Finite Group Databasebeta

← C139×#20133 #48014729

Subgroups — C139×#20133 #48014729

Order 35584.

626 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3393×C139C211yesmaximal, characteristic, complemented
2#3340×C139C211yesmaximal, characteristic, complemented
3#3325×C139C211yesmaximal, characteristic
4#3324×C139C211yesmaximal, characteristic, complemented
5#1720×C139C211yesmaximal, characteristic, complemented
6#1691×C139C211yesmaximal, characteristic, complemented
7#1689×C139C211yesmaximal, characteristic, complemented
8#1681×C139C211yesmaximal, characteristic, complemented
9#1678×C139C211yesmaximal, characteristic, complemented
10#1646×C139C211yesmaximal, characteristic, complemented
11#1639×C139C211yesmaximal, characteristic, complemented
12#1638×C139C211yesmaximal, characteristic, complemented
13#1628×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1586×C139C211yesmaximal, characteristic, complemented
16#556×C139C2211yescharacteristic
17#556×C139C2211yescharacteristic, complemented
18#555×C139C2211yescharacteristic
19D42×C139C2211yescharacteristic
20#498×C139C2211yescharacteristic, complemented
21#495×C139—21no—
22#494×C139C2211yescharacteristic, complemented
23#487×C139C2211yescharacteristic, complemented
24#486×C139C2211yescharacteristic
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#485×C139—21no—
28#482×C139—21no—
29#482×C139—21no—
30#482×C139—21no—
31#477×C139C2211yescharacteristic, complemented
32#476×C139C2211yescharacteristic
33#474×C139C2211yescharacteristic
34#474×C139C2211yescharacteristic
35#469×C139—21no—
36#468×C139—21no—
37#465×C139—21no—
38#464×C139—21no—
39#464×C139—21no—
40#461×C139C2211yescharacteristic
41#461×C139C2211yescharacteristic, complemented
42#460×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#450×C139—21no—
45#447×C139—21no—
46C8×Q8×C139C2211yescharacteristic, complemented
47C4×Q16×C139—21no—
48C4×SD16×C139C2211yescharacteristic
49C4×D8×C139C2211yescharacteristic
50#436×C139C2211yescharacteristic
51#436×C139C2211yescharacteristic
52C8×D4×C139C2211yescharacteristic, complemented
53#427×C139—21no—
54#418×C139—21no—
55#418×C139—21no—
56#335×C139C2211yescharacteristic, complemented
57#334×C139C2211yescharacteristic, complemented
58#333×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#332×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic, complemented
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic, complemented
66#322×C139C2211yescharacteristic, complemented
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139D411yescharacteristic
75C2×D8×C139—21no—
76C2×D8×C139D411yescharacteristic
77C2×M16×C139—21no—
78C2×M16×C139—21no—
79C22×C8×C139—21no—
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83#127×C139C2311yescharacteristic
84#126×C139—41no—
85#126×C139—41no—
86#124×C139—21no—
87#124×C139—21no—
88#124×C139—41no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—21no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—21no—
94#121×C139—21no—
95#120×C139—41no—
96C4×Q8×C139—21no—
97C4×Q8×C139—21no—
98C4×Q8×C139C2311yescharacteristic
99C4×D4×C139C2311yescharacteristic
100C4×D4×C139C2311yescharacteristic
101C4×D4×C139C2311yescharacteristic
102#117×C139—21no—
103#117×C139—21no—
104#117×C139—21no—
105#117×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#107×C139—21no—
109#107×C139D411yescharacteristic
110#106×C139—21no—
111#106×C139—21no—
112#106×C139—21no—
113#106×C139D411yescharacteristic
114C4⋊C8×C139—21no—
115C4⋊C8×C139C2311yescharacteristic
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118C4⋊C8×C139C2311yescharacteristic
119#103×C139—21no—
120#103×C139—21no—
121#103×C139—21no—
122#103×C139—41no—
123#103×C139D411yescharacteristic
124#102×C139—21no—
125#102×C139—21no—
126#102×C139—21no—
127#102×C139—21no—
128#102×C139—21no—
129#102×C139—21no—
130#102×C139—21no—
131#102×C139—21no—
132#102×C139—21no—
133#102×C139—41no—
134#102×C139D411yescharacteristic
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C4×C8×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C24×C139—41no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139C2×D411yescharacteristic
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—41no—
153C2×D4×C139—41no—
154C2×D4×C139—42no—
155C2×D4×C139—42no—
156C2×D4×C139—41no—
157C2×D4×C139—81no—
158C2×D4×C139—81no—
159C2×D4×C139C2×D411yescharacteristic
160C2×D4×C139C2×D411yescharacteristic
161C2×D4×C139C2×D411yescharacteristic
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165Q16×C139—42no—
166Q16×C139—81no—
167SD16×C139—41no—
168SD16×C139—81no—
169SD16×C139—81no—
170SD16×C139—81no—
171D8×C139—41no—
172D8×C139—81no—
173M16×C139—81no—
174M16×C139—81no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—42no—
181C2×C8×C139C2×D411yescharacteristic
182C2×C8×C139C2×D411yescharacteristic
183C2×C8×C139C2×D411yescharacteristic
184C2×C8×C139C2×D411yescharacteristic
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×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—21no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C22⋊C4×C139—41no—
208C42×C139—21no—
209C42×C139—41no—
210C42×C139—41no—
211C42×C139—41no—
212C42×C139C2411yescharacteristic
213C23×C139—21no—
214C23×C139—21no—
215C23×C139—21no—
216C23×C139—41no—
217C23×C139—82no—
218C23×C139—82no—
219C23×C139—161no—
220Q8×C139—21no—
221Q8×C139—21no—
222Q8×C139—41no—
223Q8×C139—41no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—81no—
227D4×C139—21no—
228D4×C139—21no—
229D4×C139—21no—
230D4×C139—21no—
231D4×C139—21no—
232D4×C139—21no—
233D4×C139—41no—
234D4×C139—41no—
235D4×C139—41no—
236D4×C139—41no—
237D4×C139—81no—
238D4×C139—82no—
239D4×C139—82no—
240D4×C139—161no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139C22×D411yescharacteristic
256C2×C4×C139C22×D411yescharacteristic
257C2×C4×C139H(5,𝔽2)11yescharacteristic
258C8×C139—21no—
259C8×C139—21no—
260C8×C139—21no—
261C8×C139—21no—
262C8×C139—41no—
263C8×C139—41no—
264C8×C139—41no—
265C8×C139—41no—
266C8×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—41no—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—81no—
277C22×C139—81no—
278C22×C139—81no—
279C22×C139—164no—
280C22×C139D4211yescharacteristic
281C4×C139—21no—
282C4×C139—41no—
283C4×C139—41no—
284C4×C139—41no—
285C4×C139—41no—
286C4×C139—41no—
287C4×C139—81no—
288C4×C139—81no—
289C4×C139—81no—
290C4×C139#57511yescharacteristic
291C4×C139#57511yescharacteristic
292C4×C139#57611yescharacteristic
293C4×C139#57711yescharacteristic
294C2×C139—81no—
295C2×C139—81no—
296C2×C139—81no—
297C2×C139—161no—
298C2×C139#326711yescharacteristic
299C2×C139#326811yescharacteristic
300C2×C139#329011yescharacteristic
301#20133C13911yesmaximal, characteristic, direct product factor, Sylow
302C139#2013311yescharacteristic, direct product factor, Sylow
303#3393C2×C13911yescharacteristic, complemented
304#3340C2×C13911yescharacteristic, complemented
305#3325C2×C13911yescharacteristic
306#3324C2×C13911yescharacteristic, complemented
307#1720C2×C13911yescharacteristic, complemented
308#1691C2×C13911yescharacteristic, complemented
309#1689C2×C13911yescharacteristic, complemented
310#1681C2×C13911yescharacteristic, complemented
311#1678C2×C13911yescharacteristic, complemented
312#1646C2×C13911yescharacteristic, complemented
313#1639C2×C13911yescharacteristic, complemented
314#1638C2×C13911yescharacteristic, complemented
315#1628C2×C13911yescharacteristic, complemented
316#1588C2×C13911yescharacteristic, complemented
317#1586C2×C13911yescharacteristic, complemented
318#556C22×C13911yescharacteristic
319#556C22×C13911yescharacteristic, complemented
320#555C22×C13911yescharacteristic
321D42C22×C13911yescharacteristic
322#498C22×C13911yescharacteristic, complemented
323#495—21no—
324#494C22×C13911yescharacteristic, complemented
325#487C22×C13911yescharacteristic, complemented
326#486C22×C13911yescharacteristic
327#486C22×C13911yescharacteristic
328#486C22×C13911yescharacteristic
329#485—21no—
330#482—21no—
331#482—21no—
332#482—21no—
333#477C22×C13911yescharacteristic, complemented
334#476C22×C13911yescharacteristic
335#474C22×C13911yescharacteristic
336#474C22×C13911yescharacteristic
337#469—21no—
338#468—21no—
339#465—21no—
340#464—21no—
341#464—21no—
342#461C22×C13911yescharacteristic
343#461C22×C13911yescharacteristic, complemented
344#460C22×C13911yescharacteristic
345#459C22×C13911yescharacteristic
346#450—21no—
347#447—21no—
348C8×Q8C22×C13911yescharacteristic, complemented
349C4×Q16—21no—
350C4×SD16C22×C13911yescharacteristic
351C4×D8C22×C13911yescharacteristic
352#436C22×C13911yescharacteristic
353#436C22×C13911yescharacteristic
354C8×D4C22×C13911yescharacteristic, complemented
355#427—21no—
356#418—21no—
357#418—21no—
358#335C22×C13911yescharacteristic, complemented
359#334C22×C13911yescharacteristic, complemented
360#333C22×C13911yescharacteristic, complemented
361#332C22×C13911yescharacteristic, complemented
362#332C22×C13911yescharacteristic, complemented
363#331C22×C13911yescharacteristic
364Q8⋊C8C22×C13911yescharacteristic, complemented
365D4⋊C8C22×C13911yescharacteristic
366D4⋊C8C22×C13911yescharacteristic
367D4⋊C8C22×C13911yescharacteristic, complemented
368#322C22×C13911yescharacteristic, complemented
369C22×D4—21no—
370C22×D4—21no—
371C2×Q16—21no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16D4×C13911yescharacteristic
377C2×D8—21no—
378C2×D8D4×C13911yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C22×C8—21no—
382C4⋊Q8C23×C13911yescharacteristic
383C4⋊Q8C23×C13911yescharacteristic
384C4⋊Q8C23×C13911yescharacteristic
385#127C23×C13911yescharacteristic
386#126—41no—
387#126—41no—
388#124—21no—
389#124—21no—
390#124—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#120—41no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8C23×C13911yescharacteristic
401C4×D4C23×C13911yescharacteristic
402C4×D4C23×C13911yescharacteristic
403C4×D4C23×C13911yescharacteristic
404#117—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107D4×C13911yescharacteristic
412#106—21no—
413#106—21no—
414#106—21no—
415#106D4×C13911yescharacteristic
416C4⋊C8—21no—
417C4⋊C8C23×C13911yescharacteristic
418C4⋊C8C23×C13911yescharacteristic
419C4⋊C8C23×C13911yescharacteristic
420C4⋊C8C23×C13911yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—41no—
425#103D4×C13911yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—41no—
436#102D4×C13911yescharacteristic
437#102D4×C13911yescharacteristic
438#102D4×C13911yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C4×C8—21no—
443C4×C8C23×C13911yescharacteristic
444C4×C8C23×C13911yescharacteristic
445C4×C8C23×C13911yescharacteristic
446C24—41no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C13911yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—41no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4C2×D4×C13911yescharacteristic
462C2×D4C2×D4×C13911yescharacteristic
463C2×D4C2×D4×C13911yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467Q16—42no—
468Q16—81no—
469SD16—41no—
470SD16—81no—
471SD16—81no—
472SD16—81no—
473D8—41no—
474D8—81no—
475M16—81no—
476M16—81no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8C2×D4×C13911yescharacteristic
484C2×C8C2×D4×C13911yescharacteristic
485C2×C8C2×D4×C13911yescharacteristic
486C2×C8C2×D4×C13911yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C13911yescharacteristic
497C4⋊C4C2×D4×C13911yescharacteristic
498C4⋊C4C2×D4×C13911yescharacteristic
499C4⋊C4C2×D4×C13911yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42—41no—
514C42C24×C13911yescharacteristic
515C23—21no—
516C23—21no—
517C23—21no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—161no—
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—82no—
541D4—82no—
542D4—161no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4C22×D4×C13911yescharacteristic
558C2×C4C22×D4×C13911yescharacteristic
559C2×C4H(5,𝔽2)×C13911yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—164no—
582C22D42×C13911yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4#575×C13911yescharacteristic
593C4#575×C13911yescharacteristic
594C4#576×C13911yescharacteristic
595C4#577×C13911yescharacteristic
596C2—81no—
597C2—81no—
598C2—81no—
599C2—161no—
600C2#3267×C13911yescharacteristic
601C2#3268×C13911yescharacteristic
602C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radical#3325×C139C2
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. #3393×C139C2semidirect
2. #3340×C139C2semidirect
4. #3324×C139C2semidirect
5. #1720×C139C2semidirect
6. #1691×C139C2semidirect
7. #1689×C139C2semidirect
8. #1681×C139C2semidirect
9. #1678×C139C2semidirect
10. #1646×C139C2semidirect
11. #1639×C139C2semidirect
12. #1638×C139C2semidirect
13. #1628×C139C2semidirect
14. #1588×C139C2semidirect
15. #1586×C139C2semidirect
17. #556×C139C22semidirect
20. #498×C139C22semidirect
22. #494×C139C22semidirect
23. #487×C139C22semidirect
31. #477×C139C22semidirect
41. #461×C139C22semidirect
46. C8×Q8×C139C22semidirect
52. C8×D4×C139C22semidirect
56. #335×C139C22semidirect
57. #334×C139C22semidirect
58. #333×C139C22semidirect
59. #332×C139C22semidirect
60. #332×C139C22semidirect
62. Q8⋊C8×C139C22semidirect
65. D4⋊C8×C139C22semidirect
66. #322×C139C22semidirect
301. #20133C139direct (N × H)
302. C139#20133direct (N × H)
303. #3393C2×C139semidirect
304. #3340C2×C139semidirect
306. #3324C2×C139semidirect
307. #1720C2×C139semidirect
308. #1691C2×C139semidirect
309. #1689C2×C139semidirect
310. #1681C2×C139semidirect
311. #1678C2×C139semidirect
312. #1646C2×C139semidirect
313. #1639C2×C139semidirect
314. #1638C2×C139semidirect
315. #1628C2×C139semidirect
316. #1588C2×C139semidirect
317. #1586C2×C139semidirect
319. #556C22×C139semidirect
322. #498C22×C139semidirect
324. #494C22×C139semidirect
325. #487C22×C139semidirect
333. #477C22×C139semidirect
343. #461C22×C139semidirect
348. C8×Q8C22×C139semidirect
354. C8×D4C22×C139semidirect
358. #335C22×C139semidirect
359. #334C22×C139semidirect
360. #333C22×C139semidirect
361. #332C22×C139semidirect
362. #332C22×C139semidirect
364. Q8⋊C8C22×C139semidirect
367. D4⋊C8C22×C139semidirect
368. #322C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3393×C1392
#3340×C1392
#3325×C1392
#3324×C1392
#1720×C1392
#1691×C1392
#1689×C1392
#1681×C1392
#1678×C1392
#1646×C1392
#1639×C1392
#1638×C1392
#1628×C1392
#1588×C1392
#1586×C1392
#20133139