Finite Group Databasebeta

← C139×#20243 #48014839

Subgroups — C139×#20243 #48014839

Order 35584.

674 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3354×C139C211yesmaximal, characteristic, complemented
2#3341×C139C211yesmaximal, characteristic, complemented
3#3325×C139C211yesmaximal, characteristic, complemented
4#3272×C139C211yesmaximal, characteristic, complemented
5#1714×C139C211yesmaximal, characteristic, complemented
6#1697×C139C211yesmaximal, characteristic, complemented
7#1695×C139C211yesmaximal, characteristic, complemented
8#1691×C139C211yesmaximal, characteristic, complemented
9#1665×C139C211yesmaximal, characteristic, complemented
10#1646×C139C211yesmaximal, characteristic, complemented
11#1635×C139C211yesmaximal, characteristic, complemented
12#1629×C139C211yesmaximal, characteristic, complemented
13#1624×C139C211yesmaximal, characteristic, complemented
14#1594×C139C211yesmaximal, characteristic, complemented
15#1581×C139C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C139—21no—
17#555×C139C2211yescharacteristic
18#555×C139C2211yescharacteristic, complemented
19#547×C139C2211yescharacteristic
20D42×C139C2211yescharacteristic
21#500×C139C2211yescharacteristic, complemented
22#498×C139C2211yescharacteristic, complemented
23#492×C139C2211yescharacteristic
24#492×C139C2211yescharacteristic
25#487×C139C2211yescharacteristic, complemented
26#486×C139C2211yescharacteristic
27#482×C139—21no—
28#482×C139—21no—
29#482×C139—21no—
30#482×C139—21no—
31#481×C139—21no—
32#476×C139C2211yescharacteristic
33#476×C139C2211yescharacteristic
34#476×C139C2211yescharacteristic
35#476×C139C2211yescharacteristic, complemented
36#474×C139C2211yescharacteristic, complemented
37#469×C139—21no—
38#469×C139—21no—
39#468×C139—21no—
40#466×C139—21no—
41#461×C139C2211yescharacteristic
42#459×C139C2211yescharacteristic
43#459×C139C2211yescharacteristic
44#450×C139—21no—
45#449×C139—21no—
46#447×C139—21no—
47C4×D8×C139C2211yescharacteristic
48C4×D8×C139C2211yescharacteristic
49#436×C139C2211yescharacteristic
50#436×C139C2211yescharacteristic
51#436×C139C2211yescharacteristic, complemented
52C8×D4×C139C2211yescharacteristic, complemented
53#428×C139—21no—
54#427×C139—21no—
55#418×C139—21no—
56#335×C139C2211yescharacteristic, complemented
57#334×C139C2211yescharacteristic, complemented
58#333×C139C2211yescharacteristic, complemented
59#333×C139C2211yescharacteristic, complemented
60#332×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic
62D4⋊C8×C139C2211yescharacteristic
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic, complemented
65D4⋊C8×C139C2211yescharacteristic, complemented
66#322×C139C2211yescharacteristic, complemented
67C2×#41×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70AGL(1,ℤ/8)×C139—44no—
71C2×SD16×C139—21no—
72C2×SD16×C139—21no—
73C2×SD16×C139—21no—
74C2×SD16×C139—41no—
75C2×D8×C139—21no—
76C2×D8×C139—21no—
77C2×D8×C139D411yescharacteristic
78C2×D8×C139D411yescharacteristic
79C2×M16×C139—21no—
80C2×M16×C139—21no—
81C2×M16×C139—21no—
82C22×C8×C139—21no—
83C4⋊Q8×C139C2311yescharacteristic
84C4⋊Q8×C139C2311yescharacteristic
85C4⋊Q8×C139C2311yescharacteristic
86#127×C139C2311yescharacteristic
87#124×C139—41no—
88#124×C139—41no—
89#123×C139—41no—
90C22⋊Q8×C139—21no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—21no—
94#121×C139—21no—
95#121×C139—21no—
96#121×C139—21no—
97#121×C139—21no—
98#120×C139—41no—
99C4×D4×C139C2311yescharacteristic
100C4×D4×C139C2311yescharacteristic
101C4×D4×C139C2311yescharacteristic
102C4×D4×C139C2311yescharacteristic
103#117×C139—21no—
104#117×C139—21no—
105#117×C139—21no—
106#117×C139—21no—
107C2×C4⋊C4×C139—21no—
108#107×C139—21no—
109#107×C139—21no—
110#107×C139—21no—
111#107×C139D411yescharacteristic
112#107×C139D411yescharacteristic
113#106×C139—21no—
114#106×C139—21no—
115#106×C139—21no—
116#106×C139—21no—
117#106×C139—21no—
118#106×C139—21no—
119C4⋊C8×C139C2311yescharacteristic
120C4⋊C8×C139C2311yescharacteristic
121C4⋊C8×C139C2311yescharacteristic
122C4⋊C8×C139C2311yescharacteristic
123#103×C139—21no—
124#103×C139—41no—
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×C139D411yescharacteristic
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137#102×C139D411yescharacteristic
138C22⋊C8×C139—21no—
139C22⋊C8×C139—21no—
140C22⋊C8×C139—21no—
141C22⋊C8×C139—21no—
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C4×C8×C139C2311yescharacteristic
145C24×C139—41no—
146#41×C139—42no—
147#41×C139—81no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—41no—
155C2×D4×C139—41no—
156C2×D4×C139—42no—
157C2×D4×C139—42no—
158C2×D4×C139—41no—
159C2×D4×C139—41no—
160C2×D4×C139—41no—
161C2×D4×C139—81no—
162C2×D4×C139—81no—
163C2×D4×C139C2×D411yescharacteristic
164C2×D4×C139C2×D411yescharacteristic
165C2×D4×C139C2×D411yescharacteristic
166C2×D4×C139C2×D411yescharacteristic
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—21no—
171C22×C4×C139—41no—
172SD16×C139—42no—
173SD16×C139—42no—
174SD16×C139—81no—
175SD16×C139—82no—
176D8×C139—22no—
177D8×C139—41no—
178D8×C139—42no—
179D8×C139—81no—
180M16×C139—42no—
181M16×C139—42no—
182M16×C139—81no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—42no—
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
191C2×C8×C139C2×D411yescharacteristic
192C2×C8×C139C2×D411yescharacteristic
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139C2×D411yescharacteristic
201C4⋊C4×C139C2×D411yescharacteristic
202C4⋊C4×C139C2×D411yescharacteristic
203C4⋊C4×C139C2×D411yescharacteristic
204C22⋊C4×C139—21no—
205C22⋊C4×C139—21no—
206C22⋊C4×C139—21no—
207C22⋊C4×C139—21no—
208C22⋊C4×C139—41no—
209C22⋊C4×C139—41no—
210C22⋊C4×C139—41no—
211C22⋊C4×C139—41no—
212C22⋊C4×C139—41no—
213C22⋊C4×C139—41no—
214C42×C139—41no—
215C42×C139—41no—
216C42×C139C2411yescharacteristic
217C23×C139—21no—
218C23×C139—21no—
219C23×C139—21no—
220C23×C139—21no—
221C23×C139—41no—
222C23×C139—82no—
223C23×C139—82no—
224C23×C139—161no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—81no—
228Q8×C139—81no—
229D4×C139—21no—
230D4×C139—21no—
231D4×C139—21no—
232D4×C139—21no—
233D4×C139—21no—
234D4×C139—21no—
235D4×C139—21no—
236D4×C139—21no—
237D4×C139—41no—
238D4×C139—41no—
239D4×C139—41no—
240D4×C139—41no—
241D4×C139—81no—
242D4×C139—82no—
243D4×C139—82no—
244D4×C139—82no—
245D4×C139—161no—
246D4×C139—161no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—82no—
263C2×C4×C139C22×D411yescharacteristic
264C2×C4×C139C22×D411yescharacteristic
265C2×C4×C139H(5,𝔽2)11yescharacteristic
266C8×C139—21no—
267C8×C139—21no—
268C8×C139—21no—
269C8×C139—41no—
270C8×C139—41no—
271C8×C139—41no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139AGL(1,ℤ/8)12yes—
275C22×C139—41no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—41no—
282C22×C139—41no—
283C22×C139—41no—
284C22×C139—41no—
285C22×C139—41no—
286C22×C139—41no—
287C22×C139—81no—
288C22×C139—81no—
289C22×C139—81no—
290C22×C139—164no—
291C22×C139D4211yescharacteristic
292C4×C139—21no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—41no—
296C4×C139—41no—
297C4×C139—81no—
298C4×C139—81no—
299C4×C139—81no—
300C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C139#57511yescharacteristic
302C4×C139#57711yescharacteristic
303C4×C139#57711yescharacteristic
304C2×C139—81no—
305C2×C139—81no—
306C2×C139—81no—
307C2×C139—81no—
308C2×C139—161no—
309C2×C139#326711yescharacteristic
310C2×C139#327211yescharacteristic
311C2×C139#328811yescharacteristic
312#20243C13911yesmaximal, characteristic, direct product factor, Sylow
313C139#2024311yescharacteristic, direct product factor, Sylow
314#3354C2×C13911yescharacteristic, complemented
315#3341C2×C13911yescharacteristic, complemented
316#3325C2×C13911yescharacteristic, complemented
317#3272C2×C13911yescharacteristic, complemented
318#1714C2×C13911yescharacteristic, complemented
319#1697C2×C13911yescharacteristic, complemented
320#1695C2×C13911yescharacteristic, complemented
321#1691C2×C13911yescharacteristic, complemented
322#1665C2×C13911yescharacteristic, complemented
323#1646C2×C13911yescharacteristic, complemented
324#1635C2×C13911yescharacteristic, complemented
325#1629C2×C13911yescharacteristic, complemented
326#1624C2×C13911yescharacteristic, complemented
327#1594C2×C13911yescharacteristic, complemented
328#1581C2×C13911yescharacteristic, complemented
329C2×AGL(1,ℤ/8)—21no—
330#555C22×C13911yescharacteristic
331#555C22×C13911yescharacteristic, complemented
332#547C22×C13911yescharacteristic
333D42C22×C13911yescharacteristic
334#500C22×C13911yescharacteristic, complemented
335#498C22×C13911yescharacteristic, complemented
336#492C22×C13911yescharacteristic
337#492C22×C13911yescharacteristic
338#487C22×C13911yescharacteristic, complemented
339#486C22×C13911yescharacteristic
340#482—21no—
341#482—21no—
342#482—21no—
343#482—21no—
344#481—21no—
345#476C22×C13911yescharacteristic
346#476C22×C13911yescharacteristic
347#476C22×C13911yescharacteristic
348#476C22×C13911yescharacteristic, complemented
349#474C22×C13911yescharacteristic, complemented
350#469—21no—
351#469—21no—
352#468—21no—
353#466—21no—
354#461C22×C13911yescharacteristic
355#459C22×C13911yescharacteristic
356#459C22×C13911yescharacteristic
357#450—21no—
358#449—21no—
359#447—21no—
360C4×D8C22×C13911yescharacteristic
361C4×D8C22×C13911yescharacteristic
362#436C22×C13911yescharacteristic
363#436C22×C13911yescharacteristic
364#436C22×C13911yescharacteristic, complemented
365C8×D4C22×C13911yescharacteristic, complemented
366#428—21no—
367#427—21no—
368#418—21no—
369#335C22×C13911yescharacteristic, complemented
370#334C22×C13911yescharacteristic, complemented
371#333C22×C13911yescharacteristic, complemented
372#333C22×C13911yescharacteristic, complemented
373#332C22×C13911yescharacteristic, complemented
374#331C22×C13911yescharacteristic
375D4⋊C8C22×C13911yescharacteristic
376D4⋊C8C22×C13911yescharacteristic
377D4⋊C8C22×C13911yescharacteristic, complemented
378D4⋊C8C22×C13911yescharacteristic, complemented
379#322C22×C13911yescharacteristic, complemented
380C2×#41—21no—
381C22×D4—21no—
382C22×D4—21no—
383AGL(1,ℤ/8)—44no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—41no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8D4×C13911yescharacteristic
391C2×D8D4×C13911yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C22×C8—21no—
396C4⋊Q8C23×C13911yescharacteristic
397C4⋊Q8C23×C13911yescharacteristic
398C4⋊Q8C23×C13911yescharacteristic
399#127C23×C13911yescharacteristic
400#124—41no—
401#124—41no—
402#123—41no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#120—41no—
412C4×D4C23×C13911yescharacteristic
413C4×D4C23×C13911yescharacteristic
414C4×D4C23×C13911yescharacteristic
415C4×D4C23×C13911yescharacteristic
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107D4×C13911yescharacteristic
425#107D4×C13911yescharacteristic
426#106—21no—
427#106—21no—
428#106—21no—
429#106—21no—
430#106—21no—
431#106—21no—
432C4⋊C8C23×C13911yescharacteristic
433C4⋊C8C23×C13911yescharacteristic
434C4⋊C8C23×C13911yescharacteristic
435C4⋊C8C23×C13911yescharacteristic
436#103—21no—
437#103—41no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102D4×C13911yescharacteristic
448#102D4×C13911yescharacteristic
449#102D4×C13911yescharacteristic
450#102D4×C13911yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C13911yescharacteristic
456C4×C8C23×C13911yescharacteristic
457C4×C8C23×C13911yescharacteristic
458C24—41no—
459#41—42no—
460#41—81no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4C2×D4×C13911yescharacteristic
477C2×D4C2×D4×C13911yescharacteristic
478C2×D4C2×D4×C13911yescharacteristic
479C2×D4C2×D4×C13911yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—82no—
489D8—22no—
490D8—41no—
491D8—42no—
492D8—81no—
493M16—42no—
494M16—42no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—42no—
502C2×C8C2×D4×C13911yescharacteristic
503C2×C8C2×D4×C13911yescharacteristic
504C2×C8C2×D4×C13911yescharacteristic
505C2×C8C2×D4×C13911yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C13911yescharacteristic
514C4⋊C4C2×D4×C13911yescharacteristic
515C4⋊C4C2×D4×C13911yescharacteristic
516C4⋊C4C2×D4×C13911yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—41no—
528C42—41no—
529C42C24×C13911yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541Q8—81no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4—161no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4C22×D4×C13911yescharacteristic
577C2×C4C22×D4×C13911yescharacteristic
578C2×C4H(5,𝔽2)×C13911yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8AGL(1,ℤ/8)×C13912yes—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C13911yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
614C4#575×C13911yescharacteristic
615C4#577×C13911yescharacteristic
616C4#577×C13911yescharacteristic
617C2—81no—
618C2—81no—
619C2—81no—
620C2—81no—
621C2—161no—
622C2#3267×C13911yescharacteristic
623C2#3272×C13911yescharacteristic
624C2#3288×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
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. #3354×C139C2semidirect
2. #3341×C139C2semidirect
3. #3325×C139C2semidirect
4. #3272×C139C2semidirect
5. #1714×C139C2semidirect
6. #1697×C139C2semidirect
7. #1695×C139C2semidirect
8. #1691×C139C2semidirect
9. #1665×C139C2semidirect
10. #1646×C139C2semidirect
11. #1635×C139C2semidirect
12. #1629×C139C2semidirect
13. #1624×C139C2semidirect
14. #1594×C139C2semidirect
15. #1581×C139C2semidirect
18. #555×C139C22semidirect
21. #500×C139C22semidirect
22. #498×C139C22semidirect
25. #487×C139C22semidirect
35. #476×C139C22semidirect
36. #474×C139C22semidirect
51. #436×C139C22semidirect
52. C8×D4×C139C22semidirect
56. #335×C139C22semidirect
57. #334×C139C22semidirect
58. #333×C139C22semidirect
59. #333×C139C22semidirect
60. #332×C139C22semidirect
64. D4⋊C8×C139C22semidirect
65. D4⋊C8×C139C22semidirect
66. #322×C139C22semidirect
312. #20243C139direct (N × H)
313. C139#20243direct (N × H)
314. #3354C2×C139semidirect
315. #3341C2×C139semidirect
316. #3325C2×C139semidirect
317. #3272C2×C139semidirect
318. #1714C2×C139semidirect
319. #1697C2×C139semidirect
320. #1695C2×C139semidirect
321. #1691C2×C139semidirect
322. #1665C2×C139semidirect
323. #1646C2×C139semidirect
324. #1635C2×C139semidirect
325. #1629C2×C139semidirect
326. #1624C2×C139semidirect
327. #1594C2×C139semidirect
328. #1581C2×C139semidirect
331. #555C22×C139semidirect
334. #500C22×C139semidirect
335. #498C22×C139semidirect
338. #487C22×C139semidirect
348. #476C22×C139semidirect
349. #474C22×C139semidirect
364. #436C22×C139semidirect
365. C8×D4C22×C139semidirect
369. #335C22×C139semidirect
370. #334C22×C139semidirect
371. #333C22×C139semidirect
372. #333C22×C139semidirect
373. #332C22×C139semidirect
377. D4⋊C8C22×C139semidirect
378. D4⋊C8C22×C139semidirect
379. #322C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3354×C1392
#3341×C1392
#3325×C1392
#3272×C1392
#1714×C1392
#1697×C1392
#1695×C1392
#1691×C1392
#1665×C1392
#1646×C1392
#1635×C1392
#1629×C1392
#1624×C1392
#1594×C1392
#1581×C1392
#20243139