Finite Group Databasebeta

← C139×#19866 #48014462

Subgroups — C139×#19866 #48014462

Order 35584.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3393×C139C211yesmaximal, characteristic
2#3360×C139C211yesmaximal, characteristic
3#3356×C139C211yesmaximal, characteristic, complemented
4#3342×C139C211yesmaximal, characteristic, complemented
5#1723×C139C211yesmaximal, characteristic, complemented
6#1693×C139C211yesmaximal, characteristic, complemented
7#1684×C139C211yesmaximal, characteristic, complemented
8#1671×C139C211yesmaximal, characteristic, complemented
9#1670×C139C211yesmaximal, characteristic, complemented
10#1650×C139C211yesmaximal, characteristic, complemented
11#1650×C139C211yesmaximal, characteristic, complemented
12#1643×C139C211yesmaximal, characteristic, complemented
13#1638×C139C211yesmaximal, characteristic, complemented
14#1581×C139C211yesmaximal, characteristic
15#1579×C139C211yesmaximal, characteristic, complemented
16#556×C139C2211yescharacteristic
17#556×C139C2211yescharacteristic
18#556×C139C2211yescharacteristic
19#554×C139C2211yescharacteristic
20#500×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#498×C139C2211yescharacteristic
23#495×C139—21no—
24#494×C139C2211yescharacteristic
25#488×C139—21no—
26#487×C139C2211yescharacteristic
27#487×C139C2211yescharacteristic
28#485×C139—21no—
29#485×C139—21no—
30#485×C139—21no—
31#483×C139—21no—
32#479×C139—21no—
33#477×C139C2211yescharacteristic
34#476×C139C2211yescharacteristic
35#475×C139C2211yescharacteristic
36#475×C139C2211yescharacteristic
37#475×C139C2211yescharacteristic
38#470×C139—21no—
39#467×C139—21no—
40#464×C139—21no—
41#464×C139—21no—
42#463×C139—21no—
43#461×C139C2211yescharacteristic
44#461×C139C2211yescharacteristic
45#461×C139C2211yescharacteristic
46C8×Q8×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48C4×Q16×C139—21no—
49C4×Q16×C139C2211yescharacteristic
50C4×SD16×C139—21no—
51C4×D8×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#428×C139—21no—
55#427×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#333×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
67C2×Q16×C139—21no—
68C2×Q16×C139—21no—
69C2×Q16×C139D411yescharacteristic
70C2×SD16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×D8×C139D411yescharacteristic
74C2×M16×C139—21no—
75C22×C8×C139—21no—
76C4⋊Q8×C139C2311yescharacteristic
77C4⋊Q8×C139C2311yescharacteristic
78C4⋊Q8×C139C2311yescharacteristic
79C4⋊Q8×C139C2311yescharacteristic
80#126×C139—41no—
81#126×C139—41no—
82#126×C139—41no—
83#125×C139—21no—
84#124×C139—21no—
85#124×C139—21no—
86#124×C139—21no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—21no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—41no—
92C4×Q8×C139—21no—
93C4×Q8×C139—21no—
94C4×Q8×C139—21no—
95C4×Q8×C139C2311yescharacteristic
96C4×Q8×C139C2311yescharacteristic
97C4×D4×C139—21no—
98C4×D4×C139C2311yescharacteristic
99C4×D4×C139C2311yescharacteristic
100#117×C139—21no—
101#117×C139—21no—
102#117×C139—21no—
103C2×C4⋊C4×C139—21no—
104#107×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—41no—
108#107×C139D411yescharacteristic
109#107×C139D411yescharacteristic
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139—21no—
114#106×C139—21no—
115#106×C139—21no—
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×C139—41no—
132#103×C139D411yescharacteristic
133#103×C139D411yescharacteristic
134#102×C139—21no—
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
144C2×Q8×C139—21no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139C2×D411yescharacteristic
149C2×Q8×C139C2×D411yescharacteristic
150C2×D4×C139C2×D411yescharacteristic
151C2×D4×C139C2×D411yescharacteristic
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—41no—
155Q16×C139—22no—
156Q16×C139—42no—
157Q16×C139—81no—
158SD16×C139—42no—
159SD16×C139—81no—
160SD16×C139—81no—
161D8×C139—41no—
162M16×C139—42no—
163C2×C8×C139—21no—
164C2×C8×C139—21no—
165C2×C8×C139—21no—
166C2×C8×C139—21no—
167C2×C8×C139—21no—
168C2×C8×C139—42no—
169C2×C8×C139C2×D411yescharacteristic
170C2×C8×C139C2×D411yescharacteristic
171C2×C8×C139C2×D411yescharacteristic
172C2×C8×C139C2×D411yescharacteristic
173C4⋊C4×C139—21no—
174C4⋊C4×C139—21no—
175C4⋊C4×C139—21no—
176C4⋊C4×C139—21no—
177C4⋊C4×C139—21no—
178C4⋊C4×C139—21no—
179C4⋊C4×C139—21no—
180C4⋊C4×C139—21no—
181C4⋊C4×C139—21no—
182C4⋊C4×C139—21no—
183C4⋊C4×C139—41no—
184C4⋊C4×C139—41no—
185C4⋊C4×C139—41no—
186C4⋊C4×C139—41no—
187C4⋊C4×C139—41no—
188C4⋊C4×C139C2×D411yescharacteristic
189C4⋊C4×C139C2×D411yescharacteristic
190C4⋊C4×C139C2×D411yescharacteristic
191C4⋊C4×C139C2×D411yescharacteristic
192C22⋊C4×C139—21no—
193C22⋊C4×C139—21no—
194C22⋊C4×C139—41no—
195C22⋊C4×C139—41no—
196C22⋊C4×C139—41no—
197C22⋊C4×C139—41no—
198C22⋊C4×C139—41no—
199C22⋊C4×C139—41no—
200C22⋊C4×C139—41no—
201C42×C139—21no—
202C42×C139—21no—
203C42×C139—41no—
204C42×C139—41no—
205C42×C139—41no—
206C42×C139C2411yescharacteristic
207C23×C139—21no—
208C23×C139—21no—
209Q8×C139—21no—
210Q8×C139—21no—
211Q8×C139—21no—
212Q8×C139—21no—
213Q8×C139—41no—
214Q8×C139—41no—
215Q8×C139—41no—
216Q8×C139—41no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—81no—
220D4×C139—21no—
221D4×C139—21no—
222D4×C139—21no—
223D4×C139—21no—
224C2×C4×C139—21no—
225C2×C4×C139—21no—
226C2×C4×C139—21no—
227C2×C4×C139—21no—
228C2×C4×C139—21no—
229C2×C4×C139—21no—
230C2×C4×C139—41no—
231C2×C4×C139—41no—
232C2×C4×C139—41no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—161no—
239C2×C4×C139C22×D411yescharacteristic
240C2×C4×C139C22×D411yescharacteristic
241C2×C4×C139H(5,𝔽2)11yescharacteristic
242C8×C139—21no—
243C8×C139—21no—
244C8×C139—21no—
245C8×C139—41no—
246C8×C139—41no—
247C8×C139—41no—
248C8×C139—41no—
249C8×C139—41no—
250C8×C139#13512yes—
251C22×C139—41no—
252C22×C139—41no—
253C22×C139—41no—
254C22×C139—41no—
255C22×C139—41no—
256C22×C139—41no—
257C22×C139D4211yescharacteristic
258C4×C139—21no—
259C4×C139—41no—
260C4×C139—41no—
261C4×C139—41no—
262C4×C139—41no—
263C4×C139—41no—
264C4×C139—41no—
265C4×C139—81no—
266C4×C139—81no—
267C4×C139—81no—
268C4×C139—81no—
269C4×C139C2×#13511yescharacteristic
270C4×C139#57511yescharacteristic
271C4×C139#57711yescharacteristic
272C4×C139#57811yescharacteristic
273C2×C139—81no—
274C2×C139—81no—
275C2×C139#327111yescharacteristic
276C2×C139#328311yescharacteristic
277C2×C139#328911yescharacteristic
278#19866C13911yesmaximal, characteristic, direct product factor, Sylow
279C139#1986611yescharacteristic, direct product factor, Sylow
280#3393C2×C13911yescharacteristic
281#3360C2×C13911yescharacteristic
282#3356C2×C13911yescharacteristic, complemented
283#3342C2×C13911yescharacteristic, complemented
284#1723C2×C13911yescharacteristic, complemented
285#1693C2×C13911yescharacteristic, complemented
286#1684C2×C13911yescharacteristic, complemented
287#1671C2×C13911yescharacteristic, complemented
288#1670C2×C13911yescharacteristic, complemented
289#1650C2×C13911yescharacteristic, complemented
290#1650C2×C13911yescharacteristic, complemented
291#1643C2×C13911yescharacteristic, complemented
292#1638C2×C13911yescharacteristic, complemented
293#1581C2×C13911yescharacteristic
294#1579C2×C13911yescharacteristic, complemented
295#556C22×C13911yescharacteristic
296#556C22×C13911yescharacteristic
297#556C22×C13911yescharacteristic
298#554C22×C13911yescharacteristic
299#500C22×C13911yescharacteristic
300#500C22×C13911yescharacteristic
301#498C22×C13911yescharacteristic
302#495—21no—
303#494C22×C13911yescharacteristic
304#488—21no—
305#487C22×C13911yescharacteristic
306#487C22×C13911yescharacteristic
307#485—21no—
308#485—21no—
309#485—21no—
310#483—21no—
311#479—21no—
312#477C22×C13911yescharacteristic
313#476C22×C13911yescharacteristic
314#475C22×C13911yescharacteristic
315#475C22×C13911yescharacteristic
316#475C22×C13911yescharacteristic
317#470—21no—
318#467—21no—
319#464—21no—
320#464—21no—
321#463—21no—
322#461C22×C13911yescharacteristic
323#461C22×C13911yescharacteristic
324#461C22×C13911yescharacteristic
325C8×Q8C22×C13911yescharacteristic
326C8×Q8C22×C13911yescharacteristic
327C4×Q16—21no—
328C4×Q16C22×C13911yescharacteristic
329C4×SD16—21no—
330C4×D8C22×C13911yescharacteristic
331#436C22×C13911yescharacteristic
332C8×D4C22×C13911yescharacteristic
333#428—21no—
334#427—21no—
335#335C22×C13911yescharacteristic
336#334C22×C13911yescharacteristic
337#333C22×C13911yescharacteristic
338#332C22×C13911yescharacteristic
339#332C22×C13911yescharacteristic
340#332C22×C13911yescharacteristic
341Q8⋊C8C22×C13911yescharacteristic
342Q8⋊C8C22×C13911yescharacteristic
343D4⋊C8C22×C13911yescharacteristic
344D4⋊C8C22×C13911yescharacteristic
345#322C22×C13911yescharacteristic
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16D4×C13911yescharacteristic
349C2×SD16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×D8D4×C13911yescharacteristic
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8C23×C13911yescharacteristic
356C4⋊Q8C23×C13911yescharacteristic
357C4⋊Q8C23×C13911yescharacteristic
358C4⋊Q8C23×C13911yescharacteristic
359#126—41no—
360#126—41no—
361#126—41no—
362#125—21no—
363#124—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C13911yescharacteristic
375C4×Q8C23×C13911yescharacteristic
376C4×D4—21no—
377C4×D4C23×C13911yescharacteristic
378C4×D4C23×C13911yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#107D4×C13911yescharacteristic
388#107D4×C13911yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C13911yescharacteristic
398C4⋊C8C23×C13911yescharacteristic
399C4⋊C8C23×C13911yescharacteristic
400C4⋊C8C23×C13911yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—41no—
411#103D4×C13911yescharacteristic
412#103D4×C13911yescharacteristic
413#102—21no—
414#102D4×C13911yescharacteristic
415#102D4×C13911yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C13911yescharacteristic
421C4×C8C23×C13911yescharacteristic
422C4×C8C23×C13911yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×D4×C13911yescharacteristic
428C2×Q8C2×D4×C13911yescharacteristic
429C2×D4C2×D4×C13911yescharacteristic
430C2×D4C2×D4×C13911yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434Q16—22no—
435Q16—42no—
436Q16—81no—
437SD16—42no—
438SD16—81no—
439SD16—81no—
440D8—41no—
441M16—42no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8C2×D4×C13911yescharacteristic
449C2×C8C2×D4×C13911yescharacteristic
450C2×C8C2×D4×C13911yescharacteristic
451C2×C8C2×D4×C13911yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C13911yescharacteristic
468C4⋊C4C2×D4×C13911yescharacteristic
469C4⋊C4C2×D4×C13911yescharacteristic
470C4⋊C4C2×D4×C13911yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C13911yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—161no—
518C2×C4C22×D4×C13911yescharacteristic
519C2×C4C22×D4×C13911yescharacteristic
520C2×C4H(5,𝔽2)×C13911yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8#135×C13912yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D42×C13911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C13911yescharacteristic
549C4#575×C13911yescharacteristic
550C4#577×C13911yescharacteristic
551C4#578×C13911yescharacteristic
552C2—81no—
553C2—81no—
554C2#3271×C13911yescharacteristic
555C2#3283×C13911yescharacteristic
556C2#3289×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. #3356×C139C2semidirect
4. #3342×C139C2semidirect
5. #1723×C139C2semidirect
6. #1693×C139C2semidirect
7. #1684×C139C2semidirect
8. #1671×C139C2semidirect
9. #1670×C139C2semidirect
10. #1650×C139C2semidirect
11. #1650×C139C2semidirect
12. #1643×C139C2semidirect
13. #1638×C139C2semidirect
15. #1579×C139C2semidirect
278. #19866C139direct (N × H)
279. C139#19866direct (N × H)
282. #3356C2×C139semidirect
283. #3342C2×C139semidirect
284. #1723C2×C139semidirect
285. #1693C2×C139semidirect
286. #1684C2×C139semidirect
287. #1671C2×C139semidirect
288. #1670C2×C139semidirect
289. #1650C2×C139semidirect
290. #1650C2×C139semidirect
291. #1643C2×C139semidirect
292. #1638C2×C139semidirect
294. #1579C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3393×C1392
#3360×C1392
#3356×C1392
#3342×C1392
#1723×C1392
#1693×C1392
#1684×C1392
#1671×C1392
#1670×C1392
#1650×C1392
#1643×C1392
#1638×C1392
#1581×C1392
#1579×C1392
#19866139