Finite Group Databasebeta

← C47×#24334 #26064032

Subgroups — C47×#24334 #26064032

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#557C211yesmaximal, characteristic, complemented
2C2×C47×#478C211yesmaximal, characteristic
3C2×C4×SD16×C47C211yesmaximal, characteristic
4C47×#2580C211yesmaximal, characteristic
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2058C211yesmaximal, characteristic, complemented
7C47×#2025C211yesmaximal, characteristic
8C47×#2023C211yesmaximal, characteristic
9C47×#1991C211yesmaximal, characteristic, complemented
10C47×#1984C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic
12C47×#1880C211yesmaximal, characteristic
13C47×#1865C211yesmaximal, characteristic, complemented
14C47×#1863C211yesmaximal, characteristic, complemented
15C47×#1805C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C47×#557—24no—
18C47×#557—24no—
19C2×C4⋊Q8×C47—21no—
20C2×C4⋊Q8×C47C2211yescharacteristic
21C2×#125×C47—21no—
22C2×#125×C47—21no—
23C2×#125×C47C2211yescharacteristic
24C2×#125×C47C2211yescharacteristic
25C2×C4×Q8×C47—21no—
26C2×C4×Q8×C47C2211yescharacteristic
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C2×C4×Q8×C47C2211yescharacteristic
30C2×C4×D4×C47C2211yescharacteristic
31C47×#478—24no—
32C4×SD16×C47—24no—
33C2×#107×C47C2211yescharacteristic
34C2×#106×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C4×C8×C47C2211yescharacteristic
44C47×#399—21no—
45C47×#393—21no—
46C47×#390C2211yescharacteristic
47C47×#390C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#385—21no—
51C47×#385—21no—
52C47×#382C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47—21no—
64C22×Q8×C47D411yescharacteristic
65C22×Q8×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47—21no—
68C2×SD16×C47—22no—
69C2×SD16×C47—22no—
70C2×SD16×C47Q814yescomplemented
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C4⋊Q8×C47—28no—
76C4⋊Q8×C47—22no—
77C4⋊Q8×C47—22no—
78#125×C47—28no—
79#125×C47—28no—
80#125×C47—22no—
81#125×C47—22no—
82#125×C47—22no—
83#125×C47D414yes—
84C4×Q8×C47—28no—
85C4×Q8×C47—22no—
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88C4×Q8×C47—22no—
89C4×Q8×C47—22no—
90C4×Q8×C47—22no—
91C4×Q8×C47—22no—
92C4×Q8×C47D414yes—
93C4×D4×C47—22no—
94C4×D4×C47—22no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C4⋊C4×C47D411yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125#107×C47—22no—
126#106×C47—22no—
127#106×C47—22no—
128C4⋊C8×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—22no—
135C4×C8×C47—22no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140C24×C47—21no—
141C2×Q8×C47—24no—
142C2×Q8×C47—22no—
143C2×Q8×C47—22no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—41no—
148C2×Q8×C47—42no—
149C2×Q8×C47—42no—
150C2×Q8×C47C2×D412yes—
151C2×Q8×C47C2×Q812yes—
152C2×Q8×C47#4112yes—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47C2×Q812yes—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—42no—
167C22×C4×C47—81no—
168C22×C4×C47—81no—
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2411yescharacteristic
176SD16×C47—28no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47C2×Q812yes—
189C4⋊C4×C47—24no—
190C4⋊C4×C47—24no—
191C4⋊C4×C47—24no—
192C4⋊C4×C47—24no—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—24no—
195C4⋊C4×C47—24no—
196C4⋊C4×C47—24no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—22no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
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—81no—
210C4⋊C4×C47—81no—
211C4⋊C4×C47C2×D412yes—
212C4⋊C4×C47C2×D412yes—
213C4⋊C4×C47C2×D412yes—
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—24no—
221C42×C47—24no—
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47C2×D412yes—
227C42×C47C2×D412yes—
228C23×C47—22no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47C22×D411yescharacteristic
236Q8×C47—22no—
237Q8×C47—22no—
238Q8×C47—22no—
239Q8×C47—44no—
240Q8×C47—48no—
241Q8×C47C22⋊Q814yes—
242D4×C47—22no—
243D4×C47—22no—
244D4×C47—41no—
245D4×C47—41no—
246C2×C4×C47—22no—
247C2×C4×C47—21no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—22no—
258C2×C4×C47—21no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
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—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—84no—
283C2×C4×C47#12012yes—
284C2×C4×C47#12012yes—
285C2×C4×C47#13512yes—
286C2×C4×C47C22×D411yescharacteristic
287C2×C4×C47C22×D411yescharacteristic
288C2×C4×C47C22×Q811yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C472−1+411yescharacteristic
291C2×C4×C472−1+411yescharacteristic
292C8×C47—22no—
293C8×C47—41no—
294C8×C47—41no—
295C8×C47—41no—
296#24334C4711yesmaximal, characteristic, direct product factor, Sylow
297C22×C47—42no—
298C22×C47—42no—
299C22×C47—42no—
300C22×C47—81no—
301C22×C47—81no—
302C22×C47—81no—
303C22×C47—81no—
304C22×C47C2×#12011yescharacteristic
305C22×C47#54811yescharacteristic
306C22×C47D4×Q811yescharacteristic
307C22×C47C2×#13511yescharacteristic
308C22×C47#57511yescharacteristic
309C22×C47#57711yescharacteristic
310C22×C47#57711yescharacteristic
311C4×C47—24no—
312C4×C47—22no—
313C4×C47—22no—
314C4×C47—22no—
315C4×C47—41no—
316C4×C47—42no—
317C4×C47—42no—
318C4×C47—41no—
319C4×C47—41no—
320C4×C47—42no—
321C4×C47—81no—
322C4×C47—81no—
323C4×C47—81no—
324C4×C47C2×C22⋊Q811yescharacteristic
325C4×C47#53611yescharacteristic
326C4×C47#54811yescharacteristic
327C4×C47D4×Q811yescharacteristic
328C2×#557C2×C4711yescharacteristic, complemented
329C2×#478C2×C4711yescharacteristic
330C2×C4×SD16C2×C4711yescharacteristic
331#2580C2×C4711yescharacteristic
332#2059C2×C4711yescharacteristic, complemented
333#2058C2×C4711yescharacteristic, complemented
334#2025C2×C4711yescharacteristic
335#2023C2×C4711yescharacteristic
336#1991C2×C4711yescharacteristic, complemented
337#1984C2×C4711yescharacteristic, complemented
338#1880C2×C4711yescharacteristic
339#1880C2×C4711yescharacteristic
340#1865C2×C4711yescharacteristic, complemented
341#1863C2×C4711yescharacteristic, complemented
342#1805C2×C4711yescharacteristic, complemented
343C2×C47—82no—
344C2×C47#240911yescharacteristic
345C2×C47#300211yescharacteristic
346C2×C47#301011yescharacteristic
347C2×C47#336511yescharacteristic
348C2×C47#337111yescharacteristic
349C2×C47#338111yescharacteristic
350C2×C47#338811yescharacteristic
351C22×SD16C22×C4711yescharacteristic
352#557—24no—
353#557—24no—
354C2×C4⋊Q8—21no—
355C2×C4⋊Q8C22×C4711yescharacteristic
356C2×#125—21no—
357C2×#125—21no—
358C2×#125C22×C4711yescharacteristic
359C2×#125C22×C4711yescharacteristic
360C2×C4×Q8—21no—
361C2×C4×Q8C22×C4711yescharacteristic
362C2×C4×Q8C22×C4711yescharacteristic
363C2×C4×Q8C22×C4711yescharacteristic
364C2×C4×Q8C22×C4711yescharacteristic
365C2×C4×D4C22×C4711yescharacteristic
366#478—24no—
367C4×SD16—24no—
368C2×#107C22×C4711yescharacteristic
369C2×#106C22×C4711yescharacteristic
370C2×#106C22×C4711yescharacteristic
371C2×C4⋊C8C22×C4711yescharacteristic
372C2×#103C22×C4711yescharacteristic
373C2×#103C22×C4711yescharacteristic
374C2×#103C22×C4711yescharacteristic
375C2×#102C22×C4711yescharacteristic
376C2×#102C22×C4711yescharacteristic
377C2×#102C22×C4711yescharacteristic
378C2×C4×C8C22×C4711yescharacteristic
379#399—21no—
380#393—21no—
381#390C22×C4711yescharacteristic
382#390C22×C4711yescharacteristic
383#389C22×C4711yescharacteristic
384#389C22×C4711yescharacteristic
385#385—21no—
386#385—21no—
387#382C22×C4711yescharacteristic
388#340C22×C4711yescharacteristic
389#340C22×C4711yescharacteristic
390#340C22×C4711yescharacteristic
391#340C22×C4711yescharacteristic
392#340C22×C4711yescharacteristic
393#340C22×C4711yescharacteristic
394#336C22×C4711yescharacteristic
395#336C22×C4711yescharacteristic
396#336C22×C4711yescharacteristic
397#336C22×C4711yescharacteristic
398C47#2433411yescharacteristic, direct product factor, Sylow
399C22×Q8—21no—
400C22×Q8D4×C4711yescharacteristic
401C22×Q8C23×C4711yescharacteristic
402C22×D4C23×C4711yescharacteristic
403C23×C4—21no—
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16Q8×C4714yescomplemented
407C22×C8C23×C4711yescharacteristic
408C22×C8C23×C4711yescharacteristic
409C22×C8C23×C4711yescharacteristic
410C22×C8C23×C4711yescharacteristic
411C4⋊Q8—28no—
412C4⋊Q8—22no—
413C4⋊Q8—22no—
414#125—28no—
415#125—28no—
416#125—22no—
417#125—22no—
418#125—22no—
419#125D4×C4714yes—
420C4×Q8—28no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8D4×C4714yes—
429C4×D4—22no—
430C4×D4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C4711yescharacteristic
442C2×C4⋊C4D4×C4711yescharacteristic
443C2×C4⋊C4D4×C4711yescharacteristic
444C2×C4⋊C4C23×C4711yescharacteristic
445C2×C4⋊C4C23×C4711yescharacteristic
446C2×C4⋊C4C23×C4711yescharacteristic
447C2×C4⋊C4C23×C4711yescharacteristic
448C2×C4⋊C4C23×C4711yescharacteristic
449C2×C4⋊C4C23×C4711yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C23×C4711yescharacteristic
459C2×C42C23×C4711yescharacteristic
460C2×C42C23×C4711yescharacteristic
461#107—22no—
462#106—22no—
463#106—22no—
464C4⋊C8—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471C4×C8—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C24—21no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—41no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8C2×D4×C4712yes—
487C2×Q8C2×Q8×C4712yes—
488C2×Q8#41×C4712yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×Q8×C4712yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×D4×C4711yescharacteristic
506C22×C4C2×D4×C4711yescharacteristic
507C22×C4C2×D4×C4711yescharacteristic
508C22×C4C2×D4×C4711yescharacteristic
509C22×C4C2×D4×C4711yescharacteristic
510C22×C4C2×D4×C4711yescharacteristic
511C22×C4C24×C4711yescharacteristic
512SD16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C2×Q8×C4712yes—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4C2×D4×C4712yes—
548C4⋊C4C2×D4×C4712yes—
549C4⋊C4C2×D4×C4712yes—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—24no—
556C42—24no—
557C42—24no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42C2×D4×C4712yes—
563C42C2×D4×C4712yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C22×D4×C4711yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—44no—
576Q8—48no—
577Q8C22⋊Q8×C4714yes—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—84no—
619C2×C4#120×C4712yes—
620C2×C4#120×C4712yes—
621C2×C4#135×C4712yes—
622C2×C4C22×D4×C4711yescharacteristic
623C2×C4C22×D4×C4711yescharacteristic
624C2×C4C22×Q8×C4711yescharacteristic
625C2×C4C2×#41×C4711yescharacteristic
626C2×C42−1+4×C4711yescharacteristic
627C2×C42−1+4×C4711yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×#120×C4711yescharacteristic
640C22C47×#54811yescharacteristic
641C22D4×Q8×C4711yescharacteristic
642C22C2×#135×C4711yescharacteristic
643C22C47×#57511yescharacteristic
644C22C47×#57711yescharacteristic
645C22C47×#57711yescharacteristic
646C4—24no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C22⋊Q8×C4711yescharacteristic
660C4C47×#53611yescharacteristic
661C4C47×#54811yescharacteristic
662C4D4×Q8×C4711yescharacteristic
663C2—82no—
664C2C47×#240911yescharacteristic
665C2C47×#300211yescharacteristic
666C2C47×#301011yescharacteristic
667C2C47×#336511yescharacteristic
668C2C47×#337111yescharacteristic
669C2C47×#338111yescharacteristic
670C2C47×#338811yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×Q8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#557C2semidirect
5. C47×#2059C2semidirect
6. C47×#2058C2semidirect
9. C47×#1991C2semidirect
10. C47×#1984C2semidirect
13. C47×#1865C2semidirect
14. C47×#1863C2semidirect
15. C47×#1805C2semidirect
70. C2×SD16×C47Q8semidirect
296. #24334C47direct (N × H)
328. C2×#557C2×C47semidirect
332. #2059C2×C47semidirect
333. #2058C2×C47semidirect
336. #1991C2×C47semidirect
337. #1984C2×C47semidirect
340. #1865C2×C47semidirect
341. #1863C2×C47semidirect
342. #1805C2×C47semidirect
398. C47#24334direct (N × H)
406. C2×SD16Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5572
C2×C47×#4782
C2×C4×SD16×C472
C47×#25802
C47×#20592
C47×#20582
C47×#20252
C47×#20232
C47×#19912
C47×#19842
C47×#18802
C47×#18652
C47×#18632
C47×#18052
#2433447