Finite Group Databasebeta

← C139×#20062 #48014658

Subgroups — C139×#20062 #48014658

Order 35584.

636 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
1Q8×D8×C139C211yesmaximal, characteristic
2#3367×C139C211yesmaximal, characteristic
3#3328×C139C211yesmaximal, characteristic, complemented
4D4×Q16×C139C211yesmaximal, characteristic, complemented
5#1723×C139C211yesmaximal, characteristic, complemented
6#1694×C139C211yesmaximal, characteristic, complemented
7#1689×C139C211yesmaximal, characteristic, complemented
8#1680×C139C211yesmaximal, characteristic, complemented
9#1679×C139C211yesmaximal, characteristic, complemented
10#1652×C139C211yesmaximal, characteristic, complemented
11#1651×C139C211yesmaximal, characteristic, complemented
12#1649×C139C211yesmaximal, characteristic, complemented
13#1649×C139C211yesmaximal, characteristic, complemented
14#1587×C139C211yesmaximal, characteristic, complemented
15#1586×C139C211yesmaximal, characteristic
16C22×Q16×C139—21no—
17#556×C139C2211yescharacteristic
18D4×Q8×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20D4×Q8×C139C2211yescharacteristic
21#500×C139—21no—
22#500×C139C2211yescharacteristic
23#500×C139C2211yescharacteristic
24#498×C139C2211yescharacteristic
25#494×C139C2211yescharacteristic
26#489×C139—21no—
27#487×C139C2211yescharacteristic
28#487×C139C2211yescharacteristic
29#485×C139—21no—
30#477×C139—21no—
31#475×C139C2211yescharacteristic
32#474×C139—21no—
33#474×C139—21no—
34#474×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#470×C139—21no—
38#467×C139—21no—
39#463×C139—21no—
40#462×C139C2211yescharacteristic
41#462×C139C2211yescharacteristic
42#462×C139C2211yescharacteristic
43#461×C139C2211yescharacteristic
44#451×C139—21no—
45#451×C139—21no—
46#451×C139—21no—
47#446×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49#440×C139—21no—
50C4×Q16×C139C2211yescharacteristic
51C4×D8×C139—21no—
52C4×D8×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55#419×C139—21no—
56#334×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C22×Q8×C139—21no—
68C22×Q8×C139—21no—
69C22×Q8×C139—21no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139—21no—
73C2×Q16×C139—21no—
74C2×Q16×C139—21no—
75C2×Q16×C139—44no—
76C2×Q16×C139D411yescharacteristic
77C2×SD16×C139—21no—
78C2×D8×C139D411yescharacteristic
79C2×M16×C139—21no—
80C22×C8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139—21no—
83C4⋊Q8×C139—21no—
84C4⋊Q8×C139C2311yescharacteristic
85C4⋊Q8×C139C2311yescharacteristic
86C4⋊Q8×C139C2311yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88#126×C139—41no—
89#124×C139—21no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—21no—
93C22⋊Q8×C139—21no—
94C22⋊Q8×C139—41no—
95C22⋊Q8×C139—41no—
96C22⋊Q8×C139—41no—
97C4×Q8×C139—21no—
98C4×Q8×C139C2311yescharacteristic
99C4×Q8×C139C2311yescharacteristic
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139C2311yescharacteristic
104C4×D4×C139C2311yescharacteristic
105#117×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—21no—
110#107×C139—21no—
111#107×C139—41no—
112#107×C139D411yescharacteristic
113#107×C139D411yescharacteristic
114#106×C139—21no—
115#106×C139—41no—
116C4⋊C8×C139—21no—
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#103×C139D411yescharacteristic
133#102×C139—21no—
134#102×C139—21no—
135#102×C139—21no—
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×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—21no—
149C2×Q8×C139—41no—
150C2×Q8×C139—41no—
151C2×Q8×C139—41no—
152C2×Q8×C139—42no—
153C2×Q8×C139—42no—
154C2×Q8×C139—42no—
155C2×Q8×C139—81no—
156C2×Q8×C139—81no—
157C2×Q8×C139—81no—
158C2×Q8×C139C2×D411yescharacteristic
159C2×Q8×C139C2×D411yescharacteristic
160C2×D4×C139C2×D411yescharacteristic
161C2×D4×C139C2×D411yescharacteristic
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167Q16×C139—22no—
168Q16×C139—42no—
169Q16×C139—42no—
170Q16×C139—42no—
171Q16×C139—81no—
172Q16×C139—81no—
173SD16×C139—42no—
174D8×C139—22no—
175M16×C139—81no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139—42no—
182C2×C8×C139C2×D411yescharacteristic
183C2×C8×C139C2×D411yescharacteristic
184C2×C8×C139C2×D411yescharacteristic
185C2×C8×C139C2×D411yescharacteristic
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—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C4⋊C4×C139C2×D411yescharacteristic
204C22⋊C4×C139—21no—
205C22⋊C4×C139—21no—
206C22⋊C4×C139—41no—
207C22⋊C4×C139—41no—
208C22⋊C4×C139—41no—
209C22⋊C4×C139—41no—
210C22⋊C4×C139—41no—
211C42×C139—21no—
212C42×C139—21no—
213C42×C139—41no—
214C42×C139C2411yescharacteristic
215C23×C139—21no—
216C23×C139—21no—
217Q8×C139—21no—
218Q8×C139—21no—
219Q8×C139—21no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—41no—
223Q8×C139—41no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—41no—
228Q8×C139—82no—
229Q8×C139—82no—
230Q8×C139—82no—
231Q8×C139AGL(1,ℤ/8)12yes—
232D4×C139—21no—
233D4×C139—21no—
234D4×C139—21no—
235D4×C139#13712yes—
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—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
250C2×C4×C139—82no—
251C2×C4×C139—82no—
252C2×C4×C139—82no—
253C2×C4×C139C22×D411yescharacteristic
254C2×C4×C139C22×D411yescharacteristic
255C2×C4×C139H(5,𝔽2)11yescharacteristic
256C8×C139—22no—
257C8×C139—21no—
258C8×C139—21no—
259C8×C139—21no—
260C8×C139—21no—
261C8×C139—41no—
262C8×C139—41no—
263C8×C139—41no—
264C8×C139—41no—
265C22×C139—22no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
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×C139—81no—
283C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C139C2×#13711yescharacteristic
285C4×C139#57611yescharacteristic
286C4×C139#57811yescharacteristic
287C2×C139—42no—
288C2×C139—81no—
289C2×C139#326411yescharacteristic
290C2×C139#327011yescharacteristic
291C2×C139#329311yescharacteristic
292#20062C13911yesmaximal, characteristic, direct product factor, Sylow
293C139#2006211yescharacteristic, direct product factor, Sylow
294Q8×D8C2×C13911yescharacteristic
295#3367C2×C13911yescharacteristic
296#3328C2×C13911yescharacteristic, complemented
297D4×Q16C2×C13911yescharacteristic, complemented
298#1723C2×C13911yescharacteristic, complemented
299#1694C2×C13911yescharacteristic, complemented
300#1689C2×C13911yescharacteristic, complemented
301#1680C2×C13911yescharacteristic, complemented
302#1679C2×C13911yescharacteristic, complemented
303#1652C2×C13911yescharacteristic, complemented
304#1651C2×C13911yescharacteristic, complemented
305#1649C2×C13911yescharacteristic, complemented
306#1649C2×C13911yescharacteristic, complemented
307#1587C2×C13911yescharacteristic, complemented
308#1586C2×C13911yescharacteristic
309C22×Q16—21no—
310#556C22×C13911yescharacteristic
311D4×Q8C22×C13911yescharacteristic
312D4×Q8C22×C13911yescharacteristic
313D4×Q8C22×C13911yescharacteristic
314#500—21no—
315#500C22×C13911yescharacteristic
316#500C22×C13911yescharacteristic
317#498C22×C13911yescharacteristic
318#494C22×C13911yescharacteristic
319#489—21no—
320#487C22×C13911yescharacteristic
321#487C22×C13911yescharacteristic
322#485—21no—
323#477—21no—
324#475C22×C13911yescharacteristic
325#474—21no—
326#474—21no—
327#474C22×C13911yescharacteristic
328#474C22×C13911yescharacteristic
329#474C22×C13911yescharacteristic
330#470—21no—
331#467—21no—
332#463—21no—
333#462C22×C13911yescharacteristic
334#462C22×C13911yescharacteristic
335#462C22×C13911yescharacteristic
336#461C22×C13911yescharacteristic
337#451—21no—
338#451—21no—
339#451—21no—
340#446C22×C13911yescharacteristic
341C8×Q8C22×C13911yescharacteristic
342#440—21no—
343C4×Q16C22×C13911yescharacteristic
344C4×D8—21no—
345C4×D8C22×C13911yescharacteristic
346#436C22×C13911yescharacteristic
347C8×D4C22×C13911yescharacteristic
348#419—21no—
349#334C22×C13911yescharacteristic
350#334C22×C13911yescharacteristic
351#332C22×C13911yescharacteristic
352#332C22×C13911yescharacteristic
353#332C22×C13911yescharacteristic
354#332C22×C13911yescharacteristic
355Q8⋊C8C22×C13911yescharacteristic
356Q8⋊C8C22×C13911yescharacteristic
357D4⋊C8C22×C13911yescharacteristic
358D4⋊C8C22×C13911yescharacteristic
359#322C22×C13911yescharacteristic
360C22×Q8—21no—
361C22×Q8—21no—
362C22×Q8—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×Q16—44no—
369C2×Q16D4×C13911yescharacteristic
370C2×SD16—21no—
371C2×D8D4×C13911yescharacteristic
372C2×M16—21no—
373C22×C8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C13911yescharacteristic
378C4⋊Q8C23×C13911yescharacteristic
379C4⋊Q8C23×C13911yescharacteristic
380C4⋊Q8C23×C13911yescharacteristic
381#126—41no—
382#124—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C22⋊Q8—41no—
389C22⋊Q8—41no—
390C4×Q8—21no—
391C4×Q8C23×C13911yescharacteristic
392C4×Q8C23×C13911yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C13911yescharacteristic
397C4×D4C23×C13911yescharacteristic
398#117—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#107—41no—
405#107D4×C13911yescharacteristic
406#107D4×C13911yescharacteristic
407#106—21no—
408#106—41no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C13911yescharacteristic
412C4⋊C8C23×C13911yescharacteristic
413C4⋊C8C23×C13911yescharacteristic
414C4⋊C8C23×C13911yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103D4×C13911yescharacteristic
425#103D4×C13911yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C13911yescharacteristic
430#102D4×C13911yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C13911yescharacteristic
436C4×C8C23×C13911yescharacteristic
437C4×C8C23×C13911yescharacteristic
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—81no—
449C2×Q8—81no—
450C2×Q8—81no—
451C2×Q8C2×D4×C13911yescharacteristic
452C2×Q8C2×D4×C13911yescharacteristic
453C2×D4C2×D4×C13911yescharacteristic
454C2×D4C2×D4×C13911yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460Q16—22no—
461Q16—42no—
462Q16—42no—
463Q16—42no—
464Q16—81no—
465Q16—81no—
466SD16—42no—
467D8—22no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8C2×D4×C13911yescharacteristic
476C2×C8C2×D4×C13911yescharacteristic
477C2×C8C2×D4×C13911yescharacteristic
478C2×C8C2×D4×C13911yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C13911yescharacteristic
494C4⋊C4C2×D4×C13911yescharacteristic
495C4⋊C4C2×D4×C13911yescharacteristic
496C4⋊C4C2×D4×C13911yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42C24×C13911yescharacteristic
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—82no—
522Q8—82no—
523Q8—82no—
524Q8AGL(1,ℤ/8)×C13912yes—
525D4—21no—
526D4—21no—
527D4—21no—
528D4#137×C13912yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4C22×D4×C13911yescharacteristic
547C2×C4C22×D4×C13911yescharacteristic
548C2×C4H(5,𝔽2)×C13911yescharacteristic
549C8—22no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22D42×C13911yescharacteristic
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
577C4C2×#137×C13911yescharacteristic
578C4#576×C13911yescharacteristic
579C4#578×C13911yescharacteristic
580C2—42no—
581C2—81no—
582C2#3264×C13911yescharacteristic
583C2#3270×C13911yescharacteristic
584C2#3293×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radicalC2×D8×C139D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #3328×C139C2semidirect
4. D4×Q16×C139C2semidirect
5. #1723×C139C2semidirect
6. #1694×C139C2semidirect
7. #1689×C139C2semidirect
8. #1680×C139C2semidirect
9. #1679×C139C2semidirect
10. #1652×C139C2semidirect
11. #1651×C139C2semidirect
12. #1649×C139C2semidirect
13. #1649×C139C2semidirect
14. #1587×C139C2semidirect
292. #20062C139direct (N × H)
293. C139#20062direct (N × H)
296. #3328C2×C139semidirect
297. D4×Q16C2×C139semidirect
298. #1723C2×C139semidirect
299. #1694C2×C139semidirect
300. #1689C2×C139semidirect
301. #1680C2×C139semidirect
302. #1679C2×C139semidirect
303. #1652C2×C139semidirect
304. #1651C2×C139semidirect
305. #1649C2×C139semidirect
306. #1649C2×C139semidirect
307. #1587C2×C139semidirect

Maximal subgroups

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

subgroupindex
Q8×D8×C1392
#3367×C1392
#3328×C1392
D4×Q16×C1392
#1723×C1392
#1694×C1392
#1689×C1392
#1680×C1392
#1679×C1392
#1652×C1392
#1651×C1392
#1649×C1392
#1587×C1392
#1586×C1392
#20062139