Finite Group Databasebeta

← C139×#20197 #48014793

Subgroups — C139×#20197 #48014793

Order 35584.

618 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3386×C139C211yesmaximal, characteristic, complemented
2#3372×C139C211yesmaximal, characteristic, complemented
3#3335×C139C211yesmaximal, characteristic
4#3276×C139C211yesmaximal, characteristic
5#1723×C139C211yesmaximal, characteristic, complemented
6#1703×C139C211yesmaximal, characteristic, complemented
7#1692×C139C211yesmaximal, characteristic, complemented
8#1690×C139C211yesmaximal, characteristic, complemented
9#1673×C139C211yesmaximal, characteristic, complemented
10#1648×C139C211yesmaximal, characteristic, complemented
11#1647×C139C211yesmaximal, characteristic
12#1643×C139C211yesmaximal, characteristic, complemented
13#1637×C139C211yesmaximal, characteristic, complemented
14#1592×C139C211yesmaximal, characteristic, complemented
15#1582×C139C211yesmaximal, characteristic, complemented
16C2×#137×C139—21no—
17#557×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#547×C139C2211yescharacteristic
21#501×C139—21no—
22#500×C139C2211yescharacteristic
23#500×C139C2211yescharacteristic
24#498×C139C2211yescharacteristic
25#494×C139C2211yescharacteristic
26#491×C139—21no—
27#487×C139C2211yescharacteristic
28#487×C139C2211yescharacteristic
29#483×C139—21no—
30#481×C139—21no—
31#479×C139—21no—
32#478×C139—21no—
33#477×C139—21no—
34#477×C139C2211yescharacteristic
35#476×C139C2211yescharacteristic
36#475×C139C2211yescharacteristic
37#475×C139C2211yescharacteristic
38#474×C139C2211yescharacteristic
39#470×C139—21no—
40#465×C139—21no—
41#462×C139C2211yescharacteristic
42#461×C139—21no—
43#461×C139C2211yescharacteristic
44#461×C139C2211yescharacteristic
45#452×C139—21no—
46#451×C139—21no—
47#446×C139C2211yescharacteristic
48#446×C139C2211yescharacteristic
49#440×C139—21no—
50#440×C139—21no—
51C4×SD16×C139C2211yescharacteristic
52C4×SD16×C139C2211yescharacteristic
53#436×C139C2211yescharacteristic
54C8×D4×C139C2211yescharacteristic
55C2×#106×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×#41×C139—21no—
68C22×Q8×C139—21no—
69#137×C139—44no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×Q16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—21no—
75C2×SD16×C139D411yescharacteristic
76C2×SD16×C139D411yescharacteristic
77C2×M16×C139—21no—
78C22×C8×C139—21no—
79C4⋊Q8×C139—21no—
80C4⋊Q8×C139—21no—
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83C4⋊Q8×C139C2311yescharacteristic
84C4⋊Q8×C139C2311yescharacteristic
85#125×C139—21no—
86#125×C139—21no—
87#125×C139—41no—
88#123×C139—41no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—41no—
93C22⋊Q8×C139—41no—
94#121×C139—21no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139C2311yescharacteristic
98C4×Q8×C139C2311yescharacteristic
99C4×D4×C139—21no—
100C4×D4×C139—21no—
101C4×D4×C139C2311yescharacteristic
102C4×D4×C139C2311yescharacteristic
103C2×C4⋊C4×C139—21no—
104C2×C4⋊C4×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139—41no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139—21no—
114#106×C139—21no—
115#106×C139D411yescharacteristic
116#106×C139D411yescharacteristic
117C4⋊C8×C139—21no—
118C4⋊C8×C139—21no—
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122C4⋊C8×C139C2311yescharacteristic
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×C139—21no—
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140#97×C139—21no—
141#97×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145#41×C139—42no—
146#41×C139—81no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—41no—
152C2×Q8×C139—42no—
153C2×Q8×C139—81no—
154C2×Q8×C139C2×D411yescharacteristic
155C2×Q8×C139C2×D411yescharacteristic
156C2×D4×C139—41no—
157C2×D4×C139C2×D411yescharacteristic
158C2×D4×C139C2×D411yescharacteristic
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—41no—
162C22×C4×C139—41no—
163C22×C4×C139—41no—
164Q16×C139—42no—
165Q16×C139—42no—
166Q16×C139—81no—
167SD16×C139—22no—
168SD16×C139—22no—
169SD16×C139—42no—
170SD16×C139—42no—
171M16×C139—42no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—42no—
178C2×C8×C139C2×D411yescharacteristic
179C2×C8×C139C2×D411yescharacteristic
180C2×C8×C139C2×D411yescharacteristic
181C2×C8×C139C2×D411yescharacteristic
182C4⋊C4×C139—21no—
183C4⋊C4×C139—21no—
184C4⋊C4×C139—21no—
185C4⋊C4×C139—21no—
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—41no—
193C4⋊C4×C139—41no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139—41no—
198C4⋊C4×C139—41no—
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C22⋊C4×C139—21no—
204C22⋊C4×C139—21no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C22⋊C4×C139—41no—
208C42×C139—21no—
209C42×C139—21no—
210C42×C139—41no—
211C42×C139C2411yescharacteristic
212C23×C139—21no—
213C23×C139—21no—
214Q8×C139—21no—
215Q8×C139—21no—
216Q8×C139—21no—
217Q8×C139—21no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222Q8×C139—41no—
223Q8×C139—41no—
224Q8×C139—81no—
225Q8×C139—82no—
226D4×C139—21no—
227D4×C139—21no—
228D4×C139—21no—
229D4×C139—82no—
230D4×C139AGL(1,ℤ/8)12yes—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—82no—
246C2×C4×C139—82no—
247C2×C4×C139—161no—
248C2×C4×C139C22×D411yescharacteristic
249C2×C4×C139C22×D411yescharacteristic
250C2×C4×C139H(5,𝔽2)11yescharacteristic
251C8×C139—21no—
252C8×C139—21no—
253C8×C139—21no—
254C8×C139—41no—
255C8×C139—41no—
256C8×C139—41no—
257C8×C139—41no—
258C8×C139—41no—
259C8×C139#13712yescomplemented
260C22×C139—22no—
261C22×C139—41no—
262C22×C139—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139D4211yescharacteristic
267C4×C139—21no—
268C4×C139—41no—
269C4×C139—41no—
270C4×C139—41no—
271C4×C139—41no—
272C4×C139—41no—
273C4×C139—41no—
274C4×C139—81no—
275C4×C139—81no—
276C4×C139—81no—
277C4×C139—81no—
278C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C139C2×#13711yescharacteristic
280C4×C139#57711yescharacteristic
281C4×C139#57811yescharacteristic
282C2×C139—42no—
283C2×C139—81no—
284C2×C139#326511yescharacteristic
285C2×C139#327611yescharacteristic
286C2×C139#328911yescharacteristic
287#20197C13911yesmaximal, characteristic, direct product factor, Sylow
288C139#2019711yescharacteristic, direct product factor, Sylow
289#3386C2×C13911yescharacteristic, complemented
290#3372C2×C13911yescharacteristic, complemented
291#3335C2×C13911yescharacteristic
292#3276C2×C13911yescharacteristic
293#1723C2×C13911yescharacteristic, complemented
294#1703C2×C13911yescharacteristic, complemented
295#1692C2×C13911yescharacteristic, complemented
296#1690C2×C13911yescharacteristic, complemented
297#1673C2×C13911yescharacteristic, complemented
298#1648C2×C13911yescharacteristic, complemented
299#1647C2×C13911yescharacteristic
300#1643C2×C13911yescharacteristic, complemented
301#1637C2×C13911yescharacteristic, complemented
302#1592C2×C13911yescharacteristic, complemented
303#1582C2×C13911yescharacteristic, complemented
304C2×#137—21no—
305#557C22×C13911yescharacteristic
306#554C22×C13911yescharacteristic
307D4×Q8C22×C13911yescharacteristic
308#547C22×C13911yescharacteristic
309#501—21no—
310#500C22×C13911yescharacteristic
311#500C22×C13911yescharacteristic
312#498C22×C13911yescharacteristic
313#494C22×C13911yescharacteristic
314#491—21no—
315#487C22×C13911yescharacteristic
316#487C22×C13911yescharacteristic
317#483—21no—
318#481—21no—
319#479—21no—
320#478—21no—
321#477—21no—
322#477C22×C13911yescharacteristic
323#476C22×C13911yescharacteristic
324#475C22×C13911yescharacteristic
325#475C22×C13911yescharacteristic
326#474C22×C13911yescharacteristic
327#470—21no—
328#465—21no—
329#462C22×C13911yescharacteristic
330#461—21no—
331#461C22×C13911yescharacteristic
332#461C22×C13911yescharacteristic
333#452—21no—
334#451—21no—
335#446C22×C13911yescharacteristic
336#446C22×C13911yescharacteristic
337#440—21no—
338#440—21no—
339C4×SD16C22×C13911yescharacteristic
340C4×SD16C22×C13911yescharacteristic
341#436C22×C13911yescharacteristic
342C8×D4C22×C13911yescharacteristic
343C2×#106—21no—
344#335C22×C13911yescharacteristic
345#334C22×C13911yescharacteristic
346#333C22×C13911yescharacteristic
347#332C22×C13911yescharacteristic
348#332C22×C13911yescharacteristic
349#332C22×C13911yescharacteristic
350Q8⋊C8C22×C13911yescharacteristic
351Q8⋊C8C22×C13911yescharacteristic
352D4⋊C8C22×C13911yescharacteristic
353D4⋊C8C22×C13911yescharacteristic
354#322C22×C13911yescharacteristic
355C2×#41—21no—
356C22×Q8—21no—
357#137—44no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16D4×C13911yescharacteristic
364C2×SD16D4×C13911yescharacteristic
365C2×M16—21no—
366C22×C8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8C23×C13911yescharacteristic
370C4⋊Q8C23×C13911yescharacteristic
371C4⋊Q8C23×C13911yescharacteristic
372C4⋊Q8C23×C13911yescharacteristic
373#125—21no—
374#125—21no—
375#125—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—41no—
381C22⋊Q8—41no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C13911yescharacteristic
386C4×Q8C23×C13911yescharacteristic
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C23×C13911yescharacteristic
390C4×D4C23×C13911yescharacteristic
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—41no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106D4×C13911yescharacteristic
404#106D4×C13911yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C13911yescharacteristic
408C4⋊C8C23×C13911yescharacteristic
409C4⋊C8C23×C13911yescharacteristic
410C4⋊C8C23×C13911yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—41no—
420#103D4×C13911yescharacteristic
421#103D4×C13911yescharacteristic
422#102—21no—
423#102—21no—
424#102D4×C13911yescharacteristic
425#102D4×C13911yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428#97—21no—
429#97—21no—
430C4×C8C23×C13911yescharacteristic
431C4×C8C23×C13911yescharacteristic
432C4×C8C23×C13911yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8C2×D4×C13911yescharacteristic
443C2×Q8C2×D4×C13911yescharacteristic
444C2×D4—41no—
445C2×D4C2×D4×C13911yescharacteristic
446C2×D4C2×D4×C13911yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—42no—
453Q16—42no—
454Q16—81no—
455SD16—22no—
456SD16—22no—
457SD16—42no—
458SD16—42no—
459M16—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8C2×D4×C13911yescharacteristic
467C2×C8C2×D4×C13911yescharacteristic
468C2×C8C2×D4×C13911yescharacteristic
469C2×C8C2×D4×C13911yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4C2×D4×C13911yescharacteristic
488C4⋊C4C2×D4×C13911yescharacteristic
489C4⋊C4C2×D4×C13911yescharacteristic
490C4⋊C4C2×D4×C13911yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42C24×C13911yescharacteristic
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—82no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4AGL(1,ℤ/8)×C13912yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—161no—
536C2×C4C22×D4×C13911yescharacteristic
537C2×C4C22×D4×C13911yescharacteristic
538C2×C4H(5,𝔽2)×C13911yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8#137×C13912yescomplemented
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22D42×C13911yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
567C4C2×#137×C13911yescharacteristic
568C4#577×C13911yescharacteristic
569C4#578×C13911yescharacteristic
570C2—42no—
571C2—81no—
572C2#3265×C13911yescharacteristic
573C2#3276×C13911yescharacteristic
574C2#3289×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#547×C139C22
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. #3386×C139C2semidirect
2. #3372×C139C2semidirect
5. #1723×C139C2semidirect
6. #1703×C139C2semidirect
7. #1692×C139C2semidirect
8. #1690×C139C2semidirect
9. #1673×C139C2semidirect
10. #1648×C139C2semidirect
12. #1643×C139C2semidirect
13. #1637×C139C2semidirect
14. #1592×C139C2semidirect
15. #1582×C139C2semidirect
259. C8×C139#137semidirect
287. #20197C139direct (N × H)
288. C139#20197direct (N × H)
289. #3386C2×C139semidirect
290. #3372C2×C139semidirect
293. #1723C2×C139semidirect
294. #1703C2×C139semidirect
295. #1692C2×C139semidirect
296. #1690C2×C139semidirect
297. #1673C2×C139semidirect
298. #1648C2×C139semidirect
300. #1643C2×C139semidirect
301. #1637C2×C139semidirect
302. #1592C2×C139semidirect
303. #1582C2×C139semidirect
547. C8#137×C139semidirect

Maximal subgroups

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

subgroupindex
#3386×C1392
#3372×C1392
#3335×C1392
#3276×C1392
#1723×C1392
#1703×C1392
#1692×C1392
#1690×C1392
#1673×C1392
#1648×C1392
#1647×C1392
#1643×C1392
#1637×C1392
#1592×C1392
#1582×C1392
#20197139