Finite Group Databasebeta

← C47×#18964 #26058662

Subgroups — C47×#18964 #26058662

Order 12032.

900 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3554C211yesmaximal, characteristic, complemented
2C47×#3254C211yesmaximal, characteristic, complemented
3C47×#3247C211yesmaximal, characteristic, complemented
4C47×#3207C211yesmaximal, characteristic, complemented
5C47×#1637C211yesmaximal, characteristic, complemented
6C47×#1636C211yesmaximal, characteristic, complemented
7C47×#1631C211yesmaximal, characteristic, complemented
8C47×#1630C211yesmaximal, characteristic, complemented
9C47×#1627C211yesmaximal, characteristic, complemented
10C47×#1626C211yesmaximal, characteristic, complemented
11C47×#1621C211yesmaximal, characteristic, complemented
12C47×#1620C211yesmaximal, characteristic, complemented
13C47×#1547C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1481C211yesmaximal, characteristic, complemented
16C47×#562—22no—
17C47×#559—21no—
18C47×#559C2211yescharacteristic
19C47×#557C2211yescharacteristic
20C47×#554—21no—
21C47×#550C2211yescharacteristic
22D4×Q8×C47C2211yescharacteristic
23C47×#548—21no—
24C47×#547—21no—
25C47×#542—21no—
26C47×#542—21no—
27C47×#540—21no—
28C47×#539—22no—
29C47×#536—21no—
30C47×#533C2211yescharacteristic
31C47×#532C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#493C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#478—21no—
39C47×#477C2211yescharacteristic
40C47×#477C2211yescharacteristic
41C47×#477C2211yescharacteristic
42C47×#476C2211yescharacteristic
43C47×#474—21no—
44C47×#468—21no—
45C47×#468—21no—
46C47×#466—21no—
47C47×#465—21no—
48C47×#463—21no—
49C47×#463—22no—
50C47×#461—21no—
51C47×#460C2211yescharacteristic
52C47×#460C2211yescharacteristic
53C47×#460C2211yescharacteristic
54C47×#459C2211yescharacteristic
55C47×#449—22no—
56C47×#431C2211yescharacteristic
57C47×#423C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×Q8⋊C8C2211yescharacteristic
68C47×Q8⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C22×Q8×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—21no—
81C2×M16×C47—21no—
82C22×C8×C47—21no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47D411yescharacteristic
86C4⋊Q8×C47D411yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89#127×C47—21no—
90#127×C47C2311yescharacteristic
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—21no—
101#124×C47—21no—
102#124×C47—21no—
103#124×C47—21no—
104#124×C47D411yescharacteristic
105#123×C47—22no—
106#123×C47—22no—
107#123×C47—22no—
108#123×C47—22no—
109#123×C47—22no—
110#123×C47—22no—
111#123×C47—21no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47—22no—
116C22⋊Q8×C47—21no—
117C22⋊Q8×C47—22no—
118C22⋊Q8×C47—21no—
119C22⋊Q8×C47D411yescharacteristic
120C22⋊Q8×C47D411yescharacteristic
121C22⋊Q8×C47D411yescharacteristic
122#121×C47—22no—
123#121×C47—22no—
124#121×C47—22no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47D412yes—
130#121×C47D411yescharacteristic
131C4×Q8×C47—21no—
132C4×Q8×C47—21no—
133C4×Q8×C47—21no—
134C4×Q8×C47C2311yescharacteristic
135C4×Q8×C47C2311yescharacteristic
136C4×Q8×C47C2311yescharacteristic
137C4×D4×C47—22no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47—21no—
144C4×D4×C47—21no—
145C4×D4×C47—21no—
146C4×D4×C47D412yes—
147C4×D4×C47C2311yescharacteristic
148#117×C47—21no—
149#117×C47—21no—
150C2×C4⋊C4×C47—22no—
151C2×C42×C47C2311yescharacteristic
152#107×C47—21no—
153#107×C47—21no—
154#107×C47—21no—
155#106×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47—21no—
158C4⋊C8×C47—21no—
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162C4⋊C8×C47C2311yescharacteristic
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—22no—
167#102×C47—21no—
168#102×C47—22no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—21no—
172#102×C47—21no—
173C22⋊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—82no—
181C2×Q8×C47—22no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—81no—
186C2×Q8×C47—81no—
187C2×Q8×C47C2×D411yescharacteristic
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2×D411yescharacteristic
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—41no—
200C2×D4×C47C2×D411yescharacteristic
201C2×D4×C47C2×D412yes—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—22no—
207C22×C4×C47—41no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211SD16×C47—81no—
212SD16×C47—81no—
213SD16×C47—81no—
214SD16×C47—82no—
215D8×C47—81no—
216D8×C47—82no—
217M16×C47—81no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—81no—
225C4⋊C4×C47—22no—
226C4⋊C4×C47—22no—
227C4⋊C4×C47—22no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47C2×D412yes—
244C4⋊C4×C47C2×D411yescharacteristic
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—21no—
254C22⋊C4×C47—21no—
255C22⋊C4×C47—21no—
256C22⋊C4×C47—21no—
257C22⋊C4×C47—21no—
258C22⋊C4×C47—21no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—41no—
263C22⋊C4×C47—41no—
264C42×C47—22no—
265C42×C47—21no—
266C42×C47—21no—
267C42×C47—21no—
268C42×C47C2×D411yescharacteristic
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2411yescharacteristic
272C23×C47—21no—
273C23×C47—22no—
274C23×C47—41no—
275C23×C47#12011yescharacteristic
276Q8×C47—21no—
277Q8×C47—21no—
278Q8×C47—21no—
279Q8×C47—21no—
280Q8×C47—21no—
281Q8×C47—21no—
282Q8×C47—42no—
283Q8×C47—41no—
284Q8×C47—41no—
285Q8×C47—81no—
286Q8×C47—82no—
287D4×C47—21no—
288D4×C47—21no—
289D4×C47—42no—
290D4×C47—42no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—81no—
300D4×C47—82no—
301D4×C47—82no—
302D4×C47—82no—
303D4×C47—82no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—82no—
321C2×C4×C47—82no—
322C2×C4×C47—82no—
323C2×C4×C47—82no—
324C2×C4×C47—82no—
325C2×C4×C47#12011yescharacteristic
326C2×C4×C47#12011yescharacteristic
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C8×C47—41no—
332C8×C47—41no—
333C8×C47—41no—
334C8×C47—41no—
335C8×C47—41no—
336C8×C47—41no—
337#18964C4711yesmaximal, characteristic, direct product factor, Sylow
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—41no—
342C22×C47—42no—
343C22×C47—41no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—81no—
350C22×C47C2×#12011yescharacteristic
351C4×C47—21no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47—41no—
356C4×C47—41no—
357C4×C47—42no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—41no—
362C4×C47—41no—
363C4×C47—81no—
364C4×C47#57611yescharacteristic
365C4×C47#57711yescharacteristic
366C4×C47#57711yescharacteristic
367C4×C47#57811yescharacteristic
368#3554C2×C4711yescharacteristic, complemented
369#3254C2×C4711yescharacteristic, complemented
370#3247C2×C4711yescharacteristic, complemented
371#3207C2×C4711yescharacteristic, complemented
372#1637C2×C4711yescharacteristic, complemented
373#1636C2×C4711yescharacteristic, complemented
374#1631C2×C4711yescharacteristic, complemented
375#1630C2×C4711yescharacteristic, complemented
376#1627C2×C4711yescharacteristic, complemented
377#1626C2×C4711yescharacteristic, complemented
378#1621C2×C4711yescharacteristic, complemented
379#1620C2×C4711yescharacteristic, complemented
380#1547C2×C4711yescharacteristic, complemented
381#1495C2×C4711yescharacteristic, complemented
382#1481C2×C4711yescharacteristic, complemented
383C2×C47—41no—
384C2×C47—81no—
385C2×C47—82no—
386C2×C47—161no—
387C2×C47#301211yescharacteristic
388C2×C47#301311yescharacteristic
389C2×C47#302111yescharacteristic
390#562—22no—
391#559—21no—
392#559C22×C4711yescharacteristic
393#557C22×C4711yescharacteristic
394#554—21no—
395#550C22×C4711yescharacteristic
396D4×Q8C22×C4711yescharacteristic
397#548—21no—
398#547—21no—
399#542—21no—
400#542—21no—
401#540—21no—
402#539—22no—
403#536—21no—
404#533C22×C4711yescharacteristic
405#532C22×C4711yescharacteristic
406#532C22×C4711yescharacteristic
407#529C22×C4711yescharacteristic
408#493C22×C4711yescharacteristic
409#492C22×C4711yescharacteristic
410#487C22×C4711yescharacteristic
411#486C22×C4711yescharacteristic
412#478—21no—
413#477C22×C4711yescharacteristic
414#477C22×C4711yescharacteristic
415#477C22×C4711yescharacteristic
416#476C22×C4711yescharacteristic
417#474—21no—
418#468—21no—
419#468—21no—
420#466—21no—
421#465—21no—
422#463—21no—
423#463—22no—
424#461—21no—
425#460C22×C4711yescharacteristic
426#460C22×C4711yescharacteristic
427#460C22×C4711yescharacteristic
428#459C22×C4711yescharacteristic
429#449—22no—
430#431C22×C4711yescharacteristic
431#423C22×C4711yescharacteristic
432C2×C4⋊C8C22×C4711yescharacteristic
433#332C22×C4711yescharacteristic
434#332C22×C4711yescharacteristic
435#331C22×C4711yescharacteristic
436#331C22×C4711yescharacteristic
437Q8⋊C8C22×C4711yescharacteristic
438Q8⋊C8C22×C4711yescharacteristic
439Q8⋊C8C22×C4711yescharacteristic
440Q8⋊C8C22×C4711yescharacteristic
441Q8⋊C8C22×C4711yescharacteristic
442Q8⋊C8C22×C4711yescharacteristic
443D4⋊C8C22×C4711yescharacteristic
444D4⋊C8C22×C4711yescharacteristic
445C47#1896411yescharacteristic, direct product factor, Sylow
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C22×Q8—21no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×SD16—21no—
453C2×SD16—22no—
454C2×D8—22no—
455C2×D8—21no—
456C2×M16—21no—
457C22×C8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460C4⋊Q8D4×C4711yescharacteristic
461C4⋊Q8D4×C4711yescharacteristic
462C4⋊Q8C23×C4711yescharacteristic
463C4⋊Q8C23×C4711yescharacteristic
464#127—21no—
465#127C23×C4711yescharacteristic
466#127C23×C4711yescharacteristic
467#126—22no—
468#126—21no—
469#125—22no—
470#125—21no—
471#125—21no—
472#125D4×C4711yescharacteristic
473#124—22no—
474#124—22no—
475#124—21no—
476#124—21no—
477#124—21no—
478#124—21no—
479#124D4×C4711yescharacteristic
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486#123—21no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8D4×C4711yescharacteristic
495C22⋊Q8D4×C4711yescharacteristic
496C22⋊Q8D4×C4711yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121D4×C4711yescharacteristic
505#121D4×C4712yes—
506C4×Q8—21no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8C23×C4711yescharacteristic
510C4×Q8C23×C4711yescharacteristic
511C4×Q8C23×C4711yescharacteristic
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4D4×C4712yes—
522C4×D4C23×C4711yescharacteristic
523#117—21no—
524#117—21no—
525C2×C4⋊C4—22no—
526C2×C42C23×C4711yescharacteristic
527#107—21no—
528#107—21no—
529#107—21no—
530#106—21no—
531C4⋊C8—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C4711yescharacteristic
535C4⋊C8C23×C4711yescharacteristic
536C4⋊C8C23×C4711yescharacteristic
537C4⋊C8C23×C4711yescharacteristic
538#103—21no—
539#103—21no—
540#103—21no—
541#103—22no—
542#102—21no—
543#102—22no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548C22⋊C8—21no—
549C4×C8C23×C4711yescharacteristic
550C4×C8C23×C4711yescharacteristic
551#41—81no—
552#41—81no—
553#41—81no—
554#41—81no—
555#41—82no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—81no—
561C2×Q8—81no—
562C2×Q8C2×D4×C4711yescharacteristic
563C2×Q8C2×D4×C4711yescharacteristic
564C2×Q8C2×D4×C4711yescharacteristic
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4C2×D4×C4711yescharacteristic
576C2×D4C2×D4×C4712yes—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4C2×D4×C4711yescharacteristic
584C22×C4C2×D4×C4711yescharacteristic
585C22×C4C2×D4×C4711yescharacteristic
586SD16—81no—
587SD16—81no—
588SD16—81no—
589SD16—82no—
590D8—81no—
591D8—82no—
592M16—81no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—81no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
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⋊C4C2×D4×C4712yes—
619C4⋊C4C2×D4×C4711yescharacteristic
620C4⋊C4C2×D4×C4711yescharacteristic
621C4⋊C4C2×D4×C4711yescharacteristic
622C4⋊C4C2×D4×C4711yescharacteristic
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—21no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×D4×C4711yescharacteristic
644C42C2×D4×C4711yescharacteristic
645C42C2×D4×C4711yescharacteristic
646C42C24×C4711yescharacteristic
647C23—21no—
648C23—22no—
649C23—41no—
650C23#120×C4711yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8—21no—
656Q8—21no—
657Q8—42no—
658Q8—41no—
659Q8—41no—
660Q8—81no—
661Q8—82no—
662D4—21no—
663D4—21no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4#120×C4711yescharacteristic
701C2×C4#120×C4711yescharacteristic
702C2×C4#120×C4711yescharacteristic
703C2×C4C22×D4×C4711yescharacteristic
704C2×C4C22×D4×C4711yescharacteristic
705C2×C4C22×D4×C4711yescharacteristic
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22C2×#120×C4711yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—81no—
738C4C47×#57611yescharacteristic
739C4C47×#57711yescharacteristic
740C4C47×#57711yescharacteristic
741C4C47×#57811yescharacteristic
742C2—41no—
743C2—81no—
744C2—82no—
745C2—161no—
746C2C47×#301211yescharacteristic
747C2C47×#301311yescharacteristic
748C2C47×#302111yescharacteristic
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×#3554C2semidirect
2. C47×#3254C2semidirect
3. C47×#3247C2semidirect
4. C47×#3207C2semidirect
5. C47×#1637C2semidirect
6. C47×#1636C2semidirect
7. C47×#1631C2semidirect
8. C47×#1630C2semidirect
9. C47×#1627C2semidirect
10. C47×#1626C2semidirect
11. C47×#1621C2semidirect
12. C47×#1620C2semidirect
13. C47×#1547C2semidirect
14. C47×#1495C2semidirect
15. C47×#1481C2semidirect
337. #18964C47direct (N × H)
368. #3554C2×C47semidirect
369. #3254C2×C47semidirect
370. #3247C2×C47semidirect
371. #3207C2×C47semidirect
372. #1637C2×C47semidirect
373. #1636C2×C47semidirect
374. #1631C2×C47semidirect
375. #1630C2×C47semidirect
376. #1627C2×C47semidirect
377. #1626C2×C47semidirect
378. #1621C2×C47semidirect
379. #1620C2×C47semidirect
380. #1547C2×C47semidirect
381. #1495C2×C47semidirect
382. #1481C2×C47semidirect
445. C47#18964direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35542
C47×#32542
C47×#32472
C47×#32072
C47×#16372
C47×#16362
C47×#16312
C47×#16302
C47×#16272
C47×#16262
C47×#16212
C47×#16202
C47×#15472
C47×#14952
C47×#14812
#1896447