Finite Group Databasebeta

← C47×#18977 #26058675

Subgroups — C47×#18977 #26058675

Order 12032.

866 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3547C211yesmaximal, characteristic
2C47×#3254C211yesmaximal, characteristic, complemented
3C47×#3248C211yesmaximal, characteristic, complemented
4C47×#3231C211yesmaximal, characteristic, complemented
5C47×#1654C211yesmaximal, characteristic, complemented
6C47×#1651C211yesmaximal, characteristic, complemented
7C47×#1649C211yesmaximal, characteristic, complemented
8C47×#1647C211yesmaximal, characteristic, complemented
9C47×#1646C211yesmaximal, characteristic, complemented
10C47×#1646C211yesmaximal, characteristic, complemented
11C47×#1644C211yesmaximal, characteristic, complemented
12C47×#1643C211yesmaximal, characteristic, complemented
13C47×#1550C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1480C211yesmaximal, 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×#533C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#500C2211yescharacteristic
35C47×#498C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#487C2211yescharacteristic
38C47×#485—22no—
39C47×#479—21no—
40C47×#479—22no—
41C47×#477—21no—
42C47×#475C2211yescharacteristic
43C47×#474C2211yescharacteristic
44C47×#474C2211yescharacteristic
45C47×#474C2211yescharacteristic
46C47×#468—21no—
47C47×#468—21no—
48C47×#467—21no—
49C47×#465—21no—
50C47×#464—21no—
51C47×#462C2211yescharacteristic
52C47×#461C2211yescharacteristic
53C47×#461C2211yescharacteristic
54C47×#461C2211yescharacteristic
55C47×#460—21no—
56C47×#431C2211yescharacteristic
57C47×#423C2211yescharacteristic
58C2×C4⋊C8×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—
73C22×Q8×C47—21no—
74C2×Q16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×M16×C47—21no—
79C22×C8×C47—21no—
80C4⋊Q8×C47—22no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47D411yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86C4⋊Q8×C47C2311yescharacteristic
87#127×C47D411yescharacteristic
88#126×C47—22no—
89#126×C47—21no—
90#125×C47—22no—
91#125×C47—21no—
92#125×C47—21no—
93#125×C47—21no—
94#125×C47D411yescharacteristic
95#124×C47—22no—
96#124×C47—22no—
97#124×C47—22no—
98#124×C47—21no—
99#124×C47D411yescharacteristic
100#123×C47—22no—
101#123×C47—22no—
102#123×C47—22no—
103#123×C47—21no—
104#123×C47—22no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—22no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—22no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47D411yescharacteristic
116C22⋊Q8×C47D412yes—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47D411yescharacteristic
126#121×C47D411yescharacteristic
127#121×C47D411yescharacteristic
128C4×Q8×C47—21no—
129C4×Q8×C47—21no—
130C4×Q8×C47—21no—
131C4×Q8×C47D412yes—
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47—22no—
134C4×D4×C47—21no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47C2311yescharacteristic
139C4×D4×C47C2311yescharacteristic
140C4×D4×C47C2311yescharacteristic
141#117×C47—22no—
142#117×C47—21no—
143#117×C47—21no—
144#117×C47—21no—
145#117×C47—21no—
146#117×C47—21no—
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#107×C47—21no—
151#107×C47—21no—
152#107×C47—21no—
153#107×C47—22no—
154#106×C47—21no—
155#106×C47—22no—
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—22no—
165#103×C47—22no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—21no—
169#103×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—
180C2×Q8×C47—22no—
181C2×Q8×C47—21no—
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×D412yes—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47C2×D411yescharacteristic
197C2×D4×C47C2×D411yescharacteristic
198C2×D4×C47C2×D411yescharacteristic
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208Q16×C47—81no—
209SD16×C47—81no—
210SD16×C47—81no—
211SD16×C47—81no—
212M16×C47—81no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—81no—
220C4⋊C4×C47—22no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—22no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—22no—
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—41no—
239C4⋊C4×C47—41no—
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D411yescharacteristic
242C4⋊C4×C47C2×D411yescharacteristic
243C4⋊C4×C47C2×D411yescharacteristic
244C4⋊C4×C47C2×D412yes—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—21no—
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—21no—
260C22⋊C4×C47—41no—
261C42×C47—22no—
262C42×C47—22no—
263C42×C47—21no—
264C42×C47—41no—
265C42×C47C2×D411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2411yescharacteristic
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47#12011yescharacteristic
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—42no—
276Q8×C47—41no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—81no—
283Q8×C47—82no—
284D4×C47—21no—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—21no—
288D4×C47—21no—
289D4×C47—21no—
290D4×C47—81no—
291D4×C47—81no—
292D4×C47—81no—
293D4×C47—81no—
294D4×C47—81no—
295D4×C47—82no—
296D4×C47—82no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—22no—
307C2×C4×C47—21no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—82no—
318C2×C4×C47—82no—
319C2×C4×C47—82no—
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47#12011yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C8×C47—41no—
327C8×C47—41no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47—41no—
331C8×C47—41no—
332#18977C4711yesmaximal, characteristic, direct product factor, Sylow
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47C2×#12011yescharacteristic
346C4×C47—21no—
347C4×C47—21no—
348C4×C47—21no—
349C4×C47—21no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—42no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—41no—
356C4×C47—42no—
357C4×C47—81no—
358C4×C47—81no—
359C4×C47#57611yescharacteristic
360C4×C47#57711yescharacteristic
361C4×C47#57711yescharacteristic
362C4×C47#57811yescharacteristic
363#3547C2×C4711yescharacteristic
364#3254C2×C4711yescharacteristic, complemented
365#3248C2×C4711yescharacteristic, complemented
366#3231C2×C4711yescharacteristic, complemented
367#1654C2×C4711yescharacteristic, complemented
368#1651C2×C4711yescharacteristic, complemented
369#1649C2×C4711yescharacteristic, complemented
370#1647C2×C4711yescharacteristic, complemented
371#1646C2×C4711yescharacteristic, complemented
372#1646C2×C4711yescharacteristic, complemented
373#1644C2×C4711yescharacteristic, complemented
374#1643C2×C4711yescharacteristic, complemented
375#1550C2×C4711yescharacteristic, complemented
376#1495C2×C4711yescharacteristic, complemented
377#1480C2×C4711yescharacteristic, complemented
378C2×C47—41no—
379C2×C47—81no—
380C2×C47—81no—
381C2×C47—81no—
382C2×C47#301211yescharacteristic
383C2×C47#301311yescharacteristic
384C2×C47#302211yescharacteristic
385#562—22no—
386#555—21no—
387#555C22×C4711yescharacteristic
388#554C22×C4711yescharacteristic
389#553—21no—
390#552—21no—
391D4×Q8C22×C4711yescharacteristic
392#548—21no—
393#547C22×C4711yescharacteristic
394#544—21no—
395#542—22no—
396#540—21no—
397#537—21no—
398#536—21no—
399#533C22×C4711yescharacteristic
400#533C22×C4711yescharacteristic
401#532C22×C4711yescharacteristic
402#529C22×C4711yescharacteristic
403#500C22×C4711yescharacteristic
404#498C22×C4711yescharacteristic
405#487C22×C4711yescharacteristic
406#487C22×C4711yescharacteristic
407#485—22no—
408#479—21no—
409#479—22no—
410#477—21no—
411#475C22×C4711yescharacteristic
412#474C22×C4711yescharacteristic
413#474C22×C4711yescharacteristic
414#474C22×C4711yescharacteristic
415#468—21no—
416#468—21no—
417#467—21no—
418#465—21no—
419#464—21no—
420#462C22×C4711yescharacteristic
421#461C22×C4711yescharacteristic
422#461C22×C4711yescharacteristic
423#461C22×C4711yescharacteristic
424#460—21no—
425#431C22×C4711yescharacteristic
426#423C22×C4711yescharacteristic
427C2×C4⋊C8C22×C4711yescharacteristic
428#333C22×C4711yescharacteristic
429#333C22×C4711yescharacteristic
430#332C22×C4711yescharacteristic
431#332C22×C4711yescharacteristic
432Q8⋊C8C22×C4711yescharacteristic
433Q8⋊C8C22×C4711yescharacteristic
434D4⋊C8C22×C4711yescharacteristic
435D4⋊C8C22×C4711yescharacteristic
436D4⋊C8C22×C4711yescharacteristic
437D4⋊C8C22×C4711yescharacteristic
438D4⋊C8C22×C4711yescharacteristic
439D4⋊C8C22×C4711yescharacteristic
440C47#1897711yescharacteristic, direct product factor, Sylow
441C2×#41—21no—
442C2×#41—21no—
443C22×Q8—21no—
444C2×Q16—21no—
445C2×SD16—21no—
446C2×SD16—21no—
447C2×SD16—21no—
448C2×M16—21no—
449C22×C8—21no—
450C4⋊Q8—22no—
451C4⋊Q8—21no—
452C4⋊Q8D4×C4711yescharacteristic
453C4⋊Q8C23×C4711yescharacteristic
454C4⋊Q8C23×C4711yescharacteristic
455C4⋊Q8C23×C4711yescharacteristic
456C4⋊Q8C23×C4711yescharacteristic
457#127D4×C4711yescharacteristic
458#126—22no—
459#126—21no—
460#125—22no—
461#125—21no—
462#125—21no—
463#125—21no—
464#125D4×C4711yescharacteristic
465#124—22no—
466#124—22no—
467#124—22no—
468#124—21no—
469#124D4×C4711yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473#123—21no—
474#123—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8D4×C4711yescharacteristic
486C22⋊Q8D4×C4712yes—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121D4×C4711yescharacteristic
496#121D4×C4711yescharacteristic
497#121D4×C4711yescharacteristic
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8D4×C4712yes—
502C4×Q8C23×C4711yescharacteristic
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4C23×C4711yescharacteristic
509C4×D4C23×C4711yescharacteristic
510C4×D4C23×C4711yescharacteristic
511#117—22no—
512#117—21no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C42C23×C4711yescharacteristic
520#107—21no—
521#107—21no—
522#107—21no—
523#107—22no—
524#106—21no—
525#106—22no—
526C4⋊C8—21no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8C23×C4711yescharacteristic
530C4⋊C8C23×C4711yescharacteristic
531C4⋊C8C23×C4711yescharacteristic
532C4⋊C8C23×C4711yescharacteristic
533#103—21no—
534#103—22no—
535#103—22no—
536#103—21no—
537#103—21no—
538#103—21no—
539#103—21no—
540#102—21no—
541#102—21no—
542#102—21no—
543C22⋊C8—21no—
544C4×C8C23×C4711yescharacteristic
545C4×C8C23×C4711yescharacteristic
546#41—81no—
547#41—81no—
548#41—81no—
549#41—81no—
550C2×Q8—22no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—81no—
556C2×Q8—81no—
557C2×Q8C2×D4×C4711yescharacteristic
558C2×Q8C2×D4×C4712yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C2×D4×C4711yescharacteristic
567C2×D4C2×D4×C4711yescharacteristic
568C2×D4C2×D4×C4711yescharacteristic
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4C2×D4×C4711yescharacteristic
576C22×C4C2×D4×C4711yescharacteristic
577C22×C4C2×D4×C4711yescharacteristic
578Q16—81no—
579SD16—81no—
580SD16—81no—
581SD16—81no—
582M16—81no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—81no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4C2×D4×C4711yescharacteristic
611C4⋊C4C2×D4×C4711yescharacteristic
612C4⋊C4C2×D4×C4711yescharacteristic
613C4⋊C4C2×D4×C4711yescharacteristic
614C4⋊C4C2×D4×C4712yes—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—41no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—41no—
635C42C2×D4×C4711yescharacteristic
636C42C2×D4×C4711yescharacteristic
637C42C2×D4×C4711yescharacteristic
638C42C24×C4711yescharacteristic
639C23—21no—
640C23—21no—
641C23—21no—
642C23#120×C4711yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—42no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—81no—
653Q8—82no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—81no—
661D4—81no—
662D4—81no—
663D4—81no—
664D4—81no—
665D4—82no—
666D4—82no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4#120×C4711yescharacteristic
691C2×C4#120×C4711yescharacteristic
692C2×C4#120×C4711yescharacteristic
693C2×C4C22×D4×C4711yescharacteristic
694C2×C4C22×D4×C4711yescharacteristic
695C2×C4C22×D4×C4711yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22C2×#120×C4711yescharacteristic
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4C47×#57611yescharacteristic
729C4C47×#57711yescharacteristic
730C4C47×#57711yescharacteristic
731C4C47×#57811yescharacteristic
732C2—41no—
733C2—81no—
734C2—81no—
735C2—81no—
736C2C47×#301211yescharacteristic
737C2C47×#301311yescharacteristic
738C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3547C2
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
2. C47×#3254C2semidirect
3. C47×#3248C2semidirect
4. C47×#3231C2semidirect
5. C47×#1654C2semidirect
6. C47×#1651C2semidirect
7. C47×#1649C2semidirect
8. C47×#1647C2semidirect
9. C47×#1646C2semidirect
10. C47×#1646C2semidirect
11. C47×#1644C2semidirect
12. C47×#1643C2semidirect
13. C47×#1550C2semidirect
14. C47×#1495C2semidirect
15. C47×#1480C2semidirect
332. #18977C47direct (N × H)
364. #3254C2×C47semidirect
365. #3248C2×C47semidirect
366. #3231C2×C47semidirect
367. #1654C2×C47semidirect
368. #1651C2×C47semidirect
369. #1649C2×C47semidirect
370. #1647C2×C47semidirect
371. #1646C2×C47semidirect
372. #1646C2×C47semidirect
373. #1644C2×C47semidirect
374. #1643C2×C47semidirect
375. #1550C2×C47semidirect
376. #1495C2×C47semidirect
377. #1480C2×C47semidirect
440. C47#18977direct (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×#32542
C47×#32482
C47×#32312
C47×#16542
C47×#16512
C47×#16492
C47×#16472
C47×#16462
C47×#16442
C47×#16432
C47×#15502
C47×#14952
C47×#14802
#1897747