Finite Group Databasebeta

← C139×#18708 #48013304

Subgroups — C139×#18708 #48013304

Order 35584.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554×C139C211yesmaximal, characteristic, complemented
2#3251×C139C211yesmaximal, characteristic, complemented
3#3216×C139C211yesmaximal, characteristic, complemented
4#3169×C139C211yesmaximal, characteristic, complemented
5#1649×C139C211yesmaximal, characteristic, complemented
6#1648×C139C211yesmaximal, characteristic, complemented
7#1641×C139C211yesmaximal, characteristic, complemented
8#1640×C139C211yesmaximal, characteristic, complemented
9#1627×C139C211yesmaximal, characteristic, complemented
10#1626×C139C211yesmaximal, characteristic, complemented
11#1621×C139C211yesmaximal, characteristic, complemented
12#1620×C139C211yesmaximal, characteristic, complemented
13#1557×C139C211yesmaximal, characteristic, complemented
14#1494×C139C211yesmaximal, characteristic, complemented
15#1493×C139C211yesmaximal, characteristic, complemented
16#562×C139—22no—
17#559×C139—21no—
18#559×C139C2211yescharacteristic
19#557×C139C2211yescharacteristic
20#554×C139—21no—
21#550×C139C2211yescharacteristic
22D4×Q8×C139C2211yescharacteristic
23#548×C139—21no—
24#547×C139—21no—
25#542×C139—21no—
26#542×C139—21no—
27#540×C139—21no—
28#539×C139—22no—
29#536×C139—21no—
30#533×C139C2211yescharacteristic
31#532×C139C2211yescharacteristic
32#532×C139C2211yescharacteristic
33#529×C139C2211yescharacteristic
34#500×C139C2211yescharacteristic
35#497×C139—21no—
36#493×C139C2211yescharacteristic
37#489×C139—21no—
38#486×C139C2211yescharacteristic
39#486×C139C2211yescharacteristic
40#478×C139—21no—
41#475×C139C2211yescharacteristic
42#474×C139C2211yescharacteristic
43#469×C139—21no—
44#468×C139—21no—
45#466×C139—22no—
46#463×C139—21no—
47#462×C139C2211yescharacteristic
48#462×C139C2211yescharacteristic
49#460×C139C2211yescharacteristic
50#460×C139C2211yescharacteristic
51#460×C139C2211yescharacteristic
52#459×C139C2211yescharacteristic
53#452×C139—21no—
54#452×C139—21no—
55C4×D8×C139—22no—
56#432×C139C2211yescharacteristic
57#423×C139C2211yescharacteristic
58C2×C4×C8×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic
62#331×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65Q8⋊C8×C139C2211yescharacteristic
66Q8⋊C8×C139C2211yescharacteristic
67Q8⋊C8×C139C2211yescharacteristic
68Q8⋊C8×C139C2211yescharacteristic
69D4⋊C8×C139C2211yescharacteristic
70D4⋊C8×C139C2211yescharacteristic
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—21no—
74C22×Q8×C139—21no—
75C2×Q16×C139—21no—
76C2×Q16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139—21no—
79C2×SD16×C139—21no—
80C2×D8×C139—22no—
81C2×D8×C139—21no—
82C2×M16×C139—21no—
83C22×C8×C139—21no—
84C4⋊Q8×C139—21no—
85C4⋊Q8×C139—21no—
86C4⋊Q8×C139D411yescharacteristic
87C4⋊Q8×C139D411yescharacteristic
88C4⋊Q8×C139C2311yescharacteristic
89C4⋊Q8×C139C2311yescharacteristic
90#127×C139—21no—
91#127×C139C2311yescharacteristic
92#127×C139C2311yescharacteristic
93#126×C139—22no—
94#126×C139—21no—
95#125×C139—22no—
96#125×C139—21no—
97#125×C139—21no—
98#125×C139D411yescharacteristic
99#124×C139—22no—
100#124×C139—22no—
101#124×C139—21no—
102#124×C139—21no—
103#124×C139—21no—
104#124×C139—21no—
105#124×C139D411yescharacteristic
106#123×C139—22no—
107#123×C139—22no—
108#123×C139—22no—
109#123×C139—22no—
110#123×C139—22no—
111#123×C139—22no—
112#123×C139—21no—
113C22⋊Q8×C139—22no—
114C22⋊Q8×C139—22no—
115C22⋊Q8×C139—22no—
116C22⋊Q8×C139—22no—
117C22⋊Q8×C139—21no—
118C22⋊Q8×C139—22no—
119C22⋊Q8×C139—21no—
120C22⋊Q8×C139D411yescharacteristic
121C22⋊Q8×C139D411yescharacteristic
122C22⋊Q8×C139D411yescharacteristic
123#121×C139—22no—
124#121×C139—22no—
125#121×C139—22no—
126#121×C139—21no—
127#121×C139—21no—
128#121×C139—21no—
129#121×C139—21no—
130#121×C139D412yes—
131#121×C139D411yescharacteristic
132C4×Q8×C139—21no—
133C4×Q8×C139—21no—
134C4×Q8×C139—21no—
135C4×Q8×C139C2311yescharacteristic
136C4×Q8×C139C2311yescharacteristic
137C4×Q8×C139C2311yescharacteristic
138C4×D4×C139—22no—
139C4×D4×C139—21no—
140C4×D4×C139—21no—
141C4×D4×C139—21no—
142C4×D4×C139—21no—
143C4×D4×C139—21no—
144C4×D4×C139—21no—
145C4×D4×C139—21no—
146C4×D4×C139—21no—
147C4×D4×C139D412yes—
148C4×D4×C139C2311yescharacteristic
149#117×C139—21no—
150#117×C139—21no—
151C2×C4⋊C4×C139—22no—
152C2×C42×C139C2311yescharacteristic
153#107×C139—22no—
154#107×C139—21no—
155#106×C139—21no—
156C4⋊C8×C139—21no—
157C4⋊C8×C139C2311yescharacteristic
158C4⋊C8×C139C2311yescharacteristic
159C4⋊C8×C139C2311yescharacteristic
160C4⋊C8×C139C2311yescharacteristic
161#103×C139—21no—
162#103×C139—21no—
163#103×C139—21no—
164#102×C139—22no—
165#102×C139—21no—
166#102×C139—22no—
167#102×C139—21no—
168#102×C139—21no—
169#102×C139—21no—
170#102×C139—21no—
171C22⋊C8×C139—21no—
172#97×C139—21no—
173C4×C8×C139—21no—
174C4×C8×C139C2311yescharacteristic
175C4×C8×C139C2311yescharacteristic
176#41×C139—81no—
177#41×C139—81no—
178#41×C139—81no—
179#41×C139—81no—
180#41×C139—81no—
181#41×C139—81no—
182C2×Q8×C139—22no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—81no—
187C2×Q8×C139—81no—
188C2×Q8×C139C2×D411yescharacteristic
189C2×Q8×C139C2×D411yescharacteristic
190C2×Q8×C139C2×D411yescharacteristic
191C2×D4×C139—22no—
192C2×D4×C139—22no—
193C2×D4×C139—21no—
194C2×D4×C139—22no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—41no—
201C2×D4×C139C2×D411yescharacteristic
202C2×D4×C139C2×D412yes—
203C22×C4×C139—22no—
204C22×C4×C139—22no—
205C22×C4×C139—22no—
206C22×C4×C139—21no—
207C22×C4×C139—22no—
208C22×C4×C139—41no—
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D411yescharacteristic
212Q16×C139—81no—
213Q16×C139—81no—
214SD16×C139—81no—
215SD16×C139—81no—
216SD16×C139—81no—
217D8×C139—44no—
218D8×C139—81no—
219M16×C139—81no—
220C2×C8×C139—21no—
221C2×C8×C139—21no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139—42no—
227C4⋊C4×C139—22no—
228C4⋊C4×C139—22no—
229C4⋊C4×C139—22no—
230C4⋊C4×C139—22no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—21no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139C2×D411yescharacteristic
246C4⋊C4×C139C2×D411yescharacteristic
247C4⋊C4×C139C2×D411yescharacteristic
248C4⋊C4×C139C2×D411yescharacteristic
249C4⋊C4×C139C2×D412yes—
250C22⋊C4×C139—22no—
251C22⋊C4×C139—22no—
252C22⋊C4×C139—22no—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—21no—
256C22⋊C4×C139—21no—
257C22⋊C4×C139—21no—
258C22⋊C4×C139—21no—
259C22⋊C4×C139—21no—
260C22⋊C4×C139—21no—
261C22⋊C4×C139—22no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—21no—
264C22⋊C4×C139—41no—
265C22⋊C4×C139—41no—
266C42×C139—22no—
267C42×C139—21no—
268C42×C139—21no—
269C42×C139—21no—
270C42×C139C2×D411yescharacteristic
271C42×C139C2×D411yescharacteristic
272C42×C139C2×D411yescharacteristic
273C42×C139C2411yescharacteristic
274C23×C139—21no—
275C23×C139—22no—
276C23×C139—41no—
277C23×C139#12011yescharacteristic
278Q8×C139—21no—
279Q8×C139—21no—
280Q8×C139—21no—
281Q8×C139—21no—
282Q8×C139—21no—
283Q8×C139—21no—
284Q8×C139—41no—
285Q8×C139—41no—
286Q8×C139—41no—
287Q8×C139—41no—
288Q8×C139—81no—
289Q8×C139—82no—
290D4×C139—21no—
291D4×C139—21no—
292D4×C139—42no—
293D4×C139—42no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—41no—
298D4×C139—41no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—81no—
303D4×C139—82no—
304D4×C139—82no—
305D4×C139—82no—
306D4×C139—82no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—22no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—82no—
324C2×C4×C139—82no—
325C2×C4×C139—82no—
326C2×C4×C139—82no—
327C2×C4×C139—82no—
328C2×C4×C139#12011yescharacteristic
329C2×C4×C139#12011yescharacteristic
330C2×C4×C139#12011yescharacteristic
331C2×C4×C139C22×D411yescharacteristic
332C2×C4×C139C22×D411yescharacteristic
333C2×C4×C139C22×D411yescharacteristic
334C8×C139—22no—
335C8×C139—41no—
336C8×C139—41no—
337C8×C139—41no—
338C8×C139—41no—
339C8×C139—41no—
340C22×C139—21no—
341C22×C139—21no—
342C22×C139—21no—
343C22×C139—41no—
344C22×C139—42no—
345C22×C139—41no—
346C22×C139—42no—
347C22×C139—42no—
348C22×C139—41no—
349C22×C139—81no—
350C22×C139—81no—
351C22×C139—81no—
352C22×C139C2×#12011yescharacteristic
353C4×C139—21no—
354C4×C139—21no—
355C4×C139—21no—
356C4×C139—21no—
357C4×C139—41no—
358C4×C139—41no—
359C4×C139—42no—
360C4×C139—41no—
361C4×C139—41no—
362C4×C139—41no—
363C4×C139—41no—
364C4×C139—41no—
365C4×C139—81no—
366C4×C139#57611yescharacteristic
367C4×C139#57611yescharacteristic
368C4×C139#57711yescharacteristic
369C4×C139#57811yescharacteristic
370C2×C139—41no—
371C2×C139—81no—
372C2×C139—82no—
373C2×C139—161no—
374C2×C139#300811yescharacteristic
375C2×C139#301311yescharacteristic
376C2×C139#301811yescharacteristic
377#18708C13911yesmaximal, characteristic, direct product factor, Sylow
378C139#1870811yescharacteristic, direct product factor, Sylow
379#3554C2×C13911yescharacteristic, complemented
380#3251C2×C13911yescharacteristic, complemented
381#3216C2×C13911yescharacteristic, complemented
382#3169C2×C13911yescharacteristic, complemented
383#1649C2×C13911yescharacteristic, complemented
384#1648C2×C13911yescharacteristic, complemented
385#1641C2×C13911yescharacteristic, complemented
386#1640C2×C13911yescharacteristic, complemented
387#1627C2×C13911yescharacteristic, complemented
388#1626C2×C13911yescharacteristic, complemented
389#1621C2×C13911yescharacteristic, complemented
390#1620C2×C13911yescharacteristic, complemented
391#1557C2×C13911yescharacteristic, complemented
392#1494C2×C13911yescharacteristic, complemented
393#1493C2×C13911yescharacteristic, complemented
394#562—22no—
395#559—21no—
396#559C22×C13911yescharacteristic
397#557C22×C13911yescharacteristic
398#554—21no—
399#550C22×C13911yescharacteristic
400D4×Q8C22×C13911yescharacteristic
401#548—21no—
402#547—21no—
403#542—21no—
404#542—21no—
405#540—21no—
406#539—22no—
407#536—21no—
408#533C22×C13911yescharacteristic
409#532C22×C13911yescharacteristic
410#532C22×C13911yescharacteristic
411#529C22×C13911yescharacteristic
412#500C22×C13911yescharacteristic
413#497—21no—
414#493C22×C13911yescharacteristic
415#489—21no—
416#486C22×C13911yescharacteristic
417#486C22×C13911yescharacteristic
418#478—21no—
419#475C22×C13911yescharacteristic
420#474C22×C13911yescharacteristic
421#469—21no—
422#468—21no—
423#466—22no—
424#463—21no—
425#462C22×C13911yescharacteristic
426#462C22×C13911yescharacteristic
427#460C22×C13911yescharacteristic
428#460C22×C13911yescharacteristic
429#460C22×C13911yescharacteristic
430#459C22×C13911yescharacteristic
431#452—21no—
432#452—21no—
433C4×D8—22no—
434#432C22×C13911yescharacteristic
435#423C22×C13911yescharacteristic
436C2×C4×C8C22×C13911yescharacteristic
437#332C22×C13911yescharacteristic
438#332C22×C13911yescharacteristic
439#331C22×C13911yescharacteristic
440#331C22×C13911yescharacteristic
441Q8⋊C8C22×C13911yescharacteristic
442Q8⋊C8C22×C13911yescharacteristic
443Q8⋊C8C22×C13911yescharacteristic
444Q8⋊C8C22×C13911yescharacteristic
445Q8⋊C8C22×C13911yescharacteristic
446Q8⋊C8C22×C13911yescharacteristic
447D4⋊C8C22×C13911yescharacteristic
448D4⋊C8C22×C13911yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C13911yescharacteristic
465C4⋊Q8D4×C13911yescharacteristic
466C4⋊Q8C23×C13911yescharacteristic
467C4⋊Q8C23×C13911yescharacteristic
468#127—21no—
469#127C23×C13911yescharacteristic
470#127C23×C13911yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C13911yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C13911yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C13911yescharacteristic
499C22⋊Q8D4×C13911yescharacteristic
500C22⋊Q8D4×C13911yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C13911yescharacteristic
509#121D4×C13912yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C13911yescharacteristic
514C4×Q8C23×C13911yescharacteristic
515C4×Q8C23×C13911yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C13912yes—
526C4×D4C23×C13911yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C13911yescharacteristic
531#107—22no—
532#107—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C13911yescharacteristic
536C4⋊C8C23×C13911yescharacteristic
537C4⋊C8C23×C13911yescharacteristic
538C4⋊C8C23×C13911yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C13911yescharacteristic
553C4×C8C23×C13911yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C13911yescharacteristic
567C2×Q8C2×D4×C13911yescharacteristic
568C2×Q8C2×D4×C13911yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C13911yescharacteristic
580C2×D4C2×D4×C13912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C13911yescharacteristic
588C22×C4C2×D4×C13911yescharacteristic
589C22×C4C2×D4×C13911yescharacteristic
590Q16—81no—
591Q16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C13911yescharacteristic
624C4⋊C4C2×D4×C13911yescharacteristic
625C4⋊C4C2×D4×C13911yescharacteristic
626C4⋊C4C2×D4×C13911yescharacteristic
627C4⋊C4C2×D4×C13912yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C13911yescharacteristic
649C42C2×D4×C13911yescharacteristic
650C42C2×D4×C13911yescharacteristic
651C42C24×C13911yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C13911yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C13911yescharacteristic
707C2×C4#120×C13911yescharacteristic
708C2×C4#120×C13911yescharacteristic
709C2×C4C22×D4×C13911yescharacteristic
710C2×C4C22×D4×C13911yescharacteristic
711C2×C4C22×D4×C13911yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C13911yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4#576×C13911yescharacteristic
745C4#576×C13911yescharacteristic
746C4#577×C13911yescharacteristic
747C4#578×C13911yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2#3008×C13911yescharacteristic
753C2#3013×C13911yescharacteristic
754C2#3018×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3554×C139C2semidirect
2. #3251×C139C2semidirect
3. #3216×C139C2semidirect
4. #3169×C139C2semidirect
5. #1649×C139C2semidirect
6. #1648×C139C2semidirect
7. #1641×C139C2semidirect
8. #1640×C139C2semidirect
9. #1627×C139C2semidirect
10. #1626×C139C2semidirect
11. #1621×C139C2semidirect
12. #1620×C139C2semidirect
13. #1557×C139C2semidirect
14. #1494×C139C2semidirect
15. #1493×C139C2semidirect
377. #18708C139direct (N × H)
378. C139#18708direct (N × H)
379. #3554C2×C139semidirect
380. #3251C2×C139semidirect
381. #3216C2×C139semidirect
382. #3169C2×C139semidirect
383. #1649C2×C139semidirect
384. #1648C2×C139semidirect
385. #1641C2×C139semidirect
386. #1640C2×C139semidirect
387. #1627C2×C139semidirect
388. #1626C2×C139semidirect
389. #1621C2×C139semidirect
390. #1620C2×C139semidirect
391. #1557C2×C139semidirect
392. #1494C2×C139semidirect
393. #1493C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3554×C1392
#3251×C1392
#3216×C1392
#3169×C1392
#1649×C1392
#1648×C1392
#1641×C1392
#1640×C1392
#1627×C1392
#1626×C1392
#1621×C1392
#1620×C1392
#1557×C1392
#1494×C1392
#1493×C1392
#18708139