Finite Group Databasebeta

← C47×#18974 #26058672

Subgroups — C47×#18974 #26058672

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3546C211yesmaximal, characteristic
2C47×#3254C211yesmaximal, characteristic, complemented
3C47×#3248C211yesmaximal, characteristic, complemented
4C47×#3228C211yesmaximal, characteristic, complemented
5C47×#1654C211yesmaximal, characteristic, complemented
6C47×#1652C211yesmaximal, characteristic, complemented
7C47×#1650C211yesmaximal, characteristic, complemented
8C47×#1647C211yesmaximal, characteristic, complemented
9C47×#1642C211yesmaximal, characteristic, complemented
10C47×#1641C211yesmaximal, characteristic, complemented
11C47×#1639C211yesmaximal, characteristic, complemented
12C47×#1639C211yesmaximal, characteristic, complemented
13C47×#1547C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1480C211yesmaximal, characteristic, complemented
16C47×#560—22no—
17C47×#556C2211yescharacteristic
18C47×#553—21no—
19C47×#550—21no—
20C47×#550C2211yescharacteristic
21C47×#547C2211yescharacteristic
22C47×#546—21no—
23C47×#546—21no—
24D42×C47C2211yescharacteristic
25C47×#542—21no—
26C47×#538—22no—
27C47×#537—21no—
28C47×#535—21no—
29C47×#535—21no—
30C47×#533C2211yescharacteristic, complemented
31C47×#532C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#500C2211yescharacteristic, complemented
35C47×#498C2211yescharacteristic, complemented
36C47×#486C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#482—22no—
39C47×#479—21no—
40C47×#478—22no—
41C47×#477—21no—
42C47×#475C2211yescharacteristic, complemented
43C47×#474C2211yescharacteristic
44C47×#474C2211yescharacteristic
45C47×#474C2211yescharacteristic, complemented
46C47×#468—21no—
47C47×#468—21no—
48C47×#467—21no—
49C47×#465—21no—
50C47×#464—21no—
51C47×#462C2211yescharacteristic, complemented
52C47×#461C2211yescharacteristic
53C47×#461C2211yescharacteristic
54C47×#461C2211yescharacteristic, complemented
55C47×#460—21no—
56C47×#431C2211yescharacteristic, complemented
57C47×#423C2211yescharacteristic, complemented
58C2×C4⋊C8×C47C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C2×Q16×C47—21no—
78C2×SD16×C47—21no—
79C2×SD16×C47—21no—
80C2×SD16×C47—21no—
81C2×M16×C47—21no—
82C22×C8×C47—21no—
83C4⋊Q8×C47D411yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86C4⋊Q8×C47C2311yescharacteristic
87#127×C47—22no—
88#127×C47—21no—
89#127×C47D411yescharacteristic
90#127×C47C2311yescharacteristic
91#126×C47—22no—
92#126×C47—22no—
93#126×C47—21no—
94#125×C47—21no—
95#125×C47D411yescharacteristic
96#124×C47—22no—
97#124×C47—21no—
98#124×C47—21no—
99#124×C47—21no—
100#124×C47D411yescharacteristic
101#123×C47—22no—
102#123×C47—22no—
103#123×C47—21no—
104#123×C47—22no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47D411yescharacteristic
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47—22no—
116#121×C47—21no—
117#121×C47—22no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47D411yescharacteristic
124#121×C47D411yescharacteristic
125#121×C47D411yescharacteristic
126#121×C47D412yes—
127#120×C47—22no—
128#120×C47—22no—
129#120×C47—22no—
130#120×C47—22no—
131C4×Q8×C47—21no—
132C4×Q8×C47—21no—
133C4×Q8×C47—21no—
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×C47D412yes—
141C4×D4×C47C2311yescharacteristic
142C4×D4×C47C2311yescharacteristic
143C4×D4×C47C2311yescharacteristic
144#117×C47—21no—
145#117×C47—21no—
146#117×C47—21no—
147C2×C4⋊C4×C47—21no—
148C2×C22⋊C4×C47—22no—
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—21no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—22no—
172#102×C47—22no—
173C22⋊C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176C24×C47—22no—
177#41×C47—81no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—81no—
181#41×C47—81no—
182#41×C47—81no—
183#41×C47—81no—
184#41×C47—81no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47C2×D411yescharacteristic
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—22no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47C2×D411yescharacteristic
208C2×D4×C47C2×D411yescharacteristic
209C2×D4×C47C2×D411yescharacteristic
210C2×D4×C47C2×D412yes—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—22no—
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220Q16×C47—81no—
221SD16×C47—81no—
222SD16×C47—81no—
223SD16×C47—81no—
224M16×C47—81no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—81no—
232C4⋊C4×C47—22no—
233C4⋊C4×C47—22no—
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×C47—21no—
244C4⋊C4×C47—41no—
245C4⋊C4×C47—41no—
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C4⋊C4×C47C2×D411yescharacteristic
249C4⋊C4×C47C2×D411yescharacteristic
250C4⋊C4×C47C2×D412yes—
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—22no—
263C22⋊C4×C47—22no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—21no—
267C22⋊C4×C47—41no—
268C42×C47—22no—
269C42×C47—21no—
270C42×C47—41no—
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2×D411yescharacteristic
274C42×C47C2411yescharacteristic
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—22no—
278C23×C47—21no—
279C23×C47—82no—
280C23×C47—82no—
281C23×C47—82no—
282C23×C47#12011yescharacteristic
283Q8×C47—21no—
284Q8×C47—21no—
285Q8×C47—41no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—41no—
289Q8×C47—41no—
290Q8×C47—41no—
291Q8×C47—81no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—21no—
297D4×C47—21no—
298D4×C47—42no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—81no—
304D4×C47—81no—
305D4×C47—81no—
306D4×C47—81no—
307D4×C47—81no—
308D4×C47—82no—
309D4×C47—82no—
310D4×C47—82no—
311D4×C47—82no—
312D4×C47—82no—
313D4×C47—82no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—22no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—82no—
334C2×C4×C47—82no—
335C2×C4×C47—82no—
336C2×C4×C47#12011yescharacteristic
337C2×C4×C47#12011yescharacteristic
338C2×C4×C47#12011yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C8×C47—41no—
343C8×C47—41no—
344C8×C47—41no—
345C8×C47—41no—
346C8×C47—41no—
347C8×C47—41no—
348#18974C4711yesmaximal, characteristic, direct product factor, Sylow
349C22×C47—21no—
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—42no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—164no—
365C22×C47C2×#12011yescharacteristic
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47—41no—
374C4×C47—42no—
375C4×C47—41no—
376C4×C47—81no—
377C4×C47—81no—
378C4×C47#57611yescharacteristic
379C4×C47#57611yescharacteristic
380C4×C47#57711yescharacteristic
381C4×C47#57711yescharacteristic
382#3546C2×C4711yescharacteristic
383#3254C2×C4711yescharacteristic, complemented
384#3248C2×C4711yescharacteristic, complemented
385#3228C2×C4711yescharacteristic, complemented
386#1654C2×C4711yescharacteristic, complemented
387#1652C2×C4711yescharacteristic, complemented
388#1650C2×C4711yescharacteristic, complemented
389#1647C2×C4711yescharacteristic, complemented
390#1642C2×C4711yescharacteristic, complemented
391#1641C2×C4711yescharacteristic, complemented
392#1639C2×C4711yescharacteristic, complemented
393#1639C2×C4711yescharacteristic, complemented
394#1547C2×C4711yescharacteristic, complemented
395#1495C2×C4711yescharacteristic, complemented
396#1480C2×C4711yescharacteristic, complemented
397C2×C47—41no—
398C2×C47—81no—
399C2×C47—82no—
400C2×C47—81no—
401C2×C47—81no—
402C2×C47#301211yescharacteristic
403C2×C47#301211yescharacteristic
404C2×C47#302211yescharacteristic
405#560—22no—
406#556C22×C4711yescharacteristic
407#553—21no—
408#550—21no—
409#550C22×C4711yescharacteristic
410#547C22×C4711yescharacteristic
411#546—21no—
412#546—21no—
413D42C22×C4711yescharacteristic
414#542—21no—
415#538—22no—
416#537—21no—
417#535—21no—
418#535—21no—
419#533C22×C4711yescharacteristic, complemented
420#532C22×C4711yescharacteristic
421#532C22×C4711yescharacteristic
422#529C22×C4711yescharacteristic
423#500C22×C4711yescharacteristic, complemented
424#498C22×C4711yescharacteristic, complemented
425#486C22×C4711yescharacteristic
426#486C22×C4711yescharacteristic
427#482—22no—
428#479—21no—
429#478—22no—
430#477—21no—
431#475C22×C4711yescharacteristic, complemented
432#474C22×C4711yescharacteristic
433#474C22×C4711yescharacteristic
434#474C22×C4711yescharacteristic, complemented
435#468—21no—
436#468—21no—
437#467—21no—
438#465—21no—
439#464—21no—
440#462C22×C4711yescharacteristic, complemented
441#461C22×C4711yescharacteristic
442#461C22×C4711yescharacteristic
443#461C22×C4711yescharacteristic, complemented
444#460—21no—
445#431C22×C4711yescharacteristic, complemented
446#423C22×C4711yescharacteristic, complemented
447C2×C4⋊C8C22×C4711yescharacteristic, complemented
448#332C22×C4711yescharacteristic, complemented
449#332C22×C4711yescharacteristic, complemented
450#331C22×C4711yescharacteristic
451#331C22×C4711yescharacteristic
452Q8⋊C8C22×C4711yescharacteristic, complemented
453Q8⋊C8C22×C4711yescharacteristic, complemented
454D4⋊C8C22×C4711yescharacteristic
455D4⋊C8C22×C4711yescharacteristic
456D4⋊C8C22×C4711yescharacteristic
457D4⋊C8C22×C4711yescharacteristic
458D4⋊C8C22×C4711yescharacteristic, complemented
459D4⋊C8C22×C4711yescharacteristic, complemented
460C47#1897411yescharacteristic, direct product factor, Sylow
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C4711yescharacteristic
474C4⋊Q8C23×C4711yescharacteristic
475C4⋊Q8C23×C4711yescharacteristic
476C4⋊Q8C23×C4711yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C4711yescharacteristic
480#127C23×C4711yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C4711yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C4711yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C4711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C4711yescharacteristic
514#121D4×C4711yescharacteristic
515#121D4×C4711yescharacteristic
516#121D4×C4712yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C4711yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C4712yes—
531C4×D4C23×C4711yescharacteristic
532C4×D4C23×C4711yescharacteristic
533C4×D4C23×C4711yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C4711yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C4711yescharacteristic
550C4⋊C8C23×C4711yescharacteristic
551C4⋊C8C23×C4711yescharacteristic
552C4⋊C8C23×C4711yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C4711yescharacteristic
565C4×C8C23×C4711yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C4711yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C4711yescharacteristic
598C2×D4C2×D4×C4711yescharacteristic
599C2×D4C2×D4×C4711yescharacteristic
600C2×D4C2×D4×C4712yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C4711yescharacteristic
608C22×C4C2×D4×C4711yescharacteristic
609C22×C4C2×D4×C4711yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C4711yescharacteristic
637C4⋊C4C2×D4×C4711yescharacteristic
638C4⋊C4C2×D4×C4711yescharacteristic
639C4⋊C4C2×D4×C4711yescharacteristic
640C4⋊C4C2×D4×C4712yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C4711yescharacteristic
662C42C2×D4×C4711yescharacteristic
663C42C2×D4×C4711yescharacteristic
664C42C24×C4711yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C4711yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C4711yescharacteristic
727C2×C4#120×C4711yescharacteristic
728C2×C4#120×C4711yescharacteristic
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C22×D4×C4711yescharacteristic
731C2×C4C22×D4×C4711yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C4711yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4C47×#57611yescharacteristic
768C4C47×#57611yescharacteristic
769C4C47×#57711yescharacteristic
770C4C47×#57711yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C47×#301211yescharacteristic
777C2C47×#301211yescharacteristic
778C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3546C2
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×#3228C2semidirect
5. C47×#1654C2semidirect
6. C47×#1652C2semidirect
7. C47×#1650C2semidirect
8. C47×#1647C2semidirect
9. C47×#1642C2semidirect
10. C47×#1641C2semidirect
11. C47×#1639C2semidirect
12. C47×#1639C2semidirect
13. C47×#1547C2semidirect
14. C47×#1495C2semidirect
15. C47×#1480C2semidirect
30. C47×#533C22semidirect
34. C47×#500C22semidirect
35. C47×#498C22semidirect
42. C47×#475C22semidirect
45. C47×#474C22semidirect
51. C47×#462C22semidirect
54. C47×#461C22semidirect
56. C47×#431C22semidirect
57. C47×#423C22semidirect
58. C2×C4⋊C8×C47C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
348. #18974C47direct (N × H)
383. #3254C2×C47semidirect
384. #3248C2×C47semidirect
385. #3228C2×C47semidirect
386. #1654C2×C47semidirect
387. #1652C2×C47semidirect
388. #1650C2×C47semidirect
389. #1647C2×C47semidirect
390. #1642C2×C47semidirect
391. #1641C2×C47semidirect
392. #1639C2×C47semidirect
393. #1639C2×C47semidirect
394. #1547C2×C47semidirect
395. #1495C2×C47semidirect
396. #1480C2×C47semidirect
419. #533C22×C47semidirect
423. #500C22×C47semidirect
424. #498C22×C47semidirect
431. #475C22×C47semidirect
434. #474C22×C47semidirect
440. #462C22×C47semidirect
443. #461C22×C47semidirect
445. #431C22×C47semidirect
446. #423C22×C47semidirect
447. C2×C4⋊C8C22×C47semidirect
448. #332C22×C47semidirect
449. #332C22×C47semidirect
452. Q8⋊C8C22×C47semidirect
453. Q8⋊C8C22×C47semidirect
458. D4⋊C8C22×C47semidirect
459. D4⋊C8C22×C47semidirect
460. C47#18974direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35462
C47×#32542
C47×#32482
C47×#32282
C47×#16542
C47×#16522
C47×#16502
C47×#16472
C47×#16422
C47×#16412
C47×#16392
C47×#15472
C47×#14952
C47×#14802
#1897447