Finite Group Databasebeta

← C139×#18706 #48013302

Subgroups — C139×#18706 #48013302

Order 35584.

908 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3547×C139C211yesmaximal, characteristic, complemented
2#3251×C139C211yesmaximal, characteristic, complemented
3#3214×C139C211yesmaximal, characteristic, complemented
4#3167×C139C211yesmaximal, characteristic, complemented
5#1654×C139C211yesmaximal, characteristic, complemented
6#1651×C139C211yesmaximal, characteristic, complemented
7#1646×C139C211yesmaximal, characteristic, complemented
8#1643×C139C211yesmaximal, characteristic, complemented
9#1627×C139C211yesmaximal, characteristic, complemented
10#1625×C139C211yesmaximal, characteristic, complemented
11#1624×C139C211yesmaximal, characteristic, complemented
12#1622×C139C211yesmaximal, characteristic, complemented
13#1559×C139C211yesmaximal, characteristic, complemented
14#1494×C139C211yesmaximal, characteristic, complemented
15#1492×C139C211yesmaximal, characteristic, complemented
16#562×C139—22no—
17#555×C139—21no—
18#555×C139C2211yescharacteristic
19#554×C139C2211yescharacteristic
20#553×C139—21no—
21#552×C139—21no—
22D4×Q8×C139C2211yescharacteristic
23#548×C139—21no—
24#547×C139C2211yescharacteristic
25#544×C139—21no—
26#542×C139—22no—
27#540×C139—21no—
28#537×C139—21no—
29#536×C139—21no—
30#533×C139C2211yescharacteristic
31#532×C139C2211yescharacteristic
32#532×C139C2211yescharacteristic
33#529×C139C2211yescharacteristic
34#498×C139C2211yescharacteristic
35#496×C139—21no—
36#492×C139C2211yescharacteristic
37#489×C139—21no—
38#487×C139C2211yescharacteristic
39#486×C139C2211yescharacteristic
40#478×C139—21no—
41#475×C139C2211yescharacteristic
42#474×C139C2211yescharacteristic
43#469×C139—21no—
44#468×C139—21no—
45#465×C139—22no—
46#463×C139—21no—
47#461×C139C2211yescharacteristic
48#461×C139C2211yescharacteristic
49#460×C139C2211yescharacteristic
50#459×C139C2211yescharacteristic
51#459×C139C2211yescharacteristic
52#459×C139C2211yescharacteristic
53#449×C139—21no—
54#449×C139—21no—
55C4×SD16×C139—22no—
56#432×C139C2211yescharacteristic
57#423×C139C2211yescharacteristic
58C2×C4×C8×C139C2211yescharacteristic
59#333×C139C2211yescharacteristic
60#333×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62#332×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64Q8⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66D4⋊C8×C139C2211yescharacteristic
67D4⋊C8×C139C2211yescharacteristic
68D4⋊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×SD16×C139—22no—
76C2×SD16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139—21no—
79C2×D8×C139—21no—
80C2×D8×C139—21no—
81C2×D8×C139—21no—
82C2×M16×C139—21no—
83C22×C8×C139—21no—
84C4⋊Q8×C139—22no—
85C4⋊Q8×C139—21no—
86C4⋊Q8×C139D411yescharacteristic
87C4⋊Q8×C139C2311yescharacteristic
88C4⋊Q8×C139C2311yescharacteristic
89C4⋊Q8×C139C2311yescharacteristic
90#127×C139D411yescharacteristic
91#127×C139C2311yescharacteristic
92#126×C139—22no—
93#126×C139—21no—
94#125×C139—22no—
95#125×C139—21no—
96#125×C139—21no—
97#125×C139D411yescharacteristic
98#124×C139—22no—
99#124×C139—22no—
100#124×C139—22no—
101#124×C139—21no—
102#124×C139—21no—
103#124×C139D411yescharacteristic
104#123×C139—22no—
105#123×C139—22no—
106#123×C139—22no—
107#123×C139—21no—
108#123×C139—22no—
109C22⋊Q8×C139—22no—
110C22⋊Q8×C139—22no—
111C22⋊Q8×C139—21no—
112C22⋊Q8×C139—22no—
113C22⋊Q8×C139—21no—
114C22⋊Q8×C139—21no—
115C22⋊Q8×C139—21no—
116C22⋊Q8×C139—22no—
117C22⋊Q8×C139D412yes—
118C22⋊Q8×C139D411yescharacteristic
119#121×C139—22no—
120#121×C139—22no—
121#121×C139—22no—
122#121×C139—22no—
123#121×C139—21no—
124#121×C139—21no—
125#121×C139—21no—
126#121×C139—21no—
127#121×C139—21no—
128#121×C139—21no—
129#121×C139D411yescharacteristic
130#121×C139D411yescharacteristic
131#121×C139D411yescharacteristic
132C4×Q8×C139—21no—
133C4×Q8×C139D412yes—
134C4×Q8×C139C2311yescharacteristic
135C4×D4×C139—22no—
136C4×D4×C139—21no—
137C4×D4×C139—21no—
138C4×D4×C139—21no—
139C4×D4×C139—21no—
140C4×D4×C139—21no—
141C4×D4×C139—21no—
142C4×D4×C139C2311yescharacteristic
143C4×D4×C139C2311yescharacteristic
144C4×D4×C139C2311yescharacteristic
145#117×C139—22no—
146#117×C139—21no—
147#117×C139—21no—
148#117×C139—21no—
149#117×C139—21no—
150C2×C4⋊C4×C139—21no—
151C2×C4⋊C4×C139—21no—
152C2×C42×C139C2311yescharacteristic
153#107×C139—21no—
154#106×C139—22no—
155#106×C139—21no—
156C4⋊C8×C139—21no—
157C4⋊C8×C139C2311yescharacteristic
158C4⋊C8×C139C2311yescharacteristic
159C4⋊C8×C139C2311yescharacteristic
160C4⋊C8×C139C2311yescharacteristic
161#103×C139—22no—
162#103×C139—21no—
163#103×C139—21no—
164#103×C139—21no—
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×D412yes—
190C2×D4×C139—22no—
191C2×D4×C139—22no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
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×D411yescharacteristic
203C2×D4×C139C2×D411yescharacteristic
204C22×C4×C139—22no—
205C22×C4×C139—22no—
206C22×C4×C139—22no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—41no—
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D411yescharacteristic
214SD16×C139—44no—
215SD16×C139—81no—
216SD16×C139—81no—
217SD16×C139—81no—
218D8×C139—81no—
219D8×C139—81no—
220D8×C139—81no—
221M16×C139—81no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—42no—
229C4⋊C4×C139—22no—
230C4⋊C4×C139—22no—
231C4⋊C4×C139—22no—
232C4⋊C4×C139—22no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—22no—
238C4⋊C4×C139—22no—
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×D412yes—
249C4⋊C4×C139C2×D411yescharacteristic
250C22⋊C4×C139—22no—
251C22⋊C4×C139—22no—
252C22⋊C4×C139—22no—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—21no—
257C22⋊C4×C139—21no—
258C22⋊C4×C139—21no—
259C22⋊C4×C139—21no—
260C22⋊C4×C139—21no—
261C22⋊C4×C139—21no—
262C22⋊C4×C139—21no—
263C22⋊C4×C139—21no—
264C22⋊C4×C139—21no—
265C22⋊C4×C139—41no—
266C22⋊C4×C139—41no—
267C42×C139—22no—
268C42×C139—22no—
269C42×C139—21no—
270C42×C139C2×D411yescharacteristic
271C42×C139C2×D411yescharacteristic
272C42×C139C2×D411yescharacteristic
273C42×C139C2411yescharacteristic
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—41no—
278C23×C139#12011yescharacteristic
279Q8×C139—21no—
280Q8×C139—21no—
281Q8×C139—42no—
282Q8×C139—41no—
283Q8×C139—41no—
284Q8×C139—41no—
285Q8×C139—41no—
286Q8×C139—81no—
287Q8×C139—82no—
288D4×C139—21no—
289D4×C139—21no—
290D4×C139—21no—
291D4×C139—21no—
292D4×C139—21no—
293D4×C139—21no—
294D4×C139—42no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—41no—
298D4×C139—41no—
299D4×C139—81no—
300D4×C139—81no—
301D4×C139—81no—
302D4×C139—81no—
303D4×C139—81no—
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—22no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—22no—
317C2×C4×C139—21no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—82no—
327C2×C4×C139—82no—
328C2×C4×C139—82no—
329C2×C4×C139—82no—
330C2×C4×C139#12011yescharacteristic
331C2×C4×C139#12011yescharacteristic
332C2×C4×C139#12011yescharacteristic
333C2×C4×C139C22×D411yescharacteristic
334C2×C4×C139C22×D411yescharacteristic
335C2×C4×C139C22×D411yescharacteristic
336C8×C139—22no—
337C8×C139—41no—
338C8×C139—41no—
339C8×C139—41no—
340C8×C139—41no—
341C8×C139—41no—
342C22×C139—21no—
343C22×C139—21no—
344C22×C139—21no—
345C22×C139—41no—
346C22×C139—41no—
347C22×C139—41no—
348C22×C139—41no—
349C22×C139—41no—
350C22×C139—41no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139C2×#12011yescharacteristic
358C4×C139—21no—
359C4×C139—21no—
360C4×C139—21no—
361C4×C139—21no—
362C4×C139—41no—
363C4×C139—41no—
364C4×C139—41no—
365C4×C139—42no—
366C4×C139—41no—
367C4×C139—41no—
368C4×C139—42no—
369C4×C139—81no—
370C4×C139#57611yescharacteristic
371C4×C139#57711yescharacteristic
372C4×C139#57711yescharacteristic
373C4×C139#57711yescharacteristic
374C2×C139—41no—
375C2×C139—81no—
376C2×C139—81no—
377C2×C139—81no—
378C2×C139—161no—
379C2×C139#301011yescharacteristic
380C2×C139#301211yescharacteristic
381C2×C139#301811yescharacteristic
382#18706C13911yesmaximal, characteristic, direct product factor, Sylow
383C139#1870611yescharacteristic, direct product factor, Sylow
384#3547C2×C13911yescharacteristic, complemented
385#3251C2×C13911yescharacteristic, complemented
386#3214C2×C13911yescharacteristic, complemented
387#3167C2×C13911yescharacteristic, complemented
388#1654C2×C13911yescharacteristic, complemented
389#1651C2×C13911yescharacteristic, complemented
390#1646C2×C13911yescharacteristic, complemented
391#1643C2×C13911yescharacteristic, complemented
392#1627C2×C13911yescharacteristic, complemented
393#1625C2×C13911yescharacteristic, complemented
394#1624C2×C13911yescharacteristic, complemented
395#1622C2×C13911yescharacteristic, complemented
396#1559C2×C13911yescharacteristic, complemented
397#1494C2×C13911yescharacteristic, complemented
398#1492C2×C13911yescharacteristic, complemented
399#562—22no—
400#555—21no—
401#555C22×C13911yescharacteristic
402#554C22×C13911yescharacteristic
403#553—21no—
404#552—21no—
405D4×Q8C22×C13911yescharacteristic
406#548—21no—
407#547C22×C13911yescharacteristic
408#544—21no—
409#542—22no—
410#540—21no—
411#537—21no—
412#536—21no—
413#533C22×C13911yescharacteristic
414#532C22×C13911yescharacteristic
415#532C22×C13911yescharacteristic
416#529C22×C13911yescharacteristic
417#498C22×C13911yescharacteristic
418#496—21no—
419#492C22×C13911yescharacteristic
420#489—21no—
421#487C22×C13911yescharacteristic
422#486C22×C13911yescharacteristic
423#478—21no—
424#475C22×C13911yescharacteristic
425#474C22×C13911yescharacteristic
426#469—21no—
427#468—21no—
428#465—22no—
429#463—21no—
430#461C22×C13911yescharacteristic
431#461C22×C13911yescharacteristic
432#460C22×C13911yescharacteristic
433#459C22×C13911yescharacteristic
434#459C22×C13911yescharacteristic
435#459C22×C13911yescharacteristic
436#449—21no—
437#449—21no—
438C4×SD16—22no—
439#432C22×C13911yescharacteristic
440#423C22×C13911yescharacteristic
441C2×C4×C8C22×C13911yescharacteristic
442#333C22×C13911yescharacteristic
443#333C22×C13911yescharacteristic
444#332C22×C13911yescharacteristic
445#332C22×C13911yescharacteristic
446Q8⋊C8C22×C13911yescharacteristic
447Q8⋊C8C22×C13911yescharacteristic
448D4⋊C8C22×C13911yescharacteristic
449D4⋊C8C22×C13911yescharacteristic
450D4⋊C8C22×C13911yescharacteristic
451D4⋊C8C22×C13911yescharacteristic
452D4⋊C8C22×C13911yescharacteristic
453D4⋊C8C22×C13911yescharacteristic
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C22×Q8—21no—
458C2×SD16—22no—
459C2×SD16—21no—
460C2×SD16—21no—
461C2×SD16—21no—
462C2×D8—21no—
463C2×D8—21no—
464C2×D8—21no—
465C2×M16—21no—
466C22×C8—21no—
467C4⋊Q8—22no—
468C4⋊Q8—21no—
469C4⋊Q8D4×C13911yescharacteristic
470C4⋊Q8C23×C13911yescharacteristic
471C4⋊Q8C23×C13911yescharacteristic
472C4⋊Q8C23×C13911yescharacteristic
473#127D4×C13911yescharacteristic
474#127C23×C13911yescharacteristic
475#126—22no—
476#126—21no—
477#125—22no—
478#125—21no—
479#125—21no—
480#125D4×C13911yescharacteristic
481#124—22no—
482#124—22no—
483#124—22no—
484#124—21no—
485#124—21no—
486#124D4×C13911yescharacteristic
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—21no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—22no—
500C22⋊Q8D4×C13911yescharacteristic
501C22⋊Q8D4×C13912yes—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121D4×C13911yescharacteristic
513#121D4×C13911yescharacteristic
514#121D4×C13911yescharacteristic
515C4×Q8—21no—
516C4×Q8D4×C13912yes—
517C4×Q8C23×C13911yescharacteristic
518C4×D4—22no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4C23×C13911yescharacteristic
526C4×D4C23×C13911yescharacteristic
527C4×D4C23×C13911yescharacteristic
528#117—22no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C42C23×C13911yescharacteristic
536#107—21no—
537#106—22no—
538#106—21no—
539C4⋊C8—21no—
540C4⋊C8C23×C13911yescharacteristic
541C4⋊C8C23×C13911yescharacteristic
542C4⋊C8C23×C13911yescharacteristic
543C4⋊C8C23×C13911yescharacteristic
544#103—22no—
545#103—21no—
546#103—21no—
547#103—21no—
548#102—21no—
549#102—22no—
550#102—21no—
551#102—21no—
552#102—21no—
553#102—21no—
554C22⋊C8—21no—
555#97—21no—
556C4×C8—21no—
557C4×C8C23×C13911yescharacteristic
558C4×C8C23×C13911yescharacteristic
559#41—81no—
560#41—81no—
561#41—81no—
562#41—81no—
563#41—81no—
564#41—81no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—81no—
570C2×Q8—81no—
571C2×Q8C2×D4×C13911yescharacteristic
572C2×Q8C2×D4×C13912yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4C2×D4×C13911yescharacteristic
585C2×D4C2×D4×C13911yescharacteristic
586C2×D4C2×D4×C13911yescharacteristic
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—41no—
594C22×C4C2×D4×C13911yescharacteristic
595C22×C4C2×D4×C13911yescharacteristic
596C22×C4C2×D4×C13911yescharacteristic
597SD16—44no—
598SD16—81no—
599SD16—81no—
600SD16—81no—
601D8—81no—
602D8—81no—
603D8—81no—
604M16—81no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—42no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4C2×D4×C13911yescharacteristic
629C4⋊C4C2×D4×C13911yescharacteristic
630C4⋊C4C2×D4×C13911yescharacteristic
631C4⋊C4C2×D4×C13912yes—
632C4⋊C4C2×D4×C13911yescharacteristic
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C42—22no—
651C42—22no—
652C42—21no—
653C42C2×D4×C13911yescharacteristic
654C42C2×D4×C13911yescharacteristic
655C42C2×D4×C13911yescharacteristic
656C42C24×C13911yescharacteristic
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23#120×C13911yescharacteristic
662Q8—21no—
663Q8—21no—
664Q8—42no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669Q8—81no—
670Q8—82no—
671D4—21no—
672D4—21no—
673D4—21no—
674D4—21no—
675D4—21no—
676D4—21no—
677D4—42no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—81no—
683D4—81no—
684D4—81no—
685D4—81no—
686D4—81no—
687D4—82no—
688D4—82no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4#120×C13911yescharacteristic
714C2×C4#120×C13911yescharacteristic
715C2×C4#120×C13911yescharacteristic
716C2×C4C22×D4×C13911yescharacteristic
717C2×C4C22×D4×C13911yescharacteristic
718C2×C4C22×D4×C13911yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22C2×#120×C13911yescharacteristic
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—81no—
753C4#576×C13911yescharacteristic
754C4#577×C13911yescharacteristic
755C4#577×C13911yescharacteristic
756C4#577×C13911yescharacteristic
757C2—41no—
758C2—81no—
759C2—81no—
760C2—81no—
761C2—161no—
762C2#3010×C13911yescharacteristic
763C2#3012×C13911yescharacteristic
764C2#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. #3547×C139C2semidirect
2. #3251×C139C2semidirect
3. #3214×C139C2semidirect
4. #3167×C139C2semidirect
5. #1654×C139C2semidirect
6. #1651×C139C2semidirect
7. #1646×C139C2semidirect
8. #1643×C139C2semidirect
9. #1627×C139C2semidirect
10. #1625×C139C2semidirect
11. #1624×C139C2semidirect
12. #1622×C139C2semidirect
13. #1559×C139C2semidirect
14. #1494×C139C2semidirect
15. #1492×C139C2semidirect
382. #18706C139direct (N × H)
383. C139#18706direct (N × H)
384. #3547C2×C139semidirect
385. #3251C2×C139semidirect
386. #3214C2×C139semidirect
387. #3167C2×C139semidirect
388. #1654C2×C139semidirect
389. #1651C2×C139semidirect
390. #1646C2×C139semidirect
391. #1643C2×C139semidirect
392. #1627C2×C139semidirect
393. #1625C2×C139semidirect
394. #1624C2×C139semidirect
395. #1622C2×C139semidirect
396. #1559C2×C139semidirect
397. #1494C2×C139semidirect
398. #1492C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3547×C1392
#3251×C1392
#3214×C1392
#3167×C1392
#1654×C1392
#1651×C1392
#1646×C1392
#1643×C1392
#1627×C1392
#1625×C1392
#1624×C1392
#1622×C1392
#1559×C1392
#1494×C1392
#1492×C1392
#18706139