Finite Group Databasebeta

← C47×#24310 #26064008

Subgroups — C47×#24310 #26064008

Order 12032.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#544C211yesmaximal, characteristic
2C2×C47×#479C211yesmaximal, characteristic, complemented
3C2×C47×#475C211yesmaximal, characteristic, complemented
4C47×#2323C211yesmaximal, characteristic
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2058C211yesmaximal, characteristic, complemented
7C47×#2026C211yesmaximal, characteristic, complemented
8C47×#2024C211yesmaximal, characteristic, complemented
9C47×#1989C211yesmaximal, characteristic, complemented
10C47×#1987C211yesmaximal, characteristic, complemented
11C47×#1873C211yesmaximal, characteristic
12C47×#1872C211yesmaximal, characteristic
13C47×#1854C211yesmaximal, characteristic
14C47×#1853C211yesmaximal, characteristic
15C47×#1798C211yesmaximal, characteristic
16C47×#544—24no—
17C47×#544—24no—
18C2×C4⋊Q8×C47—21no—
19C2×C4⋊Q8×C47C2211yescharacteristic
20C2×C4⋊Q8×C47C2211yescharacteristic
21C2×#125×C47—21no—
22C2×#125×C47C2211yescharacteristic
23C2×#125×C47C2211yescharacteristic
24C2×C22⋊Q8×C47—21no—
25C2×C22⋊Q8×C47—21no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C4×Q8×C47C2211yescharacteristic
28C2×#117×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C47×#479—24no—
32C47×#475—24no—
33C2×#107×C47C2211yescharacteristic
34C2×#106×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×#106×C47C2211yescharacteristic
37C2×C4⋊C8×C47C2211yescharacteristic
38C2×C4⋊C8×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C47×#391C2211yescharacteristic
46C47×#389—21no—
47C47×#389C2211yescharacteristic
48C47×#388—21no—
49C47×#388—21no—
50C47×#387—21no—
51C47×#380C2211yescharacteristic
52C4×C4⋊C4×C47C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47—21no—
64C22×Q8×C47—21no—
65C22×Q8×C47C2311yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2311yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C4⋊Q8×C47—28no—
73C4⋊Q8×C47—22no—
74C4⋊Q8×C47—22no—
75C4⋊Q8×C47—22no—
76C4⋊Q8×C47D414yes—
77#125×C47—28no—
78#125×C47—22no—
79#125×C47—22no—
80#125×C47—22no—
81#125×C47D414yes—
82C22⋊Q8×C47—28no—
83C22⋊Q8×C47—28no—
84C22⋊Q8×C47—22no—
85C22⋊Q8×C47Q814yescomplemented
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88#117×C47—22no—
89#117×C47—22no—
90#117×C47—22no—
91#117×C47—22no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
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—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47D411yescharacteristic
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C42×C47—21no—
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#107×C47—22no—
124#106×C47—22no—
125#106×C47—22no—
126#106×C47—22no—
127C4⋊C8×C47—22no—
128C4⋊C8×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—22no—
133C22⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140C24×C47C2×D411yescharacteristic
141C2×Q8×C47—24no—
142C2×Q8×C47—24no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—81no—
149C2×Q8×C47—81no—
150C2×Q8×C47—81no—
151C2×Q8×C47—81no—
152C2×Q8×C47C2×Q812yes—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—24no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—81no—
167C22×C4×C47—81no—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×Q812yes—
174C22×C4×C47#4112yes—
175C22×C4×C47C2411yescharacteristic
176C2×C8×C47—21no—
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—
188C4⋊C4×C47—24no—
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—22no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—24no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
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—42no—
208C4⋊C4×C47—81no—
209C4⋊C4×C47C2×D412yes—
210C4⋊C4×C47C2×D412yes—
211C4⋊C4×C47C2×D412yes—
212C4⋊C4×C47C2×D412yes—
213C4⋊C4×C47C2×Q812yes—
214C22⋊C4×C47—24no—
215C22⋊C4×C47—24no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—81no—
219C42×C47—24no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—42no—
223C42×C47—81no—
224C42×C47C2×D412yes—
225C42×C47C2×D412yes—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47C22⋊Q812yes—
233C23×C47C22×D411yescharacteristic
234Q8×C47—22no—
235Q8×C47—22no—
236Q8×C47—41no—
237Q8×C47—41no—
238Q8×C47—84no—
239Q8×C47—84no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—22no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—21no—
251C2×C4×C47—22no—
252C2×C4×C47—21no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
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—84no—
281C2×C4×C47#12012yes—
282C2×C4×C47#12012yes—
283C2×C4×C47C22⋊Q812yes—
284C2×C4×C47C22×D411yescharacteristic
285C2×C4×C47C22×D411yescharacteristic
286C2×C4×C47C22×Q811yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C2×C4×C472−1+411yescharacteristic
289C2×C4×C472−1+411yescharacteristic
290C8×C47—41no—
291C8×C47—41no—
292C8×C47—41no—
293C8×C47—41no—
294#24310C4711yesmaximal, characteristic, direct product factor, Sylow
295C22×C47—22no—
296C22×C47—22no—
297C22×C47—22no—
298C22×C47—41no—
299C22×C47—41no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47C2×#12011yescharacteristic
303C22×C47C2×C22⋊Q811yescharacteristic
304C22×C47#53611yescharacteristic
305C22×C47#57711yescharacteristic
306C22×C47#57711yescharacteristic
307C22×C47#57711yescharacteristic
308C22×C47#57811yescharacteristic
309C4×C47—22no—
310C4×C47—22no—
311C4×C47—22no—
312C4×C47—42no—
313C4×C47—42no—
314C4×C47—41no—
315C4×C47—42no—
316C4×C47—42no—
317C4×C47—42no—
318C4×C47—41no—
319C4×C47—42no—
320C4×C47—81no—
321C4×C47—81no—
322C4×C47#54811yescharacteristic
323C4×C47#54811yescharacteristic
324C4×C47D4×Q811yescharacteristic
325C4×C47D4×Q811yescharacteristic
326C2×#544C2×C4711yescharacteristic
327C2×#479C2×C4711yescharacteristic, complemented
328C2×#475C2×C4711yescharacteristic, complemented
329#2323C2×C4711yescharacteristic
330#2059C2×C4711yescharacteristic, complemented
331#2058C2×C4711yescharacteristic, complemented
332#2026C2×C4711yescharacteristic, complemented
333#2024C2×C4711yescharacteristic, complemented
334#1989C2×C4711yescharacteristic, complemented
335#1987C2×C4711yescharacteristic, complemented
336#1873C2×C4711yescharacteristic
337#1872C2×C4711yescharacteristic
338#1854C2×C4711yescharacteristic
339#1853C2×C4711yescharacteristic
340#1798C2×C4711yescharacteristic
341C2×C47—42no—
342C2×C47#240911yescharacteristic
343C2×C47#300911yescharacteristic
344C2×C47#301311yescharacteristic
345C2×C47#308211yescharacteristic
346C2×C47#308411yescharacteristic
347C2×C47#324211yescharacteristic
348C2×C47#324411yescharacteristic
349#544—24no—
350#544—24no—
351C2×C4⋊Q8—21no—
352C2×C4⋊Q8C22×C4711yescharacteristic
353C2×C4⋊Q8C22×C4711yescharacteristic
354C2×#125—21no—
355C2×#125C22×C4711yescharacteristic
356C2×#125C22×C4711yescharacteristic
357C2×C22⋊Q8—21no—
358C2×C22⋊Q8—21no—
359C2×C22⋊Q8C22×C4711yescharacteristic
360C2×C4×Q8C22×C4711yescharacteristic
361C2×#117C22×C4711yescharacteristic
362C2×#117C22×C4711yescharacteristic
363C22×C4⋊C4C22×C4711yescharacteristic
364#479—24no—
365#475—24no—
366C2×#107C22×C4711yescharacteristic
367C2×#106C22×C4711yescharacteristic
368C2×#106C22×C4711yescharacteristic
369C2×#106C22×C4711yescharacteristic
370C2×C4⋊C8C22×C4711yescharacteristic
371C2×C4⋊C8C22×C4711yescharacteristic
372C2×#103C22×C4711yescharacteristic
373C2×#103C22×C4711yescharacteristic
374C2×#103C22×C4711yescharacteristic
375C2×#103C22×C4711yescharacteristic
376C2×C22⋊C8C22×C4711yescharacteristic
377C2×C22⋊C8C22×C4711yescharacteristic
378#391C22×C4711yescharacteristic
379#389—21no—
380#389C22×C4711yescharacteristic
381#388—21no—
382#388—21no—
383#387—21no—
384#380C22×C4711yescharacteristic
385C4×C4⋊C4C22×C4711yescharacteristic
386#340C22×C4711yescharacteristic
387#340C22×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
396C47#2431011yescharacteristic, direct product factor, Sylow
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8C23×C4711yescharacteristic
400C23×C4—21no—
401C23×C4C23×C4711yescharacteristic
402C22×C8C23×C4711yescharacteristic
403C22×C8C23×C4711yescharacteristic
404C22×C8C23×C4711yescharacteristic
405C22×C8C23×C4711yescharacteristic
406C4⋊Q8—28no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410C4⋊Q8D4×C4714yes—
411#125—28no—
412#125—22no—
413#125—22no—
414#125—22no—
415#125D4×C4714yes—
416C22⋊Q8—28no—
417C22⋊Q8—28no—
418C22⋊Q8—22no—
419C22⋊Q8Q8×C4714yescomplemented
420C4×Q8—22no—
421C4×Q8—22no—
422#117—22no—
423#117—22no—
424#117—22no—
425#117—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C4711yescharacteristic
439C2×C4⋊C4D4×C4711yescharacteristic
440C2×C4⋊C4C23×C4711yescharacteristic
441C2×C4⋊C4C23×C4711yescharacteristic
442C2×C4⋊C4C23×C4711yescharacteristic
443C2×C4⋊C4C23×C4711yescharacteristic
444C2×C4⋊C4C23×C4711yescharacteristic
445C2×C4⋊C4C23×C4711yescharacteristic
446C2×C4⋊C4C23×C4711yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4D4×C4711yescharacteristic
451C2×C22⋊C4D4×C4711yescharacteristic
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42C23×C4711yescharacteristic
456C2×C42C23×C4711yescharacteristic
457#107—22no—
458#106—22no—
459#106—22no—
460#106—22no—
461C4⋊C8—22no—
462C4⋊C8—22no—
463#103—22no—
464#103—22no—
465#103—22no—
466#103—22no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474C24C2×D4×C4711yescharacteristic
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—81no—
483C2×Q8—81no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8C2×Q8×C4712yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C4711yescharacteristic
503C22×C4C2×D4×C4711yescharacteristic
504C22×C4C2×D4×C4711yescharacteristic
505C22×C4C2×D4×C4711yescharacteristic
506C22×C4C2×D4×C4711yescharacteristic
507C22×C4C2×Q8×C4712yes—
508C22×C4#41×C4712yes—
509C22×C4C24×C4711yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
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—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4C2×D4×C4712yes—
544C4⋊C4C2×D4×C4712yes—
545C4⋊C4C2×D4×C4712yes—
546C4⋊C4C2×D4×C4712yes—
547C4⋊C4C2×Q8×C4712yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—81no—
553C42—24no—
554C42—21no—
555C42—21no—
556C42—42no—
557C42—81no—
558C42C2×D4×C4712yes—
559C42C2×D4×C4712yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C22⋊Q8×C4712yes—
567C23C22×D4×C4711yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573Q8—84no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
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—84no—
615C2×C4#120×C4712yes—
616C2×C4#120×C4712yes—
617C2×C4C22⋊Q8×C4712yes—
618C2×C4C22×D4×C4711yescharacteristic
619C2×C4C22×D4×C4711yescharacteristic
620C2×C4C22×Q8×C4711yescharacteristic
621C2×C4C2×#41×C4711yescharacteristic
622C2×C42−1+4×C4711yescharacteristic
623C2×C42−1+4×C4711yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#120×C4711yescharacteristic
636C22C2×C22⋊Q8×C4711yescharacteristic
637C22C47×#53611yescharacteristic
638C22C47×#57711yescharacteristic
639C22C47×#57711yescharacteristic
640C22C47×#57711yescharacteristic
641C22C47×#57811yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4C47×#54811yescharacteristic
656C4C47×#54811yescharacteristic
657C4D4×Q8×C4711yescharacteristic
658C4D4×Q8×C4711yescharacteristic
659C2—42no—
660C2C47×#240911yescharacteristic
661C2C47×#300911yescharacteristic
662C2C47×#301311yescharacteristic
663C2C47×#308211yescharacteristic
664C2C47×#308411yescharacteristic
665C2C47×#324211yescharacteristic
666C2C47×#324411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#479C2semidirect
3. C2×C47×#475C2semidirect
5. C47×#2059C2semidirect
6. C47×#2058C2semidirect
7. C47×#2026C2semidirect
8. C47×#2024C2semidirect
9. C47×#1989C2semidirect
10. C47×#1987C2semidirect
85. C22⋊Q8×C47Q8semidirect
294. #24310C47direct (N × H)
327. C2×#479C2×C47semidirect
328. C2×#475C2×C47semidirect
330. #2059C2×C47semidirect
331. #2058C2×C47semidirect
332. #2026C2×C47semidirect
333. #2024C2×C47semidirect
334. #1989C2×C47semidirect
335. #1987C2×C47semidirect
396. C47#24310direct (N × H)
419. C22⋊Q8Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5442
C2×C47×#4792
C2×C47×#4752
C47×#23232
C47×#20592
C47×#20582
C47×#20262
C47×#20242
C47×#19892
C47×#19872
C47×#18732
C47×#18722
C47×#18542
C47×#18532
C47×#17982
#2431047