Finite Group Databasebeta

← C47×#18741 #26058439

Subgroups — C47×#18741 #26058439

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3547C211yesmaximal, characteristic
2C47×#3246C211yesmaximal, characteristic, complemented
3C47×#3233C211yesmaximal, characteristic, complemented
4C47×#3185C211yesmaximal, characteristic, complemented
5C47×#1654C211yesmaximal, characteristic, complemented
6C47×#1651C211yesmaximal, characteristic, complemented
7C47×#1646C211yesmaximal, characteristic, complemented
8C47×#1643C211yesmaximal, characteristic, complemented
9C47×#1637C211yesmaximal, characteristic, complemented
10C47×#1635C211yesmaximal, characteristic, complemented
11C47×#1634C211yesmaximal, characteristic, complemented
12C47×#1632C211yesmaximal, 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×#533C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#499—21no—
35C47×#498C2211yescharacteristic
36C47×#494C2211yescharacteristic
37C47×#488—21no—
38C47×#487C2211yescharacteristic
39C47×#487C2211yescharacteristic
40C47×#485—21no—
41C47×#482—21no—
42C47×#477C2211yescharacteristic
43C47×#476C2211yescharacteristic
44C47×#476C2211yescharacteristic
45C47×#476C2211yescharacteristic
46C47×#475—21no—
47C47×#475C2211yescharacteristic
48C47×#474C2211yescharacteristic
49C47×#470—22no—
50C47×#465—21no—
51C47×#465—21no—
52C47×#461C2211yescharacteristic
53C47×#461C2211yescharacteristic
54C47×#460—21no—
55C47×#441—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—
73C22×Q8×C47—21no—
74C2×Q16×C47—22no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×M16×C47—21no—
78C22×C8×C47—21no—
79C4⋊Q8×C47—22no—
80C4⋊Q8×C47—21no—
81C4⋊Q8×C47D411yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47D411yescharacteristic
87#126×C47—22no—
88#126×C47—21no—
89#125×C47—22no—
90#125×C47—21no—
91#125×C47—21no—
92#125×C47—21no—
93#125×C47D411yescharacteristic
94#124×C47—22no—
95#124×C47—22no—
96#124×C47—22no—
97#124×C47—21no—
98#124×C47D411yescharacteristic
99#123×C47—22no—
100#123×C47—22no—
101#123×C47—22no—
102#123×C47—21no—
103#123×C47—22no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—22no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—21no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47D412yes—
115C22⋊Q8×C47D411yescharacteristic
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47D411yescharacteristic
125#121×C47D411yescharacteristic
126#121×C47D411yescharacteristic
127C4×Q8×C47—21no—
128C4×Q8×C47—21no—
129C4×Q8×C47—21no—
130C4×Q8×C47D412yes—
131C4×Q8×C47C2311yescharacteristic
132C4×D4×C47—22no—
133C4×D4×C47—21no—
134C4×D4×C47—21no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137C4×D4×C47C2311yescharacteristic
138C4×D4×C47C2311yescharacteristic
139C4×D4×C47C2311yescharacteristic
140#117×C47—22no—
141#117×C47—21no—
142#117×C47—21no—
143#117×C47—21no—
144#117×C47—21no—
145#117×C47—21no—
146C2×C4⋊C4×C47—21no—
147C2×C4⋊C4×C47—21no—
148C2×C42×C47C2311yescharacteristic
149#107×C47—21no—
150#107×C47—21no—
151#106×C47—21no—
152#106×C47—21no—
153#106×C47—22no—
154#106×C47—21no—
155#106×C47—21no—
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#103×C47—21no—
165#103×C47—21no—
166#103×C47—22no—
167#102×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
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—
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—44no—
209SD16×C47—81no—
210SD16×C47—81no—
211M16×C47—42no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—81no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—22no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
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—41no—
238C4⋊C4×C47—41no—
239C4⋊C4×C47C2×D411yescharacteristic
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D412yes—
242C4⋊C4×C47C2×D411yescharacteristic
243C4⋊C4×C47C2×D411yescharacteristic
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—21no—
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—41no—
260C42×C47—22no—
261C42×C47—22no—
262C42×C47—21no—
263C42×C47—41no—
264C42×C47C2×D411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2411yescharacteristic
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47#12011yescharacteristic
272Q8×C47—21no—
273Q8×C47—21no—
274Q8×C47—42no—
275Q8×C47—42no—
276Q8×C47—41no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—81no—
281Q8×C47—82no—
282D4×C47—21no—
283D4×C47—21no—
284D4×C47—21no—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—21no—
288D4×C47—81no—
289D4×C47—81no—
290D4×C47—81no—
291D4×C47—81no—
292D4×C47—81no—
293D4×C47—82no—
294D4×C47—82no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—21no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
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—82no—
316C2×C4×C47—82no—
317C2×C4×C47—82no—
318C2×C4×C47#12011yescharacteristic
319C2×C4×C47#12011yescharacteristic
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C8×C47—22no—
325C8×C47—41no—
326C8×C47—41no—
327C8×C47—41no—
328C8×C47—41no—
329C8×C47—41no—
330#18741C4711yesmaximal, characteristic, direct product factor, Sylow
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47C2×#12011yescharacteristic
344C4×C47—21no—
345C4×C47—21no—
346C4×C47—21no—
347C4×C47—21no—
348C4×C47—41no—
349C4×C47—41no—
350C4×C47—42no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—42no—
355C4×C47—81no—
356C4×C47—81no—
357C4×C47#57711yescharacteristic
358C4×C47#57711yescharacteristic
359C4×C47#57711yescharacteristic
360C4×C47#57811yescharacteristic
361#3547C2×C4711yescharacteristic
362#3246C2×C4711yescharacteristic, complemented
363#3233C2×C4711yescharacteristic, complemented
364#3185C2×C4711yescharacteristic, complemented
365#1654C2×C4711yescharacteristic, complemented
366#1651C2×C4711yescharacteristic, complemented
367#1646C2×C4711yescharacteristic, complemented
368#1643C2×C4711yescharacteristic, complemented
369#1637C2×C4711yescharacteristic, complemented
370#1635C2×C4711yescharacteristic, complemented
371#1634C2×C4711yescharacteristic, complemented
372#1632C2×C4711yescharacteristic, complemented
373#1542C2×C4711yescharacteristic, complemented
374#1484C2×C4711yescharacteristic, complemented
375#1483C2×C4711yescharacteristic, complemented
376C2×C47—41no—
377C2×C47—81no—
378C2×C47—81no—
379C2×C47—81no—
380C2×C47#300911yescharacteristic
381C2×C47#301311yescharacteristic
382C2×C47#301811yescharacteristic
383#562—22no—
384#555—21no—
385#555C22×C4711yescharacteristic
386#554C22×C4711yescharacteristic
387#553—21no—
388#552—21no—
389D4×Q8C22×C4711yescharacteristic
390#548—21no—
391#547C22×C4711yescharacteristic
392#544—21no—
393#542—22no—
394#540—21no—
395#537—21no—
396#536—21no—
397#533C22×C4711yescharacteristic
398#533C22×C4711yescharacteristic
399#532C22×C4711yescharacteristic
400#529C22×C4711yescharacteristic
401#499—21no—
402#498C22×C4711yescharacteristic
403#494C22×C4711yescharacteristic
404#488—21no—
405#487C22×C4711yescharacteristic
406#487C22×C4711yescharacteristic
407#485—21no—
408#482—21no—
409#477C22×C4711yescharacteristic
410#476C22×C4711yescharacteristic
411#476C22×C4711yescharacteristic
412#476C22×C4711yescharacteristic
413#475—21no—
414#475C22×C4711yescharacteristic
415#474C22×C4711yescharacteristic
416#470—22no—
417#465—21no—
418#465—21no—
419#461C22×C4711yescharacteristic
420#461C22×C4711yescharacteristic
421#460—21no—
422#441—22no—
423#431C22×C4711yescharacteristic
424C2×C4⋊C8C22×C4711yescharacteristic
425C4×M16C22×C4711yescharacteristic
426#333C22×C4711yescharacteristic
427#333C22×C4711yescharacteristic
428#332C22×C4711yescharacteristic
429#332C22×C4711yescharacteristic
430Q8⋊C8C22×C4711yescharacteristic
431Q8⋊C8C22×C4711yescharacteristic
432D4⋊C8C22×C4711yescharacteristic
433D4⋊C8C22×C4711yescharacteristic
434D4⋊C8C22×C4711yescharacteristic
435D4⋊C8C22×C4711yescharacteristic
436D4⋊C8C22×C4711yescharacteristic
437D4⋊C8C22×C4711yescharacteristic
438C47#1874111yescharacteristic, direct product factor, Sylow
439C2×#41—21no—
440C2×#41—21no—
441C22×Q8—21no—
442C2×Q16—22no—
443C2×SD16—21no—
444C2×SD16—21no—
445C2×M16—21no—
446C22×C8—21no—
447C4⋊Q8—22no—
448C4⋊Q8—21no—
449C4⋊Q8D4×C4711yescharacteristic
450C4⋊Q8C23×C4711yescharacteristic
451C4⋊Q8C23×C4711yescharacteristic
452C4⋊Q8C23×C4711yescharacteristic
453C4⋊Q8C23×C4711yescharacteristic
454#127D4×C4711yescharacteristic
455#126—22no—
456#126—21no—
457#125—22no—
458#125—21no—
459#125—21no—
460#125—21no—
461#125D4×C4711yescharacteristic
462#124—22no—
463#124—22no—
464#124—22no—
465#124—21no—
466#124D4×C4711yescharacteristic
467#123—22no—
468#123—22no—
469#123—22no—
470#123—21no—
471#123—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—21no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—22no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8D4×C4711yescharacteristic
483C22⋊Q8D4×C4712yes—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121D4×C4711yescharacteristic
493#121D4×C4711yescharacteristic
494#121D4×C4711yescharacteristic
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8D4×C4712yes—
499C4×Q8C23×C4711yescharacteristic
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4C23×C4711yescharacteristic
506C4×D4C23×C4711yescharacteristic
507C4×D4C23×C4711yescharacteristic
508#117—22no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C42C23×C4711yescharacteristic
517#107—21no—
518#107—21no—
519#106—22no—
520#106—21no—
521#106—21no—
522#106—21no—
523#106—21no—
524C4⋊C8—21no—
525C4⋊C8C23×C4711yescharacteristic
526C4⋊C8C23×C4711yescharacteristic
527C4⋊C8C23×C4711yescharacteristic
528C4⋊C8C23×C4711yescharacteristic
529#103—22no—
530#103—21no—
531#103—21no—
532#103—22no—
533#103—21no—
534#103—21no—
535#102—21no—
536#102—21no—
537#102—21no—
538#102—21no—
539C22⋊C8—21no—
540#97—21no—
541C4×C8—21no—
542C4×C8C23×C4711yescharacteristic
543C4×C8C23×C4711yescharacteristic
544#41—81no—
545#41—81no—
546#41—81no—
547#41—81no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—81no—
554C2×Q8—81no—
555C2×Q8C2×D4×C4711yescharacteristic
556C2×Q8C2×D4×C4712yes—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4C2×D4×C4711yescharacteristic
565C2×D4C2×D4×C4711yescharacteristic
566C2×D4C2×D4×C4711yescharacteristic
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4C2×D4×C4711yescharacteristic
574C22×C4C2×D4×C4711yescharacteristic
575C22×C4C2×D4×C4711yescharacteristic
576Q16—44no—
577SD16—81no—
578SD16—81no—
579M16—42no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—81no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4C2×D4×C4711yescharacteristic
608C4⋊C4C2×D4×C4711yescharacteristic
609C4⋊C4C2×D4×C4712yes—
610C4⋊C4C2×D4×C4711yescharacteristic
611C4⋊C4C2×D4×C4711yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—41no—
628C42—22no—
629C42—22no—
630C42—21no—
631C42—41no—
632C42C2×D4×C4711yescharacteristic
633C42C2×D4×C4711yescharacteristic
634C42C2×D4×C4711yescharacteristic
635C42C24×C4711yescharacteristic
636C23—21no—
637C23—21no—
638C23—21no—
639C23#120×C4711yescharacteristic
640Q8—21no—
641Q8—21no—
642Q8—42no—
643Q8—42no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—81no—
649Q8—82no—
650D4—21no—
651D4—21no—
652D4—21no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—81no—
657D4—81no—
658D4—81no—
659D4—81no—
660D4—81no—
661D4—82no—
662D4—82no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4#120×C4711yescharacteristic
687C2×C4#120×C4711yescharacteristic
688C2×C4#120×C4711yescharacteristic
689C2×C4C22×D4×C4711yescharacteristic
690C2×C4C22×D4×C4711yescharacteristic
691C2×C4C22×D4×C4711yescharacteristic
692C8—22no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22C2×#120×C4711yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—81no—
723C4—81no—
724C4C47×#57711yescharacteristic
725C4C47×#57711yescharacteristic
726C4C47×#57711yescharacteristic
727C4C47×#57811yescharacteristic
728C2—41no—
729C2—81no—
730C2—81no—
731C2—81no—
732C2C47×#300911yescharacteristic
733C2C47×#301311yescharacteristic
734C2C47×#301811yescharacteristic
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×#3246C2semidirect
3. C47×#3233C2semidirect
4. C47×#3185C2semidirect
5. C47×#1654C2semidirect
6. C47×#1651C2semidirect
7. C47×#1646C2semidirect
8. C47×#1643C2semidirect
9. C47×#1637C2semidirect
10. C47×#1635C2semidirect
11. C47×#1634C2semidirect
12. C47×#1632C2semidirect
13. C47×#1542C2semidirect
14. C47×#1484C2semidirect
15. C47×#1483C2semidirect
330. #18741C47direct (N × H)
362. #3246C2×C47semidirect
363. #3233C2×C47semidirect
364. #3185C2×C47semidirect
365. #1654C2×C47semidirect
366. #1651C2×C47semidirect
367. #1646C2×C47semidirect
368. #1643C2×C47semidirect
369. #1637C2×C47semidirect
370. #1635C2×C47semidirect
371. #1634C2×C47semidirect
372. #1632C2×C47semidirect
373. #1542C2×C47semidirect
374. #1484C2×C47semidirect
375. #1483C2×C47semidirect
438. C47#18741direct (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×#32462
C47×#32332
C47×#31852
C47×#16542
C47×#16512
C47×#16462
C47×#16432
C47×#16372
C47×#16352
C47×#16342
C47×#16322
C47×#15422
C47×#14842
C47×#14832
#1874147