Finite Group Databasebeta

← C47×#18811 #26058509

Subgroups — C47×#18811 #26058509

Order 12032.

988 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3519C211yesmaximal, characteristic
2C47×#3252C211yesmaximal, characteristic, complemented
3C47×#3210C211yesmaximal, characteristic, complemented
4C47×#3077C211yesmaximal, characteristic, complemented
5C47×#1646C211yesmaximal, characteristic, complemented
6C47×#1644C211yesmaximal, characteristic, complemented
7C47×#1641C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1634C211yesmaximal, characteristic, complemented
10C47×#1632C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1629C211yesmaximal, characteristic, complemented
13C47×#1560C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1486C211yesmaximal, characteristic, complemented
16C47×#555C2211yescharacteristic
17C47×#554C2211yescharacteristic
18C47×#553—21no—
19C47×#553—21no—
20C47×#550C2211yescharacteristic
21C47×#546—22no—
22C47×#546—21no—
23D42×C47—21no—
24D42×C47C2211yescharacteristic
25C47×#540—21no—
26C47×#538—22no—
27C47×#533C2211yescharacteristic, complemented
28C47×#532C2211yescharacteristic
29C47×#529C2211yescharacteristic
30C47×#525—21no—
31C2×#121×C47—21no—
32C47×#518—21no—
33C2×C4×D4×C47C2211yescharacteristic
34C47×#494C2211yescharacteristic, complemented
35C47×#492C2211yescharacteristic, complemented
36C47×#487C2211yescharacteristic, complemented
37C47×#486C2211yescharacteristic, complemented
38C47×#479—21no—
39C47×#478—21no—
40C47×#478—21no—
41C47×#477C2211yescharacteristic, complemented
42C47×#476C2211yescharacteristic
43C47×#476C2211yescharacteristic, complemented
44C47×#476C2211yescharacteristic, complemented
45C47×#474C2211yescharacteristic
46C47×#474C2211yescharacteristic, complemented
47C47×#470—21no—
48C47×#468—21no—
49C47×#464—22no—
50C47×#464—21no—
51C47×#462C2211yescharacteristic, complemented
52C47×#461C2211yescharacteristic, complemented
53C47×#452—22no—
54C47×#431C2211yescharacteristic, complemented
55C47×#428—21no—
56C47×#423C2211yescharacteristic, complemented
57C47×#423C2211yescharacteristic, complemented
58C47×#418—21no—
59C47×#333C2211yescharacteristic, complemented
60C47×#333C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic, complemented
62C47×#331C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic, complemented
68C47×D4⋊C8C2211yescharacteristic, complemented
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47D412yes—
73C22×D4×C47—22no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47D411yescharacteristic
77C23×C4×C47—21no—
78C2×Q16×C47—22no—
79C2×Q16×C47—21no—
80C2×SD16×C47—22no—
81C2×SD16×C47—21no—
82C2×M16×C47—21no—
83C2×M16×C47—21no—
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86C4⋊Q8×C47C2311yescharacteristic
87#127×C47—21no—
88#127×C47C2311yescharacteristic
89#126×C47—22no—
90#126×C47—21no—
91#125×C47—21no—
92#125×C47—21no—
93#125×C47D411yescharacteristic
94#124×C47—22no—
95#124×C47D411yescharacteristic
96#124×C47D412yes—
97#123×C47—22no—
98#123×C47—22no—
99#123×C47—22no—
100#123×C47—21no—
101C22⋊Q8×C47—21no—
102C22⋊Q8×C47—22no—
103C22⋊Q8×C47—21no—
104C22⋊Q8×C47—21no—
105C22⋊Q8×C47D411yescharacteristic
106#121×C47—22no—
107#121×C47—22no—
108#121×C47—22no—
109#121×C47—22no—
110#121×C47—21no—
111#121×C47—22no—
112#121×C47—21no—
113#121×C47—21no—
114#121×C47—21no—
115#121×C47—21no—
116#121×C47—21no—
117#121×C47—21no—
118#121×C47D411yescharacteristic
119#120×C47—22no—
120#120×C47—22no—
121#120×C47—22no—
122C4×Q8×C47—21no—
123C4×Q8×C47—21no—
124C4×Q8×C47C2311yescharacteristic
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47—21no—
132C4×D4×C47—21no—
133C4×D4×C47—21no—
134C4×D4×C47—21no—
135C4×D4×C47D411yescharacteristic
136C4×D4×C47D411yescharacteristic
137C4×D4×C47C2311yescharacteristic
138C4×D4×C47C2311yescharacteristic
139C4×D4×C47C2311yescharacteristic
140#117×C47—21no—
141#117×C47—21no—
142#117×C47—21no—
143#117×C47—21no—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47D411yescharacteristic
146C2×C22⋊C4×C47—22no—
147C2×C22⋊C4×C47—22no—
148C2×C22⋊C4×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#107×C47—21no—
151#107×C47—21no—
152#107×C47—21no—
153#106×C47—21no—
154#106×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—22no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—21no—
167#102×C47—22no—
168#102×C47—21no—
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
176C24×C47—22no—
177C24×C47—21no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—82no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47C2×D411yescharacteristic
184C2×Q8×C47C2×D412yes—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—41no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—81no—
200C2×D4×C47—81no—
201C2×D4×C47—84no—
202C2×D4×C47C2×D411yescharacteristic
203C2×D4×C47C2×D411yescharacteristic
204C2×D4×C47C2×D411yescharacteristic
205C2×D4×C47C2×D412yes—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—22no—
214C22×C4×C47—21no—
215C22×C4×C47—81no—
216C22×C4×C47—81no—
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220Q16×C47—81no—
221Q16×C47—82no—
222SD16×C47—81no—
223SD16×C47—82no—
224M16×C47—42no—
225M16×C47—81no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
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—21no—
245C4⋊C4×C47—41no—
246C4⋊C4×C47—41no—
247C4⋊C4×C47C2×D411yescharacteristic
248C4⋊C4×C47C2×D411yescharacteristic
249C4⋊C4×C47C2×D411yescharacteristic
250C4⋊C4×C47C2×D411yescharacteristic
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—22no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
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—21no—
278C23×C47—22no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47—44no—
282C23×C47—81no—
283C23×C47—82no—
284C23×C47—82no—
285C23×C47#12011yescharacteristic
286Q8×C47—21no—
287Q8×C47—21no—
288Q8×C47—42no—
289Q8×C47—42no—
290Q8×C47—41no—
291Q8×C47—41no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—21no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—44no—
300D4×C47—42no—
301D4×C47—44no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—82no—
307D4×C47—82no—
308D4×C47—82no—
309D4×C47—82no—
310D4×C47#13712yes—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—22no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
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—81no—
331C2×C4×C47—81no—
332C2×C4×C47—82no—
333C2×C4×C47—81no—
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#18811C4711yesmaximal, characteristic, direct product factor, Sylow
349C22×C47—21no—
350C22×C47—22no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—42no—
358C22×C47—41no—
359C22×C47—42no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—84no—
365C22×C47—164no—
366C22×C47C2×#12011yescharacteristic
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47—41no—
374C4×C47—41no—
375C4×C47—41no—
376C4×C47—42no—
377C4×C47—81no—
378C4×C47—81no—
379C4×C47C2×#13711yescharacteristic
380C4×C47#57511yescharacteristic
381C4×C47#57611yescharacteristic
382C4×C47#57711yescharacteristic
383#3519C2×C4711yescharacteristic
384#3252C2×C4711yescharacteristic, complemented
385#3210C2×C4711yescharacteristic, complemented
386#3077C2×C4711yescharacteristic, complemented
387#1646C2×C4711yescharacteristic, complemented
388#1644C2×C4711yescharacteristic, complemented
389#1641C2×C4711yescharacteristic, complemented
390#1639C2×C4711yescharacteristic, complemented
391#1634C2×C4711yescharacteristic, complemented
392#1632C2×C4711yescharacteristic, complemented
393#1631C2×C4711yescharacteristic, complemented
394#1629C2×C4711yescharacteristic, complemented
395#1560C2×C4711yescharacteristic, complemented
396#1495C2×C4711yescharacteristic, complemented
397#1486C2×C4711yescharacteristic, complemented
398C2×C47—41no—
399C2×C47—42no—
400C2×C47—81no—
401C2×C47—82no—
402C2×C47—81no—
403C2×C47#300711yescharacteristic
404C2×C47#301211yescharacteristic
405C2×C47#301911yescharacteristic
406#555C22×C4711yescharacteristic
407#554C22×C4711yescharacteristic
408#553—21no—
409#553—21no—
410#550C22×C4711yescharacteristic
411#546—22no—
412#546—21no—
413D42—21no—
414D42C22×C4711yescharacteristic
415#540—21no—
416#538—22no—
417#533C22×C4711yescharacteristic, complemented
418#532C22×C4711yescharacteristic
419#529C22×C4711yescharacteristic
420#525—21no—
421C2×#121—21no—
422#518—21no—
423C2×C4×D4C22×C4711yescharacteristic
424#494C22×C4711yescharacteristic, complemented
425#492C22×C4711yescharacteristic, complemented
426#487C22×C4711yescharacteristic, complemented
427#486C22×C4711yescharacteristic, complemented
428#479—21no—
429#478—21no—
430#478—21no—
431#477C22×C4711yescharacteristic, complemented
432#476C22×C4711yescharacteristic
433#476C22×C4711yescharacteristic, complemented
434#476C22×C4711yescharacteristic, complemented
435#474C22×C4711yescharacteristic
436#474C22×C4711yescharacteristic, complemented
437#470—21no—
438#468—21no—
439#464—22no—
440#464—21no—
441#462C22×C4711yescharacteristic, complemented
442#461C22×C4711yescharacteristic, complemented
443#452—22no—
444#431C22×C4711yescharacteristic, complemented
445#428—21no—
446#423C22×C4711yescharacteristic, complemented
447#423C22×C4711yescharacteristic, complemented
448#418—21no—
449#333C22×C4711yescharacteristic, complemented
450#333C22×C4711yescharacteristic, complemented
451#331C22×C4711yescharacteristic, complemented
452#331C22×C4711yescharacteristic, complemented
453Q8⋊C8C22×C4711yescharacteristic, complemented
454Q8⋊C8C22×C4711yescharacteristic, complemented
455D4⋊C8C22×C4711yescharacteristic
456D4⋊C8C22×C4711yescharacteristic
457D4⋊C8C22×C4711yescharacteristic, complemented
458D4⋊C8C22×C4711yescharacteristic, complemented
459D4⋊C8C22×C4711yescharacteristic, complemented
460D4⋊C8C22×C4711yescharacteristic, complemented
461C47#1881111yescharacteristic, direct product factor, Sylow
462C2×#41—21no—
463C2×#41D4×C4712yes—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4D4×C4711yescharacteristic
468C23×C4—21no—
469C2×Q16—22no—
470C2×Q16—21no—
471C2×SD16—22no—
472C2×SD16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C4⋊Q8C23×C4711yescharacteristic
476C4⋊Q8C23×C4711yescharacteristic
477C4⋊Q8C23×C4711yescharacteristic
478#127—21no—
479#127C23×C4711yescharacteristic
480#126—22no—
481#126—21no—
482#125—21no—
483#125—21no—
484#125D4×C4711yescharacteristic
485#124—22no—
486#124D4×C4711yescharacteristic
487#124D4×C4712yes—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—21no—
492C22⋊Q8—21no—
493C22⋊Q8—22no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8D4×C4711yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—21no—
502#121—22no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121D4×C4711yescharacteristic
510#120—22no—
511#120—22no—
512#120—22no—
513C4×Q8—21no—
514C4×Q8—21no—
515C4×Q8C23×C4711yescharacteristic
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4D4×C4711yescharacteristic
527C4×D4D4×C4711yescharacteristic
528C4×D4C23×C4711yescharacteristic
529C4×D4C23×C4711yescharacteristic
530C4×D4C23×C4711yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534#117—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4D4×C4711yescharacteristic
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—21no—
540C2×C42C23×C4711yescharacteristic
541#107—21no—
542#107—21no—
543#107—21no—
544#106—21no—
545#106—21no—
546#106—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8—21no—
550C4⋊C8C23×C4711yescharacteristic
551C4⋊C8C23×C4711yescharacteristic
552C4⋊C8C23×C4711yescharacteristic
553C4⋊C8C23×C4711yescharacteristic
554#103—22no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—21no—
562#102—22no—
563#102—21no—
564C22⋊C8—21no—
565C4×C8C23×C4711yescharacteristic
566C4×C8C23×C4711yescharacteristic
567C24—22no—
568C24—21no—
569#41—81no—
570#41—81no—
571#41—82no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8C2×D4×C4711yescharacteristic
575C2×Q8C2×D4×C4712yes—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4C2×D4×C4711yescharacteristic
594C2×D4C2×D4×C4711yescharacteristic
595C2×D4C2×D4×C4711yescharacteristic
596C2×D4C2×D4×C4712yes—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C4711yescharacteristic
609C22×C4C2×D4×C4711yescharacteristic
610C22×C4C2×D4×C4711yescharacteristic
611Q16—81no—
612Q16—82no—
613SD16—81no—
614SD16—82no—
615M16—42no—
616M16—81no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C4⋊C4—22no—
624C4⋊C4—22no—
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—21no—
635C4⋊C4—21no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4C2×D4×C4711yescharacteristic
639C4⋊C4C2×D4×C4711yescharacteristic
640C4⋊C4C2×D4×C4711yescharacteristic
641C4⋊C4C2×D4×C4711yescharacteristic
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—41no—
659C42—22no—
660C42—21no—
661C42—41no—
662C42C2×D4×C4711yescharacteristic
663C42C2×D4×C4711yescharacteristic
664C42C2×D4×C4711yescharacteristic
665C42C24×C4711yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—81no—
674C23—82no—
675C23—82no—
676C23#120×C4711yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—42no—
680Q8—42no—
681Q8—41no—
682Q8—41no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—42no—
690D4—44no—
691D4—42no—
692D4—44no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—82no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4#137×C4712yes—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4#120×C4711yescharacteristic
728C2×C4#120×C4711yescharacteristic
729C2×C4#120×C4711yescharacteristic
730C2×C4C22×D4×C4711yescharacteristic
731C2×C4C22×D4×C4711yescharacteristic
732C2×C4C22×D4×C4711yescharacteristic
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—84no—
755C22—164no—
756C22C2×#120×C4711yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4C2×#137×C4711yescharacteristic
770C4C47×#57511yescharacteristic
771C4C47×#57611yescharacteristic
772C4C47×#57711yescharacteristic
773C2—41no—
774C2—42no—
775C2—81no—
776C2—81no—
777C2—82no—
778C2C47×#300711yescharacteristic
779C2C47×#301211yescharacteristic
780C2C47×#301911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3519C2
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×#3252C2semidirect
3. C47×#3210C2semidirect
4. C47×#3077C2semidirect
5. C47×#1646C2semidirect
6. C47×#1644C2semidirect
7. C47×#1641C2semidirect
8. C47×#1639C2semidirect
9. C47×#1634C2semidirect
10. C47×#1632C2semidirect
11. C47×#1631C2semidirect
12. C47×#1629C2semidirect
13. C47×#1560C2semidirect
14. C47×#1495C2semidirect
15. C47×#1486C2semidirect
27. C47×#533C22semidirect
34. C47×#494C22semidirect
35. C47×#492C22semidirect
36. C47×#487C22semidirect
37. C47×#486C22semidirect
41. C47×#477C22semidirect
43. C47×#476C22semidirect
44. C47×#476C22semidirect
46. C47×#474C22semidirect
51. C47×#462C22semidirect
52. C47×#461C22semidirect
54. C47×#431C22semidirect
56. C47×#423C22semidirect
57. C47×#423C22semidirect
59. C47×#333C22semidirect
60. C47×#333C22semidirect
61. C47×#331C22semidirect
62. C47×#331C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
67. C47×D4⋊C8C22semidirect
68. C47×D4⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
348. #18811C47direct (N × H)
384. #3252C2×C47semidirect
385. #3210C2×C47semidirect
386. #3077C2×C47semidirect
387. #1646C2×C47semidirect
388. #1644C2×C47semidirect
389. #1641C2×C47semidirect
390. #1639C2×C47semidirect
391. #1634C2×C47semidirect
392. #1632C2×C47semidirect
393. #1631C2×C47semidirect
394. #1629C2×C47semidirect
395. #1560C2×C47semidirect
396. #1495C2×C47semidirect
397. #1486C2×C47semidirect
417. #533C22×C47semidirect
424. #494C22×C47semidirect
425. #492C22×C47semidirect
426. #487C22×C47semidirect
427. #486C22×C47semidirect
431. #477C22×C47semidirect
433. #476C22×C47semidirect
434. #476C22×C47semidirect
436. #474C22×C47semidirect
441. #462C22×C47semidirect
442. #461C22×C47semidirect
444. #431C22×C47semidirect
446. #423C22×C47semidirect
447. #423C22×C47semidirect
449. #333C22×C47semidirect
450. #333C22×C47semidirect
451. #331C22×C47semidirect
452. #331C22×C47semidirect
453. Q8⋊C8C22×C47semidirect
454. Q8⋊C8C22×C47semidirect
457. D4⋊C8C22×C47semidirect
458. D4⋊C8C22×C47semidirect
459. D4⋊C8C22×C47semidirect
460. D4⋊C8C22×C47semidirect
461. C47#18811direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35192
C47×#32522
C47×#32102
C47×#30772
C47×#16462
C47×#16442
C47×#16412
C47×#16392
C47×#16342
C47×#16322
C47×#16312
C47×#16292
C47×#15602
C47×#14952
C47×#14862
#1881147