43#417×C139—21no—
44C2×C4×C8×C139C2211yescharacteristic
45#333×C139C2212yescomplemented
46#332×C139C2212yescomplemented
47D4⋊C8×C139C2212yes—
48D4⋊C8×C139C2212yes—
49D4⋊C8×C139C2212yescomplemented
50D4⋊C8×C139C2212yescomplemented
51C2×#41×C139—22no—
52C2×#41×C139—21no—
53C2×#41×C139—21no—
54C22×D4×C139D411yescharacteristic
55C23×C4×C139—21no—
56AGL(1,ℤ/8)×C139—44no—
57C2×SD16×C139—22no—
58C2×SD16×C139—22no—
59C2×D8×C139—22no—
60C2×D8×C139—22no—
61C2×M16×C139—21no—
62C22×C8×C139—21no—
63C22×C8×C139—21no—
64C4⋊Q8×C139D411yescharacteristic
65C4⋊Q8×C139C2311yescharacteristic
66C4⋊Q8×C139C2311yescharacteristic
67C4⋊Q8×C139C2311yescharacteristic
68#127×C139—22no—
69#127×C139D411yescharacteristic
70#127×C139C2311yescharacteristic
71#126×C139—24no—
72#125×C139—21no—
73#124×C139—22no—
74#124×C139—24no—
75#124×C139—21no—
76#124×C139—21no—
77#123×C139—24no—
78#123×C139—24no—
79C22⋊Q8×C139—21no—
80C22⋊Q8×C139—22no—
81C22⋊Q8×C139D412yes—
82#121×C139—24no—
83#121×C139—22no—
84#121×C139—22no—
85#121×C139—22no—
86#121×C139—21no—
87#121×C139—21no—
88#121×C139—21no—
89#121×C139D412yes—
90#120×C139—24no—
91C4×Q8×C139—22no—
92C4×Q8×C139—21no—
93C4×Q8×C139D412yes—
94C4×D4×C139—24no—
95C4×D4×C139—22no—
96C4×D4×C139—24no—
97C4×D4×C139—21no—
98C4×D4×C139—21no—
99C4×D4×C139—21no—
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139D412yes—
103C4×D4×C139C2312yes—
104C4×D4×C139C2312yes—
105#117×C139—21no—
106#117×C139—22no—
107#117×C139—22no—
108C2×C4⋊C4×C139—22no—
109C2×C4⋊C4×C139D411yescharacteristic
110C2×C22⋊C4×C139—21no—
111C2×C42×C139C2311yescharacteristic
112#107×C139—22no—
113#106×C139—22no—
114C4⋊C8×C139—21no—
115C4⋊C8×C139—21no—
116C4⋊C8×C139C2312yes—
117C4⋊C8×C139C2312yes—
118#103×C139—22no—
119#103×C139—22no—
120#102×C139—22no—
121#102×C139—22no—
122#102×C139—22no—
123#102×C139—22no—
124C4×C8×C139—21no—
125C4×C8×C139C2311yescharacteristic
126C4×C8×C139C2311yescharacteristic
127C24×C139—21no—
128#41×C139—42no—
129#41×C139—42no—
130#41×C139—42no—
131#41×C139—42no—
132#41×C139—82no—
133#41×C139—82no—
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139—21no—
137C2×Q8×C139C2×D412yes—
138C2×D4×C139—22no—
139C2×D4×C139—24no—
140C2×D4×C139—24no—
141C2×D4×C139—21no—
142C2×D4×C139—21no—
143C2×D4×C139—21no—
144C2×D4×C139—22no—
145C2×D4×C139—22no—
146C2×D4×C139—21no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
149C2×D4×C139—41no—
150C2×D4×C139C2×D412yes—
151C2×D4×C139C2×D412yes—
152C22×C4×C139—24no—
153C22×C4×C139—21no—
154C22×C4×C139—22no—
155C22×C4×C139—22no—
156C22×C4×C139—22no—
157C22×C4×C139—41no—
158C22×C4×C139—81no—
159C22×C4×C139—81no—
160C22×C4×C139C2×D411yescharacteristic
161C22×C4×C139C2×D411yescharacteristic
162C22×C4×C139C2×D411yescharacteristic
163SD16×C139—44no—
164SD16×C139—44no—
165D8×C139—44no—
166D8×C139—82no—
167M16×C139—42no—
168C2×C8×C139—21no—
169C2×C8×C139—21no—
170C2×C8×C139—22no—
171C2×C8×C139—22no—
172C2×C8×C139—42no—
173C2×C8×C139—81no—
174C4⋊C4×C139—24no—
175C4⋊C4×C139—21no—
176C4⋊C4×C139—22no—
177C4⋊C4×C139—21no—
178C4⋊C4×C139—22no—
179C4⋊C4×C139—21no—
180C4⋊C4×C139—21no—
181C4⋊C4×C139—21no—
182C4⋊C4×C139—21no—
183C4⋊C4×C139—21no—
184C4⋊C4×C139C2×D412yes—
185C4⋊C4×C139C2×D412yes—
186C4⋊C4×C139C2×D412yes—
187C22⋊C4×C139—24no—
188C22⋊C4×C139—24no—
189C22⋊C4×C139—24no—
190C22⋊C4×C139—22no—
191C22⋊C4×C139—22no—
192C22⋊C4×C139—22no—
193C22⋊C4×C139—22no—
194C22⋊C4×C139—22no—
195C22⋊C4×C139—41no—
196C22⋊C4×C139—41no—
197C42×C139—24no—
198C42×C139—22no—
199C42×C139C2×D411yescharacteristic
200C42×C139C2×D411yescharacteristic
201C42×C139C2×D411yescharacteristic
202C42×C139C2411yescharacteristic
203C23×C139—22no—
204C23×C139—22no—
205C23×C139—42no—
206C23×C139—41no—
207C23×C139—81no—
208C23×C139—81no—
209C23×C139#12011yescharacteristic
210Q8×C139—42no—
211Q8×C139—41no—
212Q8×C139—41no—
213Q8×C139—42no—
214Q8×C139—41no—
215Q8×C139—41no—
216D4×C139—22no—
217D4×C139—22no—
218D4×C139—22no—
219D4×C139—22no—
220D4×C139—42no—
221D4×C139—44no—
222D4×C139—41no—
223D4×C139—41no—
224D4×C139—41no—
225D4×C139—41no—
226D4×C139—42no—
227D4×C139—42no—
228D4×C139—81no—
229D4×C139—84no—
230D4×C139—84no—
231D4×C139—82no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—22no—
235C2×C4×C139—22no—
236C2×C4×C139—22no—
237C2×C4×C139—22no—
238C2×C4×C139—41no—
239C2×C4×C139—42no—
240C2×C4×C139—42no—
241C2×C4×C139—42no—
242C2×C4×C139—42no—
243C2×C4×C139—41no—
244C2×C4×C139—82no—
245C2×C4×C139—81no—
246C2×C4×C139—84no—
247C2×C4×C139—82no—
248C2×C4×C139#12011yescharacteristic
249C2×C4×C139#12011yescharacteristic
250C2×C4×C139#12011yescharacteristic
251C2×C4×C139#13512yes—
252C2×C4×C139AGL(1,ℤ/8)12yes—
253C2×C4×C139C22×D411yescharacteristic
254C2×C4×C139C22×D411yescharacteristic
255C2×C4×C139C22×D411yescharacteristic
256C8×C139—22no—
257C8×C139—41no—
258C8×C139—42no—
259C8×C139—42no—
260C22×C139—21no—
261C22×C139—21no—
262C22×C139—42no—
263C22×C139—42no—
264C22×C139—42no—
265C22×C139—42no—
266C22×C139—42no—
267C22×C139—42no—
268C22×C139—84no—
269C22×C139—81no—
270C22×C139—81no—
271C22×C139—81no—
272C22×C139#44912yes—
273C22×C139C2×#12011yescharacteristic
274C4×C139—21no—
275C4×C139—21no—
276C4×C139—21no—
277C4×C139—42no—
278C4×C139—42no—
279C4×C139—42no—
280C4×C139—42no—
281C4×C139—81no—
282C4×C139#44912yes—
283C4×C139C2×#13511yescharacteristic
284C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C139#57611yescharacteristic
286C4×C139#57711yescharacteristic
287C2×C139—22no—
288C2×C139—82no—
289C2×C139—82no—
290C2×C139—161no—
291C2×C139C2×#44911yescharacteristic
292C2×C139#301211yescharacteristic
293C2×C139#301811yescharacteristic
294#18680C13911yesmaximal, characteristic, direct product factor, Sylow
295C139#1868011yescharacteristic, direct product factor, Sylow
296#3506C2×C13911yescharacteristic, complemented
297#3245C2×C13911yescharacteristic, complemented
298#3167C2×C13911yescharacteristic, complemented
299#3036C2×C13911yescharacteristic, complemented
300#1654C2×C13912yescomplemented
301#1646C2×C13912yescomplemented
302#1625C2×C13912yescomplemented
303#1624C2×C13912yescomplemented
304#1550C2×C13911yescharacteristic, complemented
305#1492C2×C13911yescharacteristic, complemented
306C2×D4⋊C8C2×C13911yescharacteristic, complemented
307C2×AGL(1,ℤ/8)—21no—
308#559—22no—
309#556—21no—
310#555C22×C13912yes—
311#553—22no—
312#550—21no—
313#547C22×C13912yes—
314#538—22no—
315#535—21no—
316#533C22×C13911yescharacteristic
317#532C22×C13911yescharacteristic
318#532C22×C13911yescharacteristic
319#525—22no—
320#520—21no—
321C2×C4×D4C22×C13911yescharacteristic
322#498C22×C13911yescharacteristic, complemented
323#492C22×C13911yescharacteristic, complemented
324#487C22×C13911yescharacteristic, complemented
325#486C22×C13911yescharacteristic, complemented
326#474—21no—
327#474C22×C13912yescomplemented
328#466—22no—
329#465—22no—
330#463—22no—
331#461C22×C13912yes—
332#459—21no—
333#459C22×C13912yes—
334#459C22×C13912yescomplemented
335C4×SD16—22no—
336#423C22×C13911yescharacteristic
337C2×C4⋊C8C22×C13911yescharacteristic
338#417—21no—
339C2×C4×C8C22×C13911yescharacteristic
340#333C22×C13912yescomplemented
341#332C22×C13912yescomplemented
342D4⋊C8C22×C13912yes—
343D4⋊C8C22×C13912yes—
344D4⋊C8C22×C13912yescomplemented
345D4⋊C8C22×C13912yescomplemented
346C2×#41—22no—
347C2×#41—21no—
348C2×#41—21no—
349C22×D4D4×C13911yescharacteristic
350C23×C4—21no—
351AGL(1,ℤ/8)—44no—
352C2×SD16—22no—
353C2×SD16—22no—
354C2×D8—22no—
355C2×D8—22no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8—21no—
359C4⋊Q8D4×C13911yescharacteristic
360C4⋊Q8C23×C13911yescharacteristic
361C4⋊Q8C23×C13911yescharacteristic
362C4⋊Q8C23×C13911yescharacteristic
363#127—22no—
364#127D4×C13911yescharacteristic
365#127C23×C13911yescharacteristic
366#126—24no—
367#125—21no—
368#124—22no—
369#124—24no—
370#124—21no—
371#124—21no—
372#123—24no—
373#123—24no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8D4×C13912yes—
377#121—24no—
378#121—22no—
379#121—22no—
380#121—22no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121D4×C13912yes—
385#120—24no—
386C4×Q8—22no—
387C4×Q8—21no—
388C4×Q8D4×C13912yes—
389C4×D4—24no—
390C4×D4—22no—
391C4×D4—24no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4D4×C13912yes—
398C4×D4C23×C13912yes—
399C4×D4C23×C13912yes—
400#117—21no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4D4×C13911yescharacteristic
405C2×C22⋊C4—21no—
406C2×C42C23×C13911yescharacteristic
407#107—22no—
408#106—22no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C13912yes—
412C4⋊C8C23×C13912yes—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417#102—22no—
418#102—22no—
419C4×C8—21no—
420C4×C8C23×C13911yescharacteristic
421C4×C8C23×C13911yescharacteristic
422C24—21no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41—42no—
427#41—82no—
428#41—82no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8C2×D4×C13912yes—
433C2×D4—22no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×D4×C13912yes—
446C2×D4C2×D4×C13912yes—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C2×D4×C13911yescharacteristic
456C22×C4C2×D4×C13911yescharacteristic
457C22×C4C2×D4×C13911yescharacteristic
458SD16—44no—
459SD16—44no—
460D8—44no—
461D8—82no—
462M16—42no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—42no—
468C2×C8—81no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C2×D4×C13912yes—
480C4⋊C4C2×D4×C13912yes—
481C4⋊C4C2×D4×C13912yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—24no—
493C42—22no—
494C42C2×D4×C13911yescharacteristic
495C42C2×D4×C13911yescharacteristic
496C42C2×D4×C13911yescharacteristic
497C42C24×C13911yescharacteristic
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—81no—
503C23—81no—
504C23#120×C13911yescharacteristic
505Q8—42no—
506Q8—42no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511D4—22no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4—42no—
516D4—44no—
517D4—42no—
518D4—42no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—84no—
525D4—84no—
526D4—82no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—81no—
541C2×C4—84no—
542C2×C4—82no—
543C2×C4#120×C13911yescharacteristic
544C2×C4#120×C13911yescharacteristic
545C2×C4#120×C13911yescharacteristic
546C2×C4#135×C13912yes—
547C2×C4AGL(1,ℤ/8)×C13912yes—
548C2×C4C22×D4×C13911yescharacteristic
549C2×C4C22×D4×C13911yescharacteristic
550C2×C4C22×D4×C13911yescharacteristic
551C8—22no—
552C8—41no—
553C8—42no—
554C8—42no—
555C22—21no—
556C22—21no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—84no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#449×C13912yes—
568C22C2×#120×C13911yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—81no—
577C4#449×C13912yes—
578C4C2×#135×C13911yescharacteristic
579C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
580C4#576×C13911yescharacteristic
581C4#577×C13911yescharacteristic
582C2—22no—
583C2—82no—
584C2—82no—
585C2—161no—
586C2C2×#449×C13911yescharacteristic
587C2#3012×C13911yescharacteristic
588C2#3018×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3506×C139C2semidirect
2. #3245×C139C2semidirect
3. #3167×C139C2semidirect
4. #3036×C139C2semidirect
5. #1654×C139C2semidirect
6. #1646×C139C2semidirect
7. #1625×C139C2semidirect
8. #1624×C139C2semidirect
9. #1550×C139C2semidirect
10. #1492×C139C2semidirect
11. C2×D4⋊C8×C139C2semidirect
27. #498×C139C22semidirect
28. #492×C139C22semidirect
29. #487×C139C22semidirect
30. #486×C139C22semidirect
32. #474×C139C22semidirect
39. #459×C139C22semidirect
45. #333×C139C22semidirect
46. #332×C139C22semidirect
49. D4⋊C8×C139C22semidirect
50. D4⋊C8×C139C22semidirect
294. #18680C139direct (N × H)
295. C139#18680direct (N × H)
296. #3506C2×C139semidirect
297. #3245C2×C139semidirect
298. #3167C2×C139semidirect
299. #3036C2×C139semidirect
300. #1654C2×C139semidirect
301. #1646C2×C139semidirect
302. #1625C2×C139semidirect
303. #1624C2×C139semidirect
304. #1550C2×C139semidirect
305. #1492C2×C139semidirect
306. C2×D4⋊C8C2×C139semidirect
322. #498C22×C139semidirect
323. #492C22×C139semidirect
324. #487C22×C139semidirect
325. #486C22×C139semidirect
327. #474C22×C139semidirect
334. #459C22×C139semidirect
340. #333C22×C139semidirect
341. #332C22×C139semidirect
344. D4⋊C8C22×C139semidirect
345. D4⋊C8C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3506×C1392
#3245×C1392
#3167×C1392
#3036×C1392
#1654×C1392
#1646×C1392
#1625×C1392
#1624×C1392
#1550×C1392
#1492×C1392
C2×D4⋊C8×C1392
#18680139