Finite Group Databasebeta

← C139×#19917 #48014513

Subgroups — C139×#19917 #48014513

Order 35584.

588 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3381×C139C211yesmaximal, characteristic, complemented
2#3372×C139C211yesmaximal, characteristic, complemented
3#3335×C139C211yesmaximal, characteristic
4#3331×C139C211yesmaximal, characteristic
5#1707×C139C211yesmaximal, characteristic, complemented
6#1704×C139C211yesmaximal, characteristic, complemented
7#1703×C139C211yesmaximal, characteristic, complemented
8#1672×C139C211yesmaximal, characteristic, complemented
9#1671×C139C211yesmaximal, characteristic, complemented
10#1648×C139C211yesmaximal, characteristic, complemented
11#1647×C139C211yesmaximal, characteristic
12#1632×C139C211yesmaximal, characteristic, complemented
13#1632×C139C211yesmaximal, characteristic, complemented
14#1590×C139C211yesmaximal, characteristic, complemented
15C8×SD16×C139C211yesmaximal, characteristic, complemented
16#557×C139C2211yescharacteristic
17#554×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19#547×C139C2211yescharacteristic
20#500×C139C2211yescharacteristic
21#499×C139—21no—
22#498×C139C2211yescharacteristic
23#498×C139C2211yescharacteristic
24#494×C139C2211yescharacteristic
25#491×C139—21no—
26#487×C139C2211yescharacteristic
27#487×C139C2211yescharacteristic
28#483×C139—21no—
29#483×C139—21no—
30#481×C139—21no—
31#479×C139—21no—
32#479×C139—21no—
33#478×C139—21no—
34#477×C139C2211yescharacteristic
35#477×C139C2211yescharacteristic
36#476×C139C2211yescharacteristic
37#476×C139C2211yescharacteristic
38#475×C139C2211yescharacteristic
39#474×C139C2211yescharacteristic
40#470×C139—21no—
41#465×C139—21no—
42#462×C139C2211yescharacteristic
43#461×C139—21no—
44#461×C139C2211yescharacteristic
45#452×C139—21no—
46#446×C139C2211yescharacteristic
47C8×Q8×C139C2211yescharacteristic
48#440×C139—21no—
49C4×SD16×C139—21no—
50C4×SD16×C139C2211yescharacteristic
51C4×SD16×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54C2×#106×C139—21no—
55#417×C139—21no—
56#334×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#333×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66C82×C139C2211yescharacteristic
67C2×#41×C139—21no—
68C2×Q16×C139—21no—
69C2×Q16×C139—41no—
70C2×SD16×C139—21no—
71C2×SD16×C139D411yescharacteristic
72C2×SD16×C139D411yescharacteristic
73C2×M16×C139—21no—
74C22×C8×C139—21no—
75C4⋊Q8×C139—21no—
76C4⋊Q8×C139C2311yescharacteristic
77C4⋊Q8×C139C2311yescharacteristic
78C4⋊Q8×C139C2311yescharacteristic
79C4⋊Q8×C139C2311yescharacteristic
80#125×C139—21no—
81#125×C139—21no—
82#125×C139—21no—
83#125×C139—41no—
84#123×C139—41no—
85C22⋊Q8×C139—21no—
86C22⋊Q8×C139—21no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—41no—
89C22⋊Q8×C139—41no—
90#121×C139—21no—
91C4×Q8×C139—21no—
92C4×Q8×C139—21no—
93C4×Q8×C139C2311yescharacteristic
94C4×Q8×C139C2311yescharacteristic
95C4×D4×C139—21no—
96C4×D4×C139—21no—
97C4×D4×C139C2311yescharacteristic
98C4×D4×C139C2311yescharacteristic
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139—21no—
101C2×C4⋊C4×C139—21no—
102#107×C139—21no—
103#107×C139—21no—
104#107×C139—21no—
105#107×C139—41no—
106#106×C139—21no—
107#106×C139—21no—
108#106×C139—21no—
109#106×C139—21no—
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139D411yescharacteristic
114#106×C139D411yescharacteristic
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×C139D411yescharacteristic
131#103×C139D411yescharacteristic
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—21no—
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139#97×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144#41×C139—42no—
145#41×C139—81no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139C2×D411yescharacteristic
151C2×Q8×C139C2×D411yescharacteristic
152C2×D4×C139—41no—
153C2×D4×C139C2×D411yescharacteristic
154C2×D4×C139C2×D411yescharacteristic
155C22×C4×C139—21no—
156C22×C4×C139—21no—
157C22×C4×C139—41no—
158C22×C4×C139—41no—
159C22×C4×C139—41no—
160Q16×C139—82no—
161Q16×C139—81no—
162SD16×C139—22no—
163SD16×C139—22no—
164SD16×C139—42no—
165M16×C139—81no—
166C2×C8×C139—21no—
167C2×C8×C139—21no—
168C2×C8×C139—21no—
169C2×C8×C139—21no—
170C2×C8×C139—21no—
171C2×C8×C139—42no—
172C2×C8×C139C2×D411yescharacteristic
173C2×C8×C139C2×D411yescharacteristic
174C2×C8×C139C2×D411yescharacteristic
175C2×C8×C139C2×D411yescharacteristic
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—21no—
184C4⋊C4×C139—21no—
185C4⋊C4×C139—21no—
186C4⋊C4×C139—41no—
187C4⋊C4×C139—41no—
188C4⋊C4×C139—41no—
189C4⋊C4×C139—41no—
190C4⋊C4×C139—41no—
191C4⋊C4×C139—41no—
192C4⋊C4×C139—41no—
193C4⋊C4×C139—41no—
194C4⋊C4×C139C2×D411yescharacteristic
195C4⋊C4×C139C2×D411yescharacteristic
196C4⋊C4×C139C2×D411yescharacteristic
197C4⋊C4×C139C2×D411yescharacteristic
198C22⋊C4×C139—21no—
199C22⋊C4×C139—21no—
200C22⋊C4×C139—41no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C42×C139—21no—
204C42×C139—21no—
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—81no—
218Q8×C139—81no—
219D4×C139—21no—
220D4×C139—21no—
221D4×C139—21no—
222D4×C139—82no—
223D4×C139#13512yes—
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—82no—
239C2×C4×C139—161no—
240C2×C4×C139—161no—
241C2×C4×C139C22×D411yescharacteristic
242C2×C4×C139C22×D411yescharacteristic
243C2×C4×C139H(5,𝔽2)11yescharacteristic
244C8×C139—22no—
245C8×C139—21no—
246C8×C139—21no—
247C8×C139—21no—
248C8×C139—41no—
249C8×C139—41no—
250C8×C139—41no—
251C8×C139—41no—
252C8×C139#13712yes—
253C22×C139—22no—
254C22×C139—41no—
255C22×C139—41no—
256C22×C139—41no—
257C22×C139—41no—
258C22×C139—41no—
259C22×C139D4211yescharacteristic
260C4×C139—21no—
261C4×C139—41no—
262C4×C139—41no—
263C4×C139—41no—
264C4×C139—41no—
265C4×C139—41no—
266C4×C139—41no—
267C4×C139—81no—
268C4×C139—81no—
269C4×C139—81no—
270C4×C139—81no—
271C4×C139C2×#13511yescharacteristic
272C4×C139C2×#13711yescharacteristic
273C4×C139#57711yescharacteristic
274C4×C139#57811yescharacteristic
275C2×C139—42no—
276C2×C139—81no—
277C2×C139#327611yescharacteristic
278C2×C139#328211yescharacteristic
279C2×C139#329111yescharacteristic
280#19917C13911yesmaximal, characteristic, direct product factor, Sylow
281C139#1991711yescharacteristic, direct product factor, Sylow
282#3381C2×C13911yescharacteristic, complemented
283#3372C2×C13911yescharacteristic, complemented
284#3335C2×C13911yescharacteristic
285#3331C2×C13911yescharacteristic
286#1707C2×C13911yescharacteristic, complemented
287#1704C2×C13911yescharacteristic, complemented
288#1703C2×C13911yescharacteristic, complemented
289#1672C2×C13911yescharacteristic, complemented
290#1671C2×C13911yescharacteristic, complemented
291#1648C2×C13911yescharacteristic, complemented
292#1647C2×C13911yescharacteristic
293#1632C2×C13911yescharacteristic, complemented
294#1632C2×C13911yescharacteristic, complemented
295#1590C2×C13911yescharacteristic, complemented
296C8×SD16C2×C13911yescharacteristic, complemented
297#557C22×C13911yescharacteristic
298#554C22×C13911yescharacteristic
299#554C22×C13911yescharacteristic
300#547C22×C13911yescharacteristic
301#500C22×C13911yescharacteristic
302#499—21no—
303#498C22×C13911yescharacteristic
304#498C22×C13911yescharacteristic
305#494C22×C13911yescharacteristic
306#491—21no—
307#487C22×C13911yescharacteristic
308#487C22×C13911yescharacteristic
309#483—21no—
310#483—21no—
311#481—21no—
312#479—21no—
313#479—21no—
314#478—21no—
315#477C22×C13911yescharacteristic
316#477C22×C13911yescharacteristic
317#476C22×C13911yescharacteristic
318#476C22×C13911yescharacteristic
319#475C22×C13911yescharacteristic
320#474C22×C13911yescharacteristic
321#470—21no—
322#465—21no—
323#462C22×C13911yescharacteristic
324#461—21no—
325#461C22×C13911yescharacteristic
326#452—21no—
327#446C22×C13911yescharacteristic
328C8×Q8C22×C13911yescharacteristic
329#440—21no—
330C4×SD16—21no—
331C4×SD16C22×C13911yescharacteristic
332C4×SD16C22×C13911yescharacteristic
333#436C22×C13911yescharacteristic
334C8×D4C22×C13911yescharacteristic
335C2×#106—21no—
336#417—21no—
337#334C22×C13911yescharacteristic
338#334C22×C13911yescharacteristic
339#333C22×C13911yescharacteristic
340#333C22×C13911yescharacteristic
341#332C22×C13911yescharacteristic
342#332C22×C13911yescharacteristic
343Q8⋊C8C22×C13911yescharacteristic
344Q8⋊C8C22×C13911yescharacteristic
345D4⋊C8C22×C13911yescharacteristic
346D4⋊C8C22×C13911yescharacteristic
347C82C22×C13911yescharacteristic
348C2×#41—21no—
349C2×Q16—21no—
350C2×Q16—41no—
351C2×SD16—21no—
352C2×SD16D4×C13911yescharacteristic
353C2×SD16D4×C13911yescharacteristic
354C2×M16—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8C23×C13911yescharacteristic
358C4⋊Q8C23×C13911yescharacteristic
359C4⋊Q8C23×C13911yescharacteristic
360C4⋊Q8C23×C13911yescharacteristic
361#125—21no—
362#125—21no—
363#125—21no—
364#125—41no—
365#123—41no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—41no—
370C22⋊Q8—41no—
371#121—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C13911yescharacteristic
375C4×Q8C23×C13911yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C23×C13911yescharacteristic
379C4×D4C23×C13911yescharacteristic
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106D4×C13911yescharacteristic
395#106D4×C13911yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C13911yescharacteristic
399C4⋊C8C23×C13911yescharacteristic
400C4⋊C8C23×C13911yescharacteristic
401C4⋊C8C23×C13911yescharacteristic
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—21no—
411#103D4×C13911yescharacteristic
412#103D4×C13911yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102D4×C13911yescharacteristic
417#102D4×C13911yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8C23×C13911yescharacteristic
423C4×C8C23×C13911yescharacteristic
424C4×C8C23×C13911yescharacteristic
425#41—42no—
426#41—81no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C13911yescharacteristic
432C2×Q8C2×D4×C13911yescharacteristic
433C2×D4—41no—
434C2×D4C2×D4×C13911yescharacteristic
435C2×D4C2×D4×C13911yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441Q16—82no—
442Q16—81no—
443SD16—22no—
444SD16—22no—
445SD16—42no—
446M16—81no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C13911yescharacteristic
454C2×C8C2×D4×C13911yescharacteristic
455C2×C8C2×D4×C13911yescharacteristic
456C2×C8C2×D4×C13911yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C13911yescharacteristic
476C4⋊C4C2×D4×C13911yescharacteristic
477C4⋊C4C2×D4×C13911yescharacteristic
478C4⋊C4C2×D4×C13911yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42C24×C13911yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—82no—
504D4#135×C13912yes—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C13911yescharacteristic
523C2×C4C22×D4×C13911yescharacteristic
524C2×C4H(5,𝔽2)×C13911yescharacteristic
525C8—22no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8#137×C13912yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C13911yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C13911yescharacteristic
553C4C2×#137×C13911yescharacteristic
554C4#577×C13911yescharacteristic
555C4#578×C13911yescharacteristic
556C2—42no—
557C2—81no—
558C2#3276×C13911yescharacteristic
559C2#3282×C13911yescharacteristic
560C2#3291×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. #3381×C139C2semidirect
2. #3372×C139C2semidirect
5. #1707×C139C2semidirect
6. #1704×C139C2semidirect
7. #1703×C139C2semidirect
8. #1672×C139C2semidirect
9. #1671×C139C2semidirect
10. #1648×C139C2semidirect
12. #1632×C139C2semidirect
13. #1632×C139C2semidirect
14. #1590×C139C2semidirect
15. C8×SD16×C139C2semidirect
280. #19917C139direct (N × H)
281. C139#19917direct (N × H)
282. #3381C2×C139semidirect
283. #3372C2×C139semidirect
286. #1707C2×C139semidirect
287. #1704C2×C139semidirect
288. #1703C2×C139semidirect
289. #1672C2×C139semidirect
290. #1671C2×C139semidirect
291. #1648C2×C139semidirect
293. #1632C2×C139semidirect
294. #1632C2×C139semidirect
295. #1590C2×C139semidirect
296. C8×SD16C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3381×C1392
#3372×C1392
#3335×C1392
#3331×C1392
#1707×C1392
#1704×C1392
#1703×C1392
#1672×C1392
#1671×C1392
#1648×C1392
#1647×C1392
#1632×C1392
#1590×C1392
C8×SD16×C1392
#19917139