Finite Group Databasebeta

← C47×#24635 #26064333

Subgroups — C47×#24635 #26064333

Order 12032.

904 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#464C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
3C47×#2544C211yesmaximal, characteristic
4C47×#2356C211yesmaximal, characteristic, complemented
5C47×#2056C211yesmaximal, characteristic, complemented
6C47×#2055C211yesmaximal, characteristic, complemented
7C47×#2015C211yesmaximal, characteristic, complemented
8C47×#2014C211yesmaximal, characteristic
9C47×#1983C211yesmaximal, characteristic, complemented
10C47×#1982C211yesmaximal, characteristic
11C47×#1958C211yesmaximal, characteristic, complemented
12C47×#1939C211yesmaximal, characteristic, complemented
13C47×#1927C211yesmaximal, characteristic, complemented
14C47×#1926C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C2×#127×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C47×#464—24no—
25C4×SD16×C47—24no—
26C2×#106×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×C4×C8×C47C2211yescharacteristic
41C47×#394—21no—
42C47×#394—21no—
43C47×#391C2211yescharacteristic
44C47×#391C2211yescharacteristic
45C47×#391C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#387—21no—
48C47×#387—21no—
49C47×#386—21no—
50C47×#386—21no—
51C47×#383—21no—
52C47×#382C2211yescharacteristic
53C4×C4⋊C4×C47C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C47×#376—21no—
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×Q8×C47C2311yescharacteristic
62C22×Q8×C47C2311yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47—21no—
68C2×Q16×C47—22no—
69C2×Q16×C47—41no—
70C2×Q16×C47—41no—
71C2×SD16×C47—22no—
72C2×SD16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×SD16×C47—41no—
76C2×SD16×C47—41no—
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81#127×C47—22no—
82#127×C47—41no—
83#124×C47—22no—
84#124×C47—22no—
85#124×C47—22no—
86#124×C47—41no—
87C4×Q8×C47—22no—
88C4×Q8×C47D414yescomplemented
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47D411yescharacteristic
93C2×C4⋊C4×C47D411yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C42×C47—21no—
106C2×C42×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111#106×C47—22no—
112C4⋊C8×C47—22no—
113C4⋊C8×C47—41no—
114C4⋊C8×C47—41no—
115#103×C47—22no—
116#103×C47—22no—
117#103×C47—22no—
118#103×C47—41no—
119#102×C47—22no—
120#102×C47—22no—
121#102×C47—22no—
122#102×C47—41no—
123#102×C47—41no—
124#102×C47—41no—
125C4×C8×C47—22no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47D411yescharacteristic
137#95×C47D411yescharacteristic
138C24×C47—21no—
139C24×C47—21no—
140C2×Q8×C47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47C2×D412yes—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—81no—
168C2×D4×C47—81no—
169C2×D4×C47#4112yes—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—42no—
177C22×C4×C47—81no—
178C22×C4×C47—81no—
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2411yescharacteristic
186Q16×C47—44no—
187SD16×C47—28no—
188SD16×C47—44no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47#4112yes—
201C4⋊C4×C47—24no—
202C4⋊C4×C47—22no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47C2×D412yes—
212C22⋊C4×C47—42no—
213C22⋊C4×C47—42no—
214C22⋊C4×C47—42no—
215C22⋊C4×C47—42no—
216C22⋊C4×C47—42no—
217C22⋊C4×C47—81no—
218C22⋊C4×C47—81no—
219C42×C47—24no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—42no—
225C42×C47—42no—
226C42×C47C2×D412yes—
227C42×C47#4112yes—
228C23×C47—22no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47C22×D411yescharacteristic
243Q8×C47—22no—
244Q8×C47—22no—
245Q8×C47—41no—
246Q8×C47—41no—
247Q8×C47—41no—
248Q8×C47—41no—
249Q8×C47—41no—
250Q8×C47—41no—
251D4×C47—22no—
252D4×C47—22no—
253D4×C47—41no—
254D4×C47—41no—
255D4×C47—41no—
256D4×C47—41no—
257D4×C47—41no—
258D4×C47—41no—
259D4×C47—84no—
260D4×C47—84no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—84no—
295C2×C4×C47#12112yes—
296C2×C4×C47#12112yes—
297C2×C4×C47#13512yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C2×C4×C47H(5,𝔽2)11yescharacteristic
304C8×C47—22no—
305C8×C47—41no—
306C8×C47—41no—
307C8×C47—41no—
308#24635C4711yesmaximal, characteristic, direct product factor, Sylow
309C22×C47—42no—
310C22×C47—42no—
311C22×C47—42no—
312C22×C47—81no—
313C22×C47—81no—
314C22×C47—81no—
315C22×C47—81no—
316C22×C47—81no—
317C22×C47—81no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47—81no—
321C22×C47—81no—
322C22×C47—81no—
323C22×C47C2×#12111yescharacteristic
324C22×C47#54611yescharacteristic
325C22×C47#55011yescharacteristic
326C22×C47C2×#13511yescharacteristic
327C22×C47#57511yescharacteristic
328C22×C47#57711yescharacteristic
329C22×C47#57711yescharacteristic
330C4×C47—22no—
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—42no—
334C4×C47—42no—
335C4×C47—41no—
336C4×C47—41no—
337C4×C47—41no—
338C4×C47—81no—
339C4×C47—81no—
340C4×C47—81no—
341C4×C47—81no—
342C4×C47#52511yescharacteristic
343C4×C47#53511yescharacteristic
344C4×C47#55311yescharacteristic
345C4×C47#55511yescharacteristic
346C2×#464C2×C4711yescharacteristic, complemented
347C2×C4×SD16C2×C4711yescharacteristic, complemented
348#2544C2×C4711yescharacteristic
349#2356C2×C4711yescharacteristic, complemented
350#2056C2×C4711yescharacteristic, complemented
351#2055C2×C4711yescharacteristic, complemented
352#2015C2×C4711yescharacteristic, complemented
353#2014C2×C4711yescharacteristic
354#1983C2×C4711yescharacteristic, complemented
355#1982C2×C4711yescharacteristic
356#1958C2×C4711yescharacteristic, complemented
357#1939C2×C4711yescharacteristic, complemented
358#1927C2×C4711yescharacteristic, complemented
359#1926C2×C4711yescharacteristic, complemented
360#1804C2×C4711yescharacteristic, complemented
361C2×C47—82no—
362C2×C47—161no—
363C2×C47#241411yescharacteristic
364C2×C47#303511yescharacteristic
365C2×C47#304311yescharacteristic
366C2×C47#329611yescharacteristic
367C2×C47#332311yescharacteristic
368C2×C47#339411yescharacteristic
369C2×C47#340111yescharacteristic
370C22×Q16C22×C4711yescharacteristic
371C22×SD16C22×C4711yescharacteristic
372C22×SD16C22×C4711yescharacteristic
373C2×#127C22×C4711yescharacteristic
374C2×#124C22×C4711yescharacteristic
375C2×#124C22×C4711yescharacteristic
376C2×C4×Q8C22×C4711yescharacteristic
377C2×C4×D4C22×C4711yescharacteristic
378#464—24no—
379C4×SD16—24no—
380C2×#106C22×C4711yescharacteristic
381C2×C4⋊C8C22×C4711yescharacteristic
382C2×C4⋊C8C22×C4711yescharacteristic
383C2×C4⋊C8C22×C4711yescharacteristic
384C2×#103C22×C4711yescharacteristic
385C2×#103C22×C4711yescharacteristic
386C2×#103C22×C4711yescharacteristic
387C2×#103C22×C4711yescharacteristic
388C2×#102C22×C4711yescharacteristic
389C2×#102C22×C4711yescharacteristic
390C2×#102C22×C4711yescharacteristic
391C2×#102C22×C4711yescharacteristic
392C2×#102C22×C4711yescharacteristic
393C2×#102C22×C4711yescharacteristic
394C2×C4×C8C22×C4711yescharacteristic
395#394—21no—
396#394—21no—
397#391C22×C4711yescharacteristic
398#391C22×C4711yescharacteristic
399#391C22×C4711yescharacteristic
400#390C22×C4711yescharacteristic
401#387—21no—
402#387—21no—
403#386—21no—
404#386—21no—
405#383—21no—
406#382C22×C4711yescharacteristic
407C4×C4⋊C4C22×C4711yescharacteristic
408C4×C4⋊C4C22×C4711yescharacteristic
409C4×C4⋊C4C22×C4711yescharacteristic
410#376—21no—
411#340C22×C4711yescharacteristic
412#340C22×C4711yescharacteristic
413#336C22×C4711yescharacteristic
414#336C22×C4711yescharacteristic
415C47#2463511yescharacteristic, direct product factor, Sylow
416C22×Q8C23×C4711yescharacteristic
417C22×Q8C23×C4711yescharacteristic
418C22×D4—21no—
419C22×D4—21no—
420C22×D4C23×C4711yescharacteristic
421C22×D4C23×C4711yescharacteristic
422C23×C4—21no—
423C2×Q16—22no—
424C2×Q16—41no—
425C2×Q16—41no—
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—41no—
431C2×SD16—41no—
432C22×C8C23×C4711yescharacteristic
433C22×C8C23×C4711yescharacteristic
434C22×C8C23×C4711yescharacteristic
435C22×C8C23×C4711yescharacteristic
436#127—22no—
437#127—41no—
438#124—22no—
439#124—22no—
440#124—22no—
441#124—41no—
442C4×Q8—22no—
443C4×Q8D4×C4714yescomplemented
444C4×D4—22no—
445C4×D4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C4711yescharacteristic
448C2×C4⋊C4D4×C4711yescharacteristic
449C2×C4⋊C4C23×C4711yescharacteristic
450C2×C4⋊C4C23×C4711yescharacteristic
451C2×C4⋊C4C23×C4711yescharacteristic
452C2×C4⋊C4C23×C4711yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42C23×C4711yescharacteristic
464C2×C42C23×C4711yescharacteristic
465C2×C42C23×C4711yescharacteristic
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469C4⋊C8—41no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—41no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—41no—
478#102—41no—
479#102—41no—
480C4×C8—22no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95D4×C4711yescharacteristic
492#95D4×C4711yescharacteristic
493C24—21no—
494C24—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×D4×C4712yes—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4#41×C4712yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C4711yescharacteristic
535C22×C4C2×D4×C4711yescharacteristic
536C22×C4C2×D4×C4711yescharacteristic
537C22×C4C2×D4×C4711yescharacteristic
538C22×C4C2×D4×C4711yescharacteristic
539C22×C4C2×D4×C4711yescharacteristic
540C22×C4C24×C4711yescharacteristic
541Q16—44no—
542SD16—28no—
543SD16—44no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8#41×C4712yes—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—41no—
566C4⋊C4C2×D4×C4712yes—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—24no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42C2×D4×C4712yes—
582C42#41×C4712yes—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C22×D4×C4711yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4#121×C4712yes—
651C2×C4#121×C4712yes—
652C2×C4#135×C4712yes—
653C2×C4C22×D4×C4711yescharacteristic
654C2×C4C2×#41×C4711yescharacteristic
655C2×C4C2×#41×C4711yescharacteristic
656C2×C4C2×#41×C4711yescharacteristic
657C2×C4H(5,𝔽2)×C4711yescharacteristic
658C2×C4H(5,𝔽2)×C4711yescharacteristic
659C8—22no—
660C8—41no—
661C8—41no—
662C8—41no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#121×C4711yescharacteristic
678C22C47×#54611yescharacteristic
679C22C47×#55011yescharacteristic
680C22C2×#135×C4711yescharacteristic
681C22C47×#57511yescharacteristic
682C22C47×#57711yescharacteristic
683C22C47×#57711yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—42no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4C47×#52511yescharacteristic
697C4C47×#53511yescharacteristic
698C4C47×#55311yescharacteristic
699C4C47×#55511yescharacteristic
700C2—82no—
701C2—161no—
702C2C47×#241411yescharacteristic
703C2C47×#303511yescharacteristic
704C2C47×#304311yescharacteristic
705C2C47×#329611yescharacteristic
706C2C47×#332311yescharacteristic
707C2C47×#339411yescharacteristic
708C2C47×#340111yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#127×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C47×#464C2semidirect
2. C2×C4×SD16×C47C2semidirect
4. C47×#2356C2semidirect
5. C47×#2056C2semidirect
6. C47×#2055C2semidirect
7. C47×#2015C2semidirect
9. C47×#1983C2semidirect
11. C47×#1958C2semidirect
12. C47×#1939C2semidirect
13. C47×#1927C2semidirect
14. C47×#1926C2semidirect
15. C47×#1804C2semidirect
88. C4×Q8×C47D4semidirect
308. #24635C47direct (N × H)
346. C2×#464C2×C47semidirect
347. C2×C4×SD16C2×C47semidirect
349. #2356C2×C47semidirect
350. #2056C2×C47semidirect
351. #2055C2×C47semidirect
352. #2015C2×C47semidirect
354. #1983C2×C47semidirect
356. #1958C2×C47semidirect
357. #1939C2×C47semidirect
358. #1927C2×C47semidirect
359. #1926C2×C47semidirect
360. #1804C2×C47semidirect
415. C47#24635direct (N × H)
443. C4×Q8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4642
C2×C4×SD16×C472
C47×#25442
C47×#23562
C47×#20562
C47×#20552
C47×#20152
C47×#20142
C47×#19832
C47×#19822
C47×#19582
C47×#19392
C47×#19272
C47×#19262
C47×#18042
#2463547