Finite Group Databasebeta

← C47×#18740 #26058438

Subgroups — C47×#18740 #26058438

Order 12032.

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
1C47×#3547C211yesmaximal, characteristic, complemented
2C47×#3245C211yesmaximal, characteristic, complemented
3C47×#3212C211yesmaximal, characteristic, complemented
4C47×#3182C211yesmaximal, characteristic, complemented
5C47×#1649C211yesmaximal, characteristic, complemented
6C47×#1647C211yesmaximal, characteristic, complemented
7C47×#1646C211yesmaximal, characteristic, complemented
8C47×#1644C211yesmaximal, characteristic, complemented
9C47×#1627C211yesmaximal, characteristic, complemented
10C47×#1625C211yesmaximal, characteristic, complemented
11C47×#1624C211yesmaximal, characteristic, complemented
12C47×#1622C211yesmaximal, characteristic, complemented
13C47×#1542C211yesmaximal, characteristic, complemented
14C47×#1484C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, characteristic, complemented
16C47×#562—22no—
17C47×#555—21no—
18C47×#555C2211yescharacteristic
19C47×#554C2211yescharacteristic
20C47×#553—21no—
21C47×#552—21no—
22D4×Q8×C47C2211yescharacteristic
23C47×#548—21no—
24C47×#547C2211yescharacteristic
25C47×#544—21no—
26C47×#542—22no—
27C47×#540—21no—
28C47×#537—21no—
29C47×#536—21no—
30C47×#533C2211yescharacteristic
31C47×#532C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#500C2211yescharacteristic
35C47×#495—21no—
36C47×#492C2211yescharacteristic
37C47×#488—21no—
38C47×#487C2211yescharacteristic
39C47×#486C2211yescharacteristic
40C47×#474—21no—
41C47×#474C2211yescharacteristic
42C47×#474C2211yescharacteristic
43C47×#468—22no—
44C47×#466—21no—
45C47×#466—21no—
46C47×#462C2211yescharacteristic
47C47×#461C2211yescharacteristic
48C47×#460C2211yescharacteristic
49C47×#459—21no—
50C47×#459C2211yescharacteristic
51C47×#459C2211yescharacteristic
52C47×#459C2211yescharacteristic
53C47×#452—21no—
54C47×#449—21no—
55C47×#440—22no—
56C47×#431C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C4×M16×C47C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C22×Q8×C47—21no—
75C2×Q16×C47—21no—
76C2×SD16×C47—22no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×D8×C47—21no—
80C2×D8×C47—21no—
81C2×D8×C47—21no—
82C2×M16×C47—21no—
83C22×C8×C47—21no—
84C4⋊Q8×C47—22no—
85C4⋊Q8×C47—21no—
86C4⋊Q8×C47D411yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90#127×C47D411yescharacteristic
91#127×C47C2311yescharacteristic
92#126×C47—22no—
93#126×C47—21no—
94#125×C47—22no—
95#125×C47—21no—
96#125×C47—21no—
97#125×C47D411yescharacteristic
98#124×C47—22no—
99#124×C47—22no—
100#124×C47—22no—
101#124×C47—21no—
102#124×C47—21no—
103#124×C47D411yescharacteristic
104#123×C47—22no—
105#123×C47—22no—
106#123×C47—22no—
107#123×C47—21no—
108#123×C47—22no—
109C22⋊Q8×C47—22no—
110C22⋊Q8×C47—22no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47—21no—
116C22⋊Q8×C47—22no—
117C22⋊Q8×C47D411yescharacteristic
118C22⋊Q8×C47D412yes—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—22no—
122#121×C47—22no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47D411yescharacteristic
130#121×C47D411yescharacteristic
131#121×C47D411yescharacteristic
132C4×Q8×C47—21no—
133C4×Q8×C47D412yes—
134C4×Q8×C47C2311yescharacteristic
135C4×D4×C47—22no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47C2311yescharacteristic
143C4×D4×C47C2311yescharacteristic
144C4×D4×C47C2311yescharacteristic
145#117×C47—22no—
146#117×C47—21no—
147#117×C47—21no—
148#117×C47—21no—
149#117×C47—21no—
150C2×C4⋊C4×C47—21no—
151C2×C4⋊C4×C47—21no—
152C2×C42×C47C2311yescharacteristic
153#107×C47—21no—
154#107×C47—21no—
155#107×C47—22no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161#103×C47—22no—
162#103×C47—21no—
163#103×C47—21no—
164#102×C47—21no—
165#102×C47—21no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—22no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—81no—
177#41×C47—81no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—81no—
181#41×C47—81no—
182C2×Q8×C47—22no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—81no—
187C2×Q8×C47—81no—
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2×D412yes—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—41no—
201C2×D4×C47C2×D411yescharacteristic
202C2×D4×C47C2×D411yescharacteristic
203C2×D4×C47C2×D411yescharacteristic
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—41no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214Q16×C47—81no—
215SD16×C47—44no—
216SD16×C47—81no—
217SD16×C47—81no—
218D8×C47—81no—
219D8×C47—81no—
220D8×C47—81no—
221M16×C47—42no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—81no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—22no—
231C4⋊C4×C47—22no—
232C4⋊C4×C47—22no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C4⋊C4×C47C2×D411yescharacteristic
249C4⋊C4×C47C2×D412yes—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—21no—
257C22⋊C4×C47—21no—
258C22⋊C4×C47—21no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—41no—
266C22⋊C4×C47—41no—
267C42×C47—22no—
268C42×C47—22no—
269C42×C47—21no—
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2411yescharacteristic
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—41no—
278C23×C47#12011yescharacteristic
279Q8×C47—21no—
280Q8×C47—21no—
281Q8×C47—42no—
282Q8×C47—41no—
283Q8×C47—41no—
284Q8×C47—41no—
285Q8×C47—41no—
286Q8×C47—81no—
287Q8×C47—82no—
288D4×C47—21no—
289D4×C47—21no—
290D4×C47—21no—
291D4×C47—21no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—42no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—81no—
300D4×C47—81no—
301D4×C47—81no—
302D4×C47—81no—
303D4×C47—81no—
304D4×C47—82no—
305D4×C47—82no—
306D4×C47—82no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—22no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—22no—
317C2×C4×C47—21no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—82no—
327C2×C4×C47—82no—
328C2×C4×C47—82no—
329C2×C4×C47—82no—
330C2×C4×C47#12011yescharacteristic
331C2×C4×C47#12011yescharacteristic
332C2×C4×C47#12011yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C8×C47—22no—
337C8×C47—41no—
338C8×C47—41no—
339C8×C47—41no—
340C8×C47—41no—
341C8×C47—41no—
342#18740C4711yesmaximal, characteristic, direct product factor, Sylow
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47C2×#12011yescharacteristic
359C4×C47—21no—
360C4×C47—21no—
361C4×C47—21no—
362C4×C47—21no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—42no—
366C4×C47—41no—
367C4×C47—41no—
368C4×C47—41no—
369C4×C47—42no—
370C4×C47—81no—
371C4×C47#57611yescharacteristic
372C4×C47#57611yescharacteristic
373C4×C47#57711yescharacteristic
374C4×C47#57811yescharacteristic
375#3547C2×C4711yescharacteristic, complemented
376#3245C2×C4711yescharacteristic, complemented
377#3212C2×C4711yescharacteristic, complemented
378#3182C2×C4711yescharacteristic, complemented
379#1649C2×C4711yescharacteristic, complemented
380#1647C2×C4711yescharacteristic, complemented
381#1646C2×C4711yescharacteristic, complemented
382#1644C2×C4711yescharacteristic, complemented
383#1627C2×C4711yescharacteristic, complemented
384#1625C2×C4711yescharacteristic, complemented
385#1624C2×C4711yescharacteristic, complemented
386#1622C2×C4711yescharacteristic, complemented
387#1542C2×C4711yescharacteristic, complemented
388#1484C2×C4711yescharacteristic, complemented
389#1483C2×C4711yescharacteristic, complemented
390C2×C47—41no—
391C2×C47—81no—
392C2×C47—81no—
393C2×C47—81no—
394C2×C47—161no—
395C2×C47#300811yescharacteristic
396C2×C47#301311yescharacteristic
397C2×C47#301811yescharacteristic
398#562—22no—
399#555—21no—
400#555C22×C4711yescharacteristic
401#554C22×C4711yescharacteristic
402#553—21no—
403#552—21no—
404D4×Q8C22×C4711yescharacteristic
405#548—21no—
406#547C22×C4711yescharacteristic
407#544—21no—
408#542—22no—
409#540—21no—
410#537—21no—
411#536—21no—
412#533C22×C4711yescharacteristic
413#532C22×C4711yescharacteristic
414#532C22×C4711yescharacteristic
415#529C22×C4711yescharacteristic
416#500C22×C4711yescharacteristic
417#495—21no—
418#492C22×C4711yescharacteristic
419#488—21no—
420#487C22×C4711yescharacteristic
421#486C22×C4711yescharacteristic
422#474—21no—
423#474C22×C4711yescharacteristic
424#474C22×C4711yescharacteristic
425#468—22no—
426#466—21no—
427#466—21no—
428#462C22×C4711yescharacteristic
429#461C22×C4711yescharacteristic
430#460C22×C4711yescharacteristic
431#459—21no—
432#459C22×C4711yescharacteristic
433#459C22×C4711yescharacteristic
434#459C22×C4711yescharacteristic
435#452—21no—
436#449—21no—
437#440—22no—
438#431C22×C4711yescharacteristic
439C2×C4⋊C8C22×C4711yescharacteristic
440C4×M16C22×C4711yescharacteristic
441#333C22×C4711yescharacteristic
442#333C22×C4711yescharacteristic
443#332C22×C4711yescharacteristic
444#332C22×C4711yescharacteristic
445Q8⋊C8C22×C4711yescharacteristic
446Q8⋊C8C22×C4711yescharacteristic
447D4⋊C8C22×C4711yescharacteristic
448D4⋊C8C22×C4711yescharacteristic
449D4⋊C8C22×C4711yescharacteristic
450D4⋊C8C22×C4711yescharacteristic
451D4⋊C8C22×C4711yescharacteristic
452D4⋊C8C22×C4711yescharacteristic
453C47#1874011yescharacteristic, direct product factor, Sylow
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C22×Q8—21no—
458C2×Q16—21no—
459C2×SD16—22no—
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×C4711yescharacteristic
470C4⋊Q8C23×C4711yescharacteristic
471C4⋊Q8C23×C4711yescharacteristic
472C4⋊Q8C23×C4711yescharacteristic
473#127D4×C4711yescharacteristic
474#127C23×C4711yescharacteristic
475#126—22no—
476#126—21no—
477#125—22no—
478#125—21no—
479#125—21no—
480#125D4×C4711yescharacteristic
481#124—22no—
482#124—22no—
483#124—22no—
484#124—21no—
485#124—21no—
486#124D4×C4711yescharacteristic
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×C4711yescharacteristic
501C22⋊Q8D4×C4712yes—
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×C4711yescharacteristic
513#121D4×C4711yescharacteristic
514#121D4×C4711yescharacteristic
515C4×Q8—21no—
516C4×Q8D4×C4712yes—
517C4×Q8C23×C4711yescharacteristic
518C4×D4—22no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4C23×C4711yescharacteristic
526C4×D4C23×C4711yescharacteristic
527C4×D4C23×C4711yescharacteristic
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×C4711yescharacteristic
536#107—22no—
537#107—21no—
538#107—21no—
539C4⋊C8—21no—
540C4⋊C8C23×C4711yescharacteristic
541C4⋊C8C23×C4711yescharacteristic
542C4⋊C8C23×C4711yescharacteristic
543C4⋊C8C23×C4711yescharacteristic
544#103—22no—
545#103—21no—
546#103—21no—
547#102—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×C4711yescharacteristic
558C4×C8C23×C4711yescharacteristic
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×C4711yescharacteristic
572C2×Q8C2×D4×C4712yes—
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×C4711yescharacteristic
585C2×D4C2×D4×C4711yescharacteristic
586C2×D4C2×D4×C4711yescharacteristic
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—41no—
594C22×C4C2×D4×C4711yescharacteristic
595C22×C4C2×D4×C4711yescharacteristic
596C22×C4C2×D4×C4711yescharacteristic
597Q16—81no—
598SD16—44no—
599SD16—81no—
600SD16—81no—
601D8—81no—
602D8—81no—
603D8—81no—
604M16—42no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—81no—
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×C4711yescharacteristic
629C4⋊C4C2×D4×C4711yescharacteristic
630C4⋊C4C2×D4×C4711yescharacteristic
631C4⋊C4C2×D4×C4711yescharacteristic
632C4⋊C4C2×D4×C4712yes—
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×C4711yescharacteristic
654C42C2×D4×C4711yescharacteristic
655C42C2×D4×C4711yescharacteristic
656C42C24×C4711yescharacteristic
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23#120×C4711yescharacteristic
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×C4711yescharacteristic
714C2×C4#120×C4711yescharacteristic
715C2×C4#120×C4711yescharacteristic
716C2×C4C22×D4×C4711yescharacteristic
717C2×C4C22×D4×C4711yescharacteristic
718C2×C4C22×D4×C4711yescharacteristic
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×C4711yescharacteristic
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—81no—
753C4C47×#57611yescharacteristic
754C4C47×#57611yescharacteristic
755C4C47×#57711yescharacteristic
756C4C47×#57811yescharacteristic
757C2—41no—
758C2—81no—
759C2—81no—
760C2—81no—
761C2—161no—
762C2C47×#300811yescharacteristic
763C2C47×#301311yescharacteristic
764C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3547C2semidirect
2. C47×#3245C2semidirect
3. C47×#3212C2semidirect
4. C47×#3182C2semidirect
5. C47×#1649C2semidirect
6. C47×#1647C2semidirect
7. C47×#1646C2semidirect
8. C47×#1644C2semidirect
9. C47×#1627C2semidirect
10. C47×#1625C2semidirect
11. C47×#1624C2semidirect
12. C47×#1622C2semidirect
13. C47×#1542C2semidirect
14. C47×#1484C2semidirect
15. C47×#1483C2semidirect
342. #18740C47direct (N × H)
375. #3547C2×C47semidirect
376. #3245C2×C47semidirect
377. #3212C2×C47semidirect
378. #3182C2×C47semidirect
379. #1649C2×C47semidirect
380. #1647C2×C47semidirect
381. #1646C2×C47semidirect
382. #1644C2×C47semidirect
383. #1627C2×C47semidirect
384. #1625C2×C47semidirect
385. #1624C2×C47semidirect
386. #1622C2×C47semidirect
387. #1542C2×C47semidirect
388. #1484C2×C47semidirect
389. #1483C2×C47semidirect
453. C47#18740direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35472
C47×#32452
C47×#32122
C47×#31822
C47×#16492
C47×#16472
C47×#16462
C47×#16442
C47×#16272
C47×#16252
C47×#16242
C47×#16222
C47×#15422
C47×#14842
C47×#14832
#1874047