Finite Group Databasebeta

← C139×#20031 #48014627

Subgroups — C139×#20031 #48014627

Order 35584.

660 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C139C211yesmaximal, characteristic, complemented
2#3330×C139C211yesmaximal, characteristic
3#3298×C139C211yesmaximal, characteristic, complemented
4#3276×C139C211yesmaximal, characteristic, complemented
5#1723×C139C211yesmaximal, characteristic, complemented
6#1699×C139C211yesmaximal, characteristic, complemented
7#1693×C139C211yesmaximal, characteristic, complemented
8#1680×C139C211yesmaximal, characteristic, complemented
9#1669×C139C211yesmaximal, characteristic, complemented
10#1654×C139C211yesmaximal, characteristic, complemented
11#1651×C139C211yesmaximal, characteristic, complemented
12#1649×C139C211yesmaximal, characteristic, complemented
13#1647×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1586×C139C211yesmaximal, characteristic, complemented
16C2×#137×C139—21no—
17D4×Q8×C139C2211yescharacteristic
18D4×Q8×C139C2211yescharacteristic
19#547×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#500×C139—21no—
22#500×C139C2211yescharacteristic
23#500×C139C2211yescharacteristic
24#498×C139C2211yescharacteristic
25#494×C139C2211yescharacteristic
26#487×C139C2211yescharacteristic
27#487×C139C2211yescharacteristic
28#484×C139—21no—
29#483×C139—21no—
30#475×C139C2211yescharacteristic
31#474×C139—21no—
32#474×C139—21no—
33#474×C139C2211yescharacteristic
34#474×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#470×C139—21no—
37#468×C139—21no—
38#465×C139—21no—
39#462×C139C2211yescharacteristic
40#461×C139C2211yescharacteristic
41#461×C139C2211yescharacteristic
42#461×C139C2211yescharacteristic
43#452×C139—21no—
44#451×C139—21no—
45#449×C139—21no—
46#448×C139—21no—
47C8×Q8×C139C2211yescharacteristic
48C4×SD16×C139C2211yescharacteristic
49C4×D8×C139—21no—
50C4×D8×C139C2211yescharacteristic
51#436×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#417×C139—21no—
55C2×#103×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C22×Q8×C139—21no—
70C22×Q8×C139—21no—
71#137×C139—44no—
72C2×Q16×C139—21no—
73C2×Q16×C139—21no—
74C2×Q16×C139—21no—
75C2×SD16×C139—21no—
76C2×SD16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139D411yescharacteristic
79C2×D8×C139D411yescharacteristic
80C2×M16×C139—21no—
81C2×M16×C139—21no—
82C22×C8×C139—21no—
83C4⋊Q8×C139—21no—
84C4⋊Q8×C139—21no—
85C4⋊Q8×C139C2311yescharacteristic
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88C4⋊Q8×C139C2311yescharacteristic
89#123×C139—41no—
90#123×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—21no—
94C22⋊Q8×C139—21no—
95C22⋊Q8×C139—41no—
96C22⋊Q8×C139—41no—
97#121×C139—21no—
98#121×C139—21no—
99C4×Q8×C139C2311yescharacteristic
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139C2311yescharacteristic
103C4×D4×C139C2311yescharacteristic
104C4×D4×C139C2311yescharacteristic
105C2×C4⋊C4×C139—21no—
106C2×C4⋊C4×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—21no—
110#107×C139—21no—
111#107×C139—21no—
112#107×C139—41no—
113#107×C139D411yescharacteristic
114#106×C139—21no—
115#106×C139—41no—
116#106×C139D411yescharacteristic
117C4⋊C8×C139—21no—
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122#103×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#103×C139—21no—
126#103×C139—21no—
127#103×C139—21no—
128#103×C139—21no—
129#103×C139—21no—
130#103×C139—21no—
131#103×C139D411yescharacteristic
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—21no—
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C22⋊C8×C139—21no—
141C4×C8×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145#41×C139—42no—
146#41×C139—42no—
147#41×C139—81no—
148#41×C139—81no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—21no—
152C2×Q8×C139—21no—
153C2×Q8×C139—41no—
154C2×Q8×C139—41no—
155C2×Q8×C139—42no—
156C2×Q8×C139—42no—
157C2×Q8×C139—81no—
158C2×Q8×C139—81no—
159C2×Q8×C139C2×D411yescharacteristic
160C2×D4×C139—41no—
161C2×D4×C139—41no—
162C2×D4×C139C2×D411yescharacteristic
163C2×D4×C139C2×D411yescharacteristic
164C2×D4×C139C2×D411yescharacteristic
165C22×C4×C139—21no—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—41no—
169C22×C4×C139—41no—
170C22×C4×C139—41no—
171C22×C4×C139—41no—
172Q16×C139—42no—
173Q16×C139—42no—
174Q16×C139—81no—
175SD16×C139—22no—
176SD16×C139—42no—
177SD16×C139—81no—
178SD16×C139—81no—
179D8×C139—22no—
180M16×C139—42no—
181M16×C139—81no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—81no—
188C2×C8×C139C2×D411yescharacteristic
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
191C2×C8×C139C2×D411yescharacteristic
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—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—21no—
201C4⋊C4×C139—41no—
202C4⋊C4×C139—41no—
203C4⋊C4×C139—41no—
204C4⋊C4×C139—41no—
205C4⋊C4×C139C2×D411yescharacteristic
206C4⋊C4×C139C2×D411yescharacteristic
207C4⋊C4×C139C2×D411yescharacteristic
208C4⋊C4×C139C2×D411yescharacteristic
209C22⋊C4×C139—21no—
210C22⋊C4×C139—21no—
211C22⋊C4×C139—21no—
212C22⋊C4×C139—41no—
213C22⋊C4×C139—41no—
214C22⋊C4×C139—41no—
215C22⋊C4×C139—41no—
216C42×C139—21no—
217C42×C139C2411yescharacteristic
218C23×C139—21no—
219C23×C139—21no—
220C23×C139—21no—
221Q8×C139—21no—
222Q8×C139—41no—
223Q8×C139—41no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—41no—
228Q8×C139—41no—
229Q8×C139—41no—
230Q8×C139—82no—
231Q8×C139—82no—
232Q8×C139AGL(1,ℤ/8)12yes—
233D4×C139—21no—
234D4×C139—21no—
235D4×C139—21no—
236D4×C139—21no—
237D4×C139—21no—
238D4×C139—82no—
239D4×C139—82no—
240D4×C139#13712yescomplemented
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
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—82no—
257C2×C4×C139—82no—
258C2×C4×C139—82no—
259C2×C4×C139—82no—
260C2×C4×C139C22×D411yescharacteristic
261C2×C4×C139C22×D411yescharacteristic
262C2×C4×C139H(5,𝔽2)11yescharacteristic
263C8×C139—22no—
264C8×C139—21no—
265C8×C139—21no—
266C8×C139—21no—
267C8×C139—21no—
268C8×C139—41no—
269C8×C139—41no—
270C8×C139—41no—
271C8×C139—41no—
272C22×C139—22no—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139D4211yescharacteristic
282C4×C139—22no—
283C4×C139—21no—
284C4×C139—41no—
285C4×C139—41no—
286C4×C139—41no—
287C4×C139—41no—
288C4×C139—81no—
289C4×C139—81no—
290C4×C139—81no—
291C4×C139—81no—
292C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C139C2×#13711yescharacteristic
294C4×C139#57611yescharacteristic
295C4×C139#57711yescharacteristic
296C2×C139—42no—
297C2×C139—81no—
298C2×C139—81no—
299C2×C139#326411yescharacteristic
300C2×C139#326611yescharacteristic
301C2×C139#329311yescharacteristic
302#20031C13911yesmaximal, characteristic, direct product factor, Sylow
303C139#2003111yescharacteristic, direct product factor, Sylow
304Q8×D8C2×C13911yescharacteristic, complemented
305#3330C2×C13911yescharacteristic
306#3298C2×C13911yescharacteristic, complemented
307#3276C2×C13911yescharacteristic, complemented
308#1723C2×C13911yescharacteristic, complemented
309#1699C2×C13911yescharacteristic, complemented
310#1693C2×C13911yescharacteristic, complemented
311#1680C2×C13911yescharacteristic, complemented
312#1669C2×C13911yescharacteristic, complemented
313#1654C2×C13911yescharacteristic, complemented
314#1651C2×C13911yescharacteristic, complemented
315#1649C2×C13911yescharacteristic, complemented
316#1647C2×C13911yescharacteristic, complemented
317#1588C2×C13911yescharacteristic, complemented
318#1586C2×C13911yescharacteristic, complemented
319C2×#137—21no—
320D4×Q8C22×C13911yescharacteristic
321D4×Q8C22×C13911yescharacteristic
322#547C22×C13911yescharacteristic
323#547C22×C13911yescharacteristic
324#500—21no—
325#500C22×C13911yescharacteristic
326#500C22×C13911yescharacteristic
327#498C22×C13911yescharacteristic
328#494C22×C13911yescharacteristic
329#487C22×C13911yescharacteristic
330#487C22×C13911yescharacteristic
331#484—21no—
332#483—21no—
333#475C22×C13911yescharacteristic
334#474—21no—
335#474—21no—
336#474C22×C13911yescharacteristic
337#474C22×C13911yescharacteristic
338#474C22×C13911yescharacteristic
339#470—21no—
340#468—21no—
341#465—21no—
342#462C22×C13911yescharacteristic
343#461C22×C13911yescharacteristic
344#461C22×C13911yescharacteristic
345#461C22×C13911yescharacteristic
346#452—21no—
347#451—21no—
348#449—21no—
349#448—21no—
350C8×Q8C22×C13911yescharacteristic
351C4×SD16C22×C13911yescharacteristic
352C4×D8—21no—
353C4×D8C22×C13911yescharacteristic
354#436C22×C13911yescharacteristic
355#436C22×C13911yescharacteristic
356C8×D4C22×C13911yescharacteristic
357#417—21no—
358C2×#103—21no—
359#335C22×C13911yescharacteristic
360#334C22×C13911yescharacteristic
361#332C22×C13911yescharacteristic
362#332C22×C13911yescharacteristic
363#332C22×C13911yescharacteristic
364#332C22×C13911yescharacteristic
365Q8⋊C8C22×C13911yescharacteristic
366D4⋊C8C22×C13911yescharacteristic
367D4⋊C8C22×C13911yescharacteristic
368D4⋊C8C22×C13911yescharacteristic
369#322C22×C13911yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C22×Q8—21no—
373C22×Q8—21no—
374#137—44no—
375C2×Q16—21no—
376C2×Q16—21no—
377C2×Q16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16D4×C13911yescharacteristic
382C2×D8D4×C13911yescharacteristic
383C2×M16—21no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8C23×C13911yescharacteristic
389C4⋊Q8C23×C13911yescharacteristic
390C4⋊Q8C23×C13911yescharacteristic
391C4⋊Q8C23×C13911yescharacteristic
392#123—41no—
393#123—41no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399C22⋊Q8—41no—
400#121—21no—
401#121—21no—
402C4×Q8C23×C13911yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C13911yescharacteristic
406C4×D4C23×C13911yescharacteristic
407C4×D4C23×C13911yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#107—41no—
416#107D4×C13911yescharacteristic
417#106—21no—
418#106—41no—
419#106D4×C13911yescharacteristic
420C4⋊C8—21no—
421C4⋊C8C23×C13911yescharacteristic
422C4⋊C8C23×C13911yescharacteristic
423C4⋊C8C23×C13911yescharacteristic
424C4⋊C8C23×C13911yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103D4×C13911yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102D4×C13911yescharacteristic
439#102D4×C13911yescharacteristic
440#102D4×C13911yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8C23×C13911yescharacteristic
446C4×C8C23×C13911yescharacteristic
447C4×C8C23×C13911yescharacteristic
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×Q8—81no—
462C2×Q8C2×D4×C13911yescharacteristic
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C2×D4×C13911yescharacteristic
466C2×D4C2×D4×C13911yescharacteristic
467C2×D4C2×D4×C13911yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475Q16—42no—
476Q16—42no—
477Q16—81no—
478SD16—22no—
479SD16—42no—
480SD16—81no—
481SD16—81no—
482D8—22no—
483M16—42no—
484M16—81no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—81no—
491C2×C8C2×D4×C13911yescharacteristic
492C2×C8C2×D4×C13911yescharacteristic
493C2×C8C2×D4×C13911yescharacteristic
494C2×C8C2×D4×C13911yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C13911yescharacteristic
509C4⋊C4C2×D4×C13911yescharacteristic
510C4⋊C4C2×D4×C13911yescharacteristic
511C4⋊C4C2×D4×C13911yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42C24×C13911yescharacteristic
521C23—21no—
522C23—21no—
523C23—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—82no—
534Q8—82no—
535Q8AGL(1,ℤ/8)×C13912yes—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—82no—
542D4—82no—
543D4#137×C13912yescomplemented
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4C22×D4×C13911yescharacteristic
564C2×C4C22×D4×C13911yescharacteristic
565C2×C4H(5,𝔽2)×C13911yescharacteristic
566C8—22no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22D42×C13911yescharacteristic
585C4—21no—
586C4—22no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
596C4C2×#137×C13911yescharacteristic
597C4#576×C13911yescharacteristic
598C4#577×C13911yescharacteristic
599C2—42no—
600C2—81no—
601C2—81no—
602C2#3264×C13911yescharacteristic
603C2#3266×C13911yescharacteristic
604C2#3293×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3330×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. Q8×D8×C139C2semidirect
3. #3298×C139C2semidirect
4. #3276×C139C2semidirect
5. #1723×C139C2semidirect
6. #1699×C139C2semidirect
7. #1693×C139C2semidirect
8. #1680×C139C2semidirect
9. #1669×C139C2semidirect
10. #1654×C139C2semidirect
11. #1651×C139C2semidirect
12. #1649×C139C2semidirect
13. #1647×C139C2semidirect
14. #1588×C139C2semidirect
15. #1586×C139C2semidirect
240. D4×C139#137semidirect
302. #20031C139direct (N × H)
303. C139#20031direct (N × H)
304. Q8×D8C2×C139semidirect
306. #3298C2×C139semidirect
307. #3276C2×C139semidirect
308. #1723C2×C139semidirect
309. #1699C2×C139semidirect
310. #1693C2×C139semidirect
311. #1680C2×C139semidirect
312. #1669C2×C139semidirect
313. #1654C2×C139semidirect
314. #1651C2×C139semidirect
315. #1649C2×C139semidirect
316. #1647C2×C139semidirect
317. #1588C2×C139semidirect
318. #1586C2×C139semidirect
543. D4#137×C139semidirect

Maximal subgroups

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

subgroupindex
Q8×D8×C1392
#3330×C1392
#3298×C1392
#3276×C1392
#1723×C1392
#1699×C1392
#1693×C1392
#1680×C1392
#1669×C1392
#1654×C1392
#1651×C1392
#1649×C1392
#1647×C1392
#1588×C1392
#1586×C1392
#20031139