Finite Group Databasebeta

← C139×#20105 #48014701

Subgroups — C139×#20105 #48014701

Order 35584.

620 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3398×C139C211yesmaximal, characteristic, complemented
2#3381×C139C211yesmaximal, characteristic, complemented
3#3324×C139C211yesmaximal, characteristic
4#3295×C139C211yesmaximal, characteristic
5#1720×C139C211yesmaximal, characteristic, complemented
6#1698×C139C211yesmaximal, characteristic, complemented
7#1691×C139C211yesmaximal, characteristic, complemented
8#1682×C139C211yesmaximal, characteristic, complemented
9#1669×C139C211yesmaximal, characteristic, complemented
10#1644×C139C211yesmaximal, characteristic, complemented
11#1639×C139C211yesmaximal, characteristic
12#1638×C139C211yesmaximal, characteristic, complemented
13#1626×C139C211yesmaximal, characteristic, complemented
14#1588×C139C211yesmaximal, characteristic, complemented
15#1585×C139C211yesmaximal, characteristic, complemented
16#557×C139C2211yescharacteristic, complemented
17#556×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19D42×C139C2211yescharacteristic
20#499×C139—21no—
21#498×C139C2211yescharacteristic, complemented
22#497×C139—21no—
23#494×C139C2211yescharacteristic, complemented
24#487×C139C2211yescharacteristic, complemented
25#486×C139C2211yescharacteristic
26#486×C139C2211yescharacteristic
27#486×C139C2211yescharacteristic
28#482×C139—21no—
29#481×C139—21no—
30#479×C139—21no—
31#478×C139—21no—
32#477×C139C2211yescharacteristic, complemented
33#476×C139C2211yescharacteristic
34#474×C139C2211yescharacteristic
35#474×C139C2211yescharacteristic
36#468×C139—21no—
37#465×C139—21no—
38#464×C139—21no—
39#462×C139—21no—
40#462×C139C2211yescharacteristic, complemented
41#461×C139C2211yescharacteristic
42#460×C139C2211yescharacteristic
43#460×C139C2211yescharacteristic
44#450×C139—21no—
45#450×C139—21no—
46#446×C139C2211yescharacteristic, complemented
47C8×Q8×C139C2211yescharacteristic, complemented
48#441×C139—21no—
49C4×SD16×C139—21no—
50C4×SD16×C139C2211yescharacteristic
51C4×SD16×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#418×C139—21no—
55C2×#102×C139—21no—
56#335×C139C2211yescharacteristic, complemented
57#335×C139C2211yescharacteristic, complemented
58#333×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#332×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic, complemented
63Q8⋊C8×C139C2211yescharacteristic, complemented
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic, complemented
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×Q16×C139—21no—
72C2×SD16×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×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82C4⋊Q8×C139C2311yescharacteristic
83#127×C139C2311yescharacteristic
84#126×C139—41no—
85#125×C139—21no—
86#125×C139—21no—
87#125×C139—41no—
88#124×C139—21no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—41no—
92#121×C139—21no—
93#121×C139—21no—
94#120×C139—41no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139—21no—
98C4×Q8×C139C2311yescharacteristic
99C4×Q8×C139C2311yescharacteristic
100C4×D4×C139—21no—
101C4×D4×C139C2311yescharacteristic
102C4×D4×C139C2311yescharacteristic
103#117×C139—21no—
104C2×C4⋊C4×C139—21no—
105#107×C139—21no—
106#107×C139—21no—
107#107×C139—21no—
108#106×C139—21no—
109#106×C139—21no—
110#106×C139—21no—
111#106×C139D411yescharacteristic
112#106×C139D411yescharacteristic
113C4⋊C8×C139—21no—
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#103×C139D411yescharacteristic
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—21no—
134#102×C139—41no—
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
144C24×C139—41no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139C2×D411yescharacteristic
149C2×Q8×C139C2×D411yescharacteristic
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—41no—
154C2×D4×C139—41no—
155C2×D4×C139—42no—
156C2×D4×C139—42no—
157C2×D4×C139—81no—
158C2×D4×C139—81no—
159C2×D4×C139C2×D411yescharacteristic
160C2×D4×C139C2×D411yescharacteristic
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—41no—
164Q16×C139—42no—
165Q16×C139—81no—
166Q16×C139—81no—
167SD16×C139—22no—
168SD16×C139—41no—
169SD16×C139—81no—
170SD16×C139—81no—
171SD16×C139—81no—
172M16×C139—81no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—81no—
179C2×C8×C139C2×D411yescharacteristic
180C2×C8×C139C2×D411yescharacteristic
181C2×C8×C139C2×D411yescharacteristic
182C2×C8×C139C2×D411yescharacteristic
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—41no—
192C4⋊C4×C139—41no—
193C4⋊C4×C139—41no—
194C4⋊C4×C139—41no—
195C4⋊C4×C139—41no—
196C4⋊C4×C139—41no—
197C4⋊C4×C139C2×D411yescharacteristic
198C4⋊C4×C139C2×D411yescharacteristic
199C4⋊C4×C139C2×D411yescharacteristic
200C4⋊C4×C139C2×D411yescharacteristic
201C22⋊C4×C139—21no—
202C22⋊C4×C139—21no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C22⋊C4×C139—41no—
206C22⋊C4×C139—41no—
207C42×C139—21no—
208C42×C139—21no—
209C42×C139—41no—
210C42×C139—41no—
211C42×C139C2411yescharacteristic
212C23×C139—21no—
213C23×C139—21no—
214C23×C139—41no—
215C23×C139—82no—
216C23×C139—82no—
217C23×C139—161no—
218Q8×C139—21no—
219Q8×C139—21no—
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—41no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—41no—
234D4×C139—81no—
235D4×C139—82no—
236D4×C139—82no—
237D4×C139#13712yes—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—21no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—161no—
252C2×C4×C139C22×D411yescharacteristic
253C2×C4×C139C22×D411yescharacteristic
254C2×C4×C139H(5,𝔽2)11yescharacteristic
255C8×C139—21no—
256C8×C139—21no—
257C8×C139—21no—
258C8×C139—21no—
259C8×C139—41no—
260C8×C139—41no—
261C8×C139—41no—
262C8×C139—41no—
263C8×C139—41no—
264C22×C139—22no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—81no—
271C22×C139—81no—
272C22×C139—81no—
273C22×C139—164no—
274C22×C139D4211yescharacteristic
275C4×C139—21no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—41no—
281C4×C139—41no—
282C4×C139—81no—
283C4×C139—81no—
284C4×C139—81no—
285C4×C139C2×#13711yescharacteristic
286C4×C139#57511yescharacteristic
287C4×C139#57611yescharacteristic
288C4×C139#57711yescharacteristic
289C2×C139—42no—
290C2×C139—81no—
291C2×C139—161no—
292C2×C139#326611yescharacteristic
293C2×C139#326811yescharacteristic
294C2×C139#329011yescharacteristic
295#20105C13911yesmaximal, characteristic, direct product factor, Sylow
296C139#2010511yescharacteristic, direct product factor, Sylow
297#3398C2×C13911yescharacteristic, complemented
298#3381C2×C13911yescharacteristic, complemented
299#3324C2×C13911yescharacteristic
300#3295C2×C13911yescharacteristic
301#1720C2×C13911yescharacteristic, complemented
302#1698C2×C13911yescharacteristic, complemented
303#1691C2×C13911yescharacteristic, complemented
304#1682C2×C13911yescharacteristic, complemented
305#1669C2×C13911yescharacteristic, complemented
306#1644C2×C13911yescharacteristic, complemented
307#1639C2×C13911yescharacteristic
308#1638C2×C13911yescharacteristic, complemented
309#1626C2×C13911yescharacteristic, complemented
310#1588C2×C13911yescharacteristic, complemented
311#1585C2×C13911yescharacteristic, complemented
312#557C22×C13911yescharacteristic, complemented
313#556C22×C13911yescharacteristic
314#554C22×C13911yescharacteristic
315D42C22×C13911yescharacteristic
316#499—21no—
317#498C22×C13911yescharacteristic, complemented
318#497—21no—
319#494C22×C13911yescharacteristic, complemented
320#487C22×C13911yescharacteristic, complemented
321#486C22×C13911yescharacteristic
322#486C22×C13911yescharacteristic
323#486C22×C13911yescharacteristic
324#482—21no—
325#481—21no—
326#479—21no—
327#478—21no—
328#477C22×C13911yescharacteristic, complemented
329#476C22×C13911yescharacteristic
330#474C22×C13911yescharacteristic
331#474C22×C13911yescharacteristic
332#468—21no—
333#465—21no—
334#464—21no—
335#462—21no—
336#462C22×C13911yescharacteristic, complemented
337#461C22×C13911yescharacteristic
338#460C22×C13911yescharacteristic
339#460C22×C13911yescharacteristic
340#450—21no—
341#450—21no—
342#446C22×C13911yescharacteristic, complemented
343C8×Q8C22×C13911yescharacteristic, complemented
344#441—21no—
345C4×SD16—21no—
346C4×SD16C22×C13911yescharacteristic
347C4×SD16C22×C13911yescharacteristic
348#436C22×C13911yescharacteristic
349C8×D4C22×C13911yescharacteristic
350#418—21no—
351C2×#102—21no—
352#335C22×C13911yescharacteristic, complemented
353#335C22×C13911yescharacteristic, complemented
354#333C22×C13911yescharacteristic, complemented
355#332C22×C13911yescharacteristic, complemented
356#332C22×C13911yescharacteristic, complemented
357#331C22×C13911yescharacteristic
358Q8⋊C8C22×C13911yescharacteristic, complemented
359Q8⋊C8C22×C13911yescharacteristic, complemented
360D4⋊C8C22×C13911yescharacteristic
361D4⋊C8C22×C13911yescharacteristic
362#322C22×C13911yescharacteristic, complemented
363C22×D4—21no—
364C22×D4—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16D4×C13911yescharacteristic
372C2×SD16D4×C13911yescharacteristic
373C2×M16—21no—
374C22×C8—21no—
375C4⋊Q8—21no—
376C4⋊Q8C23×C13911yescharacteristic
377C4⋊Q8C23×C13911yescharacteristic
378C4⋊Q8C23×C13911yescharacteristic
379#127C23×C13911yescharacteristic
380#126—41no—
381#125—21no—
382#125—21no—
383#125—41no—
384#124—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388#121—21no—
389#121—21no—
390#120—41no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8C23×C13911yescharacteristic
395C4×Q8C23×C13911yescharacteristic
396C4×D4—21no—
397C4×D4C23×C13911yescharacteristic
398C4×D4C23×C13911yescharacteristic
399#117—21no—
400C2×C4⋊C4—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106D4×C13911yescharacteristic
408#106D4×C13911yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C13911yescharacteristic
412C4⋊C8C23×C13911yescharacteristic
413C4⋊C8C23×C13911yescharacteristic
414C4⋊C8C23×C13911yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—41no—
419#103D4×C13911yescharacteristic
420#103D4×C13911yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—41no—
431#102D4×C13911yescharacteristic
432#102D4×C13911yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8C23×C13911yescharacteristic
438C4×C8C23×C13911yescharacteristic
439C4×C8C23×C13911yescharacteristic
440C24—41no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C13911yescharacteristic
445C2×Q8C2×D4×C13911yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—81no—
454C2×D4—81no—
455C2×D4C2×D4×C13911yescharacteristic
456C2×D4C2×D4×C13911yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460Q16—42no—
461Q16—81no—
462Q16—81no—
463SD16—22no—
464SD16—41no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8C2×D4×C13911yescharacteristic
476C2×C8C2×D4×C13911yescharacteristic
477C2×C8C2×D4×C13911yescharacteristic
478C2×C8C2×D4×C13911yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C13911yescharacteristic
494C4⋊C4C2×D4×C13911yescharacteristic
495C4⋊C4C2×D4×C13911yescharacteristic
496C4⋊C4C2×D4×C13911yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42—41no—
507C42C24×C13911yescharacteristic
508C23—21no—
509C23—21no—
510C23—41no—
511C23—82no—
512C23—82no—
513C23—161no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4—82no—
533D4#137×C13912yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—161no—
548C2×C4C22×D4×C13911yescharacteristic
549C2×C4C22×D4×C13911yescharacteristic
550C2×C4H(5,𝔽2)×C13911yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—164no—
570C22D42×C13911yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×#137×C13911yescharacteristic
582C4#575×C13911yescharacteristic
583C4#576×C13911yescharacteristic
584C4#577×C13911yescharacteristic
585C2—42no—
586C2—81no—
587C2—161no—
588C2#3266×C13911yescharacteristic
589C2#3268×C13911yescharacteristic
590C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radicalD42×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. #3398×C139C2semidirect
2. #3381×C139C2semidirect
5. #1720×C139C2semidirect
6. #1698×C139C2semidirect
7. #1691×C139C2semidirect
8. #1682×C139C2semidirect
9. #1669×C139C2semidirect
10. #1644×C139C2semidirect
12. #1638×C139C2semidirect
13. #1626×C139C2semidirect
14. #1588×C139C2semidirect
15. #1585×C139C2semidirect
16. #557×C139C22semidirect
21. #498×C139C22semidirect
23. #494×C139C22semidirect
24. #487×C139C22semidirect
32. #477×C139C22semidirect
40. #462×C139C22semidirect
46. #446×C139C22semidirect
47. C8×Q8×C139C22semidirect
56. #335×C139C22semidirect
57. #335×C139C22semidirect
58. #333×C139C22semidirect
59. #332×C139C22semidirect
60. #332×C139C22semidirect
62. Q8⋊C8×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
66. #322×C139C22semidirect
295. #20105C139direct (N × H)
296. C139#20105direct (N × H)
297. #3398C2×C139semidirect
298. #3381C2×C139semidirect
301. #1720C2×C139semidirect
302. #1698C2×C139semidirect
303. #1691C2×C139semidirect
304. #1682C2×C139semidirect
305. #1669C2×C139semidirect
306. #1644C2×C139semidirect
308. #1638C2×C139semidirect
309. #1626C2×C139semidirect
310. #1588C2×C139semidirect
311. #1585C2×C139semidirect
312. #557C22×C139semidirect
317. #498C22×C139semidirect
319. #494C22×C139semidirect
320. #487C22×C139semidirect
328. #477C22×C139semidirect
336. #462C22×C139semidirect
342. #446C22×C139semidirect
343. C8×Q8C22×C139semidirect
352. #335C22×C139semidirect
353. #335C22×C139semidirect
354. #333C22×C139semidirect
355. #332C22×C139semidirect
356. #332C22×C139semidirect
358. Q8⋊C8C22×C139semidirect
359. Q8⋊C8C22×C139semidirect
362. #322C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3398×C1392
#3381×C1392
#3324×C1392
#3295×C1392
#1720×C1392
#1698×C1392
#1691×C1392
#1682×C1392
#1669×C1392
#1644×C1392
#1639×C1392
#1638×C1392
#1626×C1392
#1588×C1392
#1585×C1392
#20105139