Finite Group Databasebeta

← C139×#20129 #48014725

Subgroups — C139×#20129 #48014725

Order 35584.

558 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3398×C139C211yesmaximal, characteristic
2#3374×C139C211yesmaximal, characteristic, complemented
3#3364×C139C211yesmaximal, characteristic
4#3342×C139C211yesmaximal, characteristic
5#1723×C139C211yesmaximal, characteristic, complemented
6#1700×C139C211yesmaximal, characteristic, complemented
7#1694×C139C211yesmaximal, characteristic, complemented
8#1679×C139C211yesmaximal, characteristic
9#1670×C139C211yesmaximal, characteristic, complemented
10#1653×C139C211yesmaximal, characteristic, complemented
11#1652×C139C211yesmaximal, characteristic
12#1650×C139C211yesmaximal, characteristic
13#1648×C139C211yesmaximal, characteristic, complemented
14#1587×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic
16#557×C139C2211yescharacteristic
17#557×C139C2211yescharacteristic
18#556×C139C2211yescharacteristic
19#556×C139C2211yescharacteristic
20#500×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic
22#498×C139C2211yescharacteristic
23#497×C139—21no—
24#494×C139C2211yescharacteristic
25#491×C139—21no—
26#488×C139—21no—
27#487×C139C2211yescharacteristic
28#487×C139C2211yescharacteristic
29#485×C139—21no—
30#485×C139—21no—
31#479×C139—21no—
32#479×C139—21no—
33#475×C139C2211yescharacteristic
34#475×C139C2211yescharacteristic
35#475×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#467×C139—21no—
38#464×C139—21no—
39#464×C139—21no—
40#462×C139—21no—
41#462×C139—21no—
42#462×C139C2211yescharacteristic
43#462×C139C2211yescharacteristic
44#462×C139C2211yescharacteristic
45#461×C139C2211yescharacteristic
46#446×C139C2211yescharacteristic
47#446×C139C2211yescharacteristic
48C8×Q8×C139C2211yescharacteristic
49#441×C139—21no—
50#441×C139—21no—
51C4×Q16×C139—21no—
52C4×Q16×C139C2211yescharacteristic
53C4×SD16×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55#427×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#332×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C2×Q16×C139—21no—
68C2×Q16×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139D411yescharacteristic
73C2×SD16×C139—21no—
74C2×SD16×C139D411yescharacteristic
75C22×C8×C139—21no—
76C4⋊Q8×C139—21no—
77C4⋊Q8×C139—21no—
78C4⋊Q8×C139C2311yescharacteristic
79C4⋊Q8×C139C2311yescharacteristic
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82#126×C139—41no—
83#126×C139—41no—
84#125×C139—21no—
85#125×C139—21no—
86#125×C139—41no—
87#125×C139—41no—
88#124×C139—21no—
89#124×C139—21no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—21no—
92C4×Q8×C139—21no—
93C4×Q8×C139—21no—
94C4×Q8×C139—21no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139—21no—
98C4×Q8×C139C2311yescharacteristic
99C4×Q8×C139C2311yescharacteristic
100C4×Q8×C139C2311yescharacteristic
101C4×D4×C139C2311yescharacteristic
102#117×C139—21no—
103#117×C139—21no—
104#107×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—41no—
108#107×C139D411yescharacteristic
109#106×C139—21no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—41no—
113#106×C139D411yescharacteristic
114C4⋊C8×C139—21no—
115C4⋊C8×C139—21no—
116C4⋊C8×C139—21no—
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121#103×C139—21no—
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—21no—
132#103×C139D411yescharacteristic
133#103×C139D411yescharacteristic
134#103×C139D411yescharacteristic
135#102×C139—21no—
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138#97×C139—21no—
139#97×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×Q8×C139C2×D411yescharacteristic
151C2×D4×C139C2×D411yescharacteristic
152C22×C4×C139—21no—
153Q16×C139—41no—
154Q16×C139—42no—
155Q16×C139—42no—
156Q16×C139—42no—
157Q16×C139—81no—
158Q16×C139—81no—
159SD16×C139—41no—
160SD16×C139—81no—
161C2×C8×C139—21no—
162C2×C8×C139—21no—
163C2×C8×C139—21no—
164C2×C8×C139—21no—
165C2×C8×C139—21no—
166C2×C8×C139—42no—
167C2×C8×C139C2×D411yescharacteristic
168C2×C8×C139C2×D411yescharacteristic
169C2×C8×C139C2×D411yescharacteristic
170C2×C8×C139C2×D411yescharacteristic
171C4⋊C4×C139—21no—
172C4⋊C4×C139—21no—
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—41no—
183C4⋊C4×C139—41no—
184C4⋊C4×C139—41no—
185C4⋊C4×C139—41no—
186C4⋊C4×C139—41no—
187C4⋊C4×C139—41no—
188C4⋊C4×C139—41no—
189C4⋊C4×C139—41no—
190C4⋊C4×C139C2×D411yescharacteristic
191C4⋊C4×C139C2×D411yescharacteristic
192C4⋊C4×C139C2×D411yescharacteristic
193C4⋊C4×C139C2×D411yescharacteristic
194C22⋊C4×C139—21no—
195C22⋊C4×C139—41no—
196C22⋊C4×C139—41no—
197C22⋊C4×C139—41no—
198C22⋊C4×C139—41no—
199C42×C139—21no—
200C42×C139—21no—
201C42×C139—21no—
202C42×C139—41no—
203C42×C139—41no—
204C42×C139—41no—
205C42×C139—41no—
206C42×C139C2411yescharacteristic
207C23×C139—21no—
208Q8×C139—21no—
209Q8×C139—21no—
210Q8×C139—21no—
211Q8×C139—21no—
212Q8×C139—21no—
213Q8×C139—21no—
214Q8×C139—41no—
215Q8×C139—41no—
216Q8×C139—41no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
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—21no—
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×C139C22×D411yescharacteristic
238C2×C4×C139C22×D411yescharacteristic
239C2×C4×C139H(5,𝔽2)11yescharacteristic
240C8×C139—22no—
241C8×C139—21no—
242C8×C139—21no—
243C8×C139—21no—
244C8×C139—21no—
245C8×C139—41no—
246C8×C139—41no—
247C8×C139—41no—
248C8×C139—41no—
249C22×C139—41no—
250C22×C139—41no—
251C22×C139—41no—
252C22×C139D4211yescharacteristic
253C4×C139—21no—
254C4×C139—41no—
255C4×C139—41no—
256C4×C139—41no—
257C4×C139—41no—
258C4×C139—41no—
259C4×C139—41no—
260C4×C139—41no—
261C4×C139—81no—
262C4×C139—81no—
263C4×C139—81no—
264C4×C139—81no—
265C4×C139#57511yescharacteristic
266C4×C139#57511yescharacteristic
267C4×C139#57711yescharacteristic
268C4×C139#57811yescharacteristic
269C2×C139—81no—
270C2×C139#326911yescharacteristic
271C2×C139#327111yescharacteristic
272C2×C139#329311yescharacteristic
273#20129C13911yesmaximal, characteristic, direct product factor, Sylow
274C139#2012911yescharacteristic, direct product factor, Sylow
275#3398C2×C13911yescharacteristic
276#3374C2×C13911yescharacteristic, complemented
277#3364C2×C13911yescharacteristic
278#3342C2×C13911yescharacteristic
279#1723C2×C13911yescharacteristic, complemented
280#1700C2×C13911yescharacteristic, complemented
281#1694C2×C13911yescharacteristic, complemented
282#1679C2×C13911yescharacteristic
283#1670C2×C13911yescharacteristic, complemented
284#1653C2×C13911yescharacteristic, complemented
285#1652C2×C13911yescharacteristic
286#1650C2×C13911yescharacteristic
287#1648C2×C13911yescharacteristic, complemented
288#1587C2×C13911yescharacteristic, complemented
289#1585C2×C13911yescharacteristic
290#557C22×C13911yescharacteristic
291#557C22×C13911yescharacteristic
292#556C22×C13911yescharacteristic
293#556C22×C13911yescharacteristic
294#500C22×C13911yescharacteristic
295#500C22×C13911yescharacteristic
296#498C22×C13911yescharacteristic
297#497—21no—
298#494C22×C13911yescharacteristic
299#491—21no—
300#488—21no—
301#487C22×C13911yescharacteristic
302#487C22×C13911yescharacteristic
303#485—21no—
304#485—21no—
305#479—21no—
306#479—21no—
307#475C22×C13911yescharacteristic
308#475C22×C13911yescharacteristic
309#475C22×C13911yescharacteristic
310#474C22×C13911yescharacteristic
311#467—21no—
312#464—21no—
313#464—21no—
314#462—21no—
315#462—21no—
316#462C22×C13911yescharacteristic
317#462C22×C13911yescharacteristic
318#462C22×C13911yescharacteristic
319#461C22×C13911yescharacteristic
320#446C22×C13911yescharacteristic
321#446C22×C13911yescharacteristic
322C8×Q8C22×C13911yescharacteristic
323#441—21no—
324#441—21no—
325C4×Q16—21no—
326C4×Q16C22×C13911yescharacteristic
327C4×SD16C22×C13911yescharacteristic
328C8×D4C22×C13911yescharacteristic
329#427—21no—
330#335C22×C13911yescharacteristic
331#334C22×C13911yescharacteristic
332#332C22×C13911yescharacteristic
333#332C22×C13911yescharacteristic
334#332C22×C13911yescharacteristic
335#332C22×C13911yescharacteristic
336Q8⋊C8C22×C13911yescharacteristic
337Q8⋊C8C22×C13911yescharacteristic
338Q8⋊C8C22×C13911yescharacteristic
339D4⋊C8C22×C13911yescharacteristic
340#322C22×C13911yescharacteristic
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16D4×C13911yescharacteristic
347C2×SD16—21no—
348C2×SD16D4×C13911yescharacteristic
349C22×C8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C23×C13911yescharacteristic
353C4⋊Q8C23×C13911yescharacteristic
354C4⋊Q8C23×C13911yescharacteristic
355C4⋊Q8C23×C13911yescharacteristic
356#126—41no—
357#126—41no—
358#125—21no—
359#125—21no—
360#125—41no—
361#125—41no—
362#124—21no—
363#124—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C13911yescharacteristic
373C4×Q8C23×C13911yescharacteristic
374C4×Q8C23×C13911yescharacteristic
375C4×D4C23×C13911yescharacteristic
376#117—21no—
377#117—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—41no—
382#107D4×C13911yescharacteristic
383#106—21no—
384#106—21no—
385#106—21no—
386#106—41no—
387#106D4×C13911yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C13911yescharacteristic
392C4⋊C8C23×C13911yescharacteristic
393C4⋊C8C23×C13911yescharacteristic
394C4⋊C8C23×C13911yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103D4×C13911yescharacteristic
407#103D4×C13911yescharacteristic
408#103D4×C13911yescharacteristic
409#102—21no—
410#102D4×C13911yescharacteristic
411C22⋊C8—21no—
412#97—21no—
413#97—21no—
414C4×C8—21no—
415C4×C8C23×C13911yescharacteristic
416C4×C8C23×C13911yescharacteristic
417C4×C8C23×C13911yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C13911yescharacteristic
423C2×Q8C2×D4×C13911yescharacteristic
424C2×Q8C2×D4×C13911yescharacteristic
425C2×D4C2×D4×C13911yescharacteristic
426C22×C4—21no—
427Q16—41no—
428Q16—42no—
429Q16—42no—
430Q16—42no—
431Q16—81no—
432Q16—81no—
433SD16—41no—
434SD16—81no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—42no—
441C2×C8C2×D4×C13911yescharacteristic
442C2×C8C2×D4×C13911yescharacteristic
443C2×C8C2×D4×C13911yescharacteristic
444C2×C8C2×D4×C13911yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C13911yescharacteristic
465C4⋊C4C2×D4×C13911yescharacteristic
466C4⋊C4C2×D4×C13911yescharacteristic
467C4⋊C4C2×D4×C13911yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42C24×C13911yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496D4—21no—
497D4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4C22×D4×C13911yescharacteristic
512C2×C4C22×D4×C13911yescharacteristic
513C2×C4H(5,𝔽2)×C13911yescharacteristic
514C8—22no—
515C8—21no—
516C8—21no—
517C8—21no—
518C8—21no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22D42×C13911yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4#575×C13911yescharacteristic
540C4#575×C13911yescharacteristic
541C4#577×C13911yescharacteristic
542C4#578×C13911yescharacteristic
543C2—81no—
544C2#3269×C13911yescharacteristic
545C2#3271×C13911yescharacteristic
546C2#3293×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radicalC2×D4×C139C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3374×C139C2semidirect
5. #1723×C139C2semidirect
6. #1700×C139C2semidirect
7. #1694×C139C2semidirect
9. #1670×C139C2semidirect
10. #1653×C139C2semidirect
13. #1648×C139C2semidirect
14. #1587×C139C2semidirect
273. #20129C139direct (N × H)
274. C139#20129direct (N × H)
276. #3374C2×C139semidirect
279. #1723C2×C139semidirect
280. #1700C2×C139semidirect
281. #1694C2×C139semidirect
283. #1670C2×C139semidirect
284. #1653C2×C139semidirect
287. #1648C2×C139semidirect
288. #1587C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3398×C1392
#3374×C1392
#3364×C1392
#3342×C1392
#1723×C1392
#1700×C1392
#1694×C1392
#1679×C1392
#1670×C1392
#1653×C1392
#1652×C1392
#1650×C1392
#1648×C1392
#1587×C1392
#1585×C1392
#20129139