Finite Group Databasebeta

← C47×#32709 #26072407

Subgroups — C47×#32709 #26072407

Order 12032.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2848C211yesmaximal, characteristic, complemented
2C47×#2847C211yesmaximal, characteristic
3C47×#2077C211yesmaximal, characteristic, complemented
4C47×#2076C211yesmaximal, characteristic, complemented
5C47×#2075C211yesmaximal, characteristic, complemented
6C47×#2036C211yesmaximal, characteristic, complemented
7C47×#2036C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2034C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#2033C211yesmaximal, characteristic, complemented
12C47×#2000C211yesmaximal, characteristic, complemented
13C47×#2000C211yesmaximal, characteristic, complemented
14C47×#2000C211yesmaximal, characteristic, complemented
15C47×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic, complemented
18C2×C22⋊Q8×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#120×C47—21no—
25C2×#107×C47C2211yescharacteristic, complemented
26C2×#107×C47C2211yescharacteristic, complemented
27C2×#106×C47C2211yescharacteristic, complemented
28C2×#103×C47C2211yescharacteristic, complemented
29C2×#103×C47C2211yescharacteristic, complemented
30C2×#103×C47C2211yescharacteristic, complemented
31C2×#102×C47C2211yescharacteristic, complemented
32C2×#102×C47C2211yescharacteristic, complemented
33C2×#102×C47C2211yescharacteristic, complemented
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C47×#386—21no—
41C47×#386—21no—
42C47×#386—21no—
43C47×#385—21no—
44C47×#385—21no—
45C47×#385—21no—
46C47×#380C2211yescharacteristic
47C47×#380C2211yescharacteristic
48C47×#380C2211yescharacteristic
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#379—21no—
53C47×#340C2211yescharacteristic, complemented
54C47×#340C2211yescharacteristic, complemented
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C25×C47D411yescharacteristic
60C22×Q8×C47C2311yescharacteristic
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47C2311yescharacteristic
65C23×C4×C47—41no—
66C23×C4×C47—41no—
67C23×C4×C47—41no—
68C23×C4×C47—41no—
69C23×C4×C47—41no—
70C23×C4×C47—41no—
71C23×C4×C47D411yescharacteristic
72C23×C4×C47D411yescharacteristic
73C23×C4×C47D411yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C2×SD16×C47—41no—
78C2×SD16×C47—41no—
79C2×SD16×C47—41no—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22⋊Q8×C47—41no—
85C22⋊Q8×C47—41no—
86C22⋊Q8×C47—41no—
87C22⋊Q8×C47—41no—
88C22⋊Q8×C47—41no—
89C22⋊Q8×C47—41no—
90#121×C47—41no—
91#121×C47—41no—
92#121×C47—41no—
93#121×C47—41no—
94#121×C47—41no—
95#121×C47—41no—
96#120×C47—44no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118#107×C47—41no—
119#107×C47—41no—
120#106×C47—41no—
121#103×C47—41no—
122#103×C47—41no—
123#103×C47—41no—
124#102×C47—41no—
125#102×C47—41no—
126#102×C47—41no—
127C22⋊C8×C47—41no—
128C22⋊C8×C47—41no—
129C22⋊C8×C47—41no—
130C22⋊C8×C47—41no—
131C22⋊C8×C47—41no—
132C22⋊C8×C47—41no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—21no—
143C24×C47—41no—
144C24×C47—41no—
145C24×C47—41no—
146C24×C47—41no—
147C24×C47C2×D411yescharacteristic
148C24×C47C2×D411yescharacteristic
149C24×C47C2×D411yescharacteristic
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×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—42no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—41no—
197C22×C4×C47—41no—
198C22×C4×C47—41no—
199C22×C4×C47—41no—
200C22×C4×C47—41no—
201C22×C4×C47—41no—
202C22×C4×C47—41no—
203C22×C4×C47—41no—
204C22×C4×C47—41no—
205C22×C4×C47—44no—
206C22×C4×C47—44no—
207C22×C4×C47—44no—
208C22×C4×C47—44no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2411yescharacteristic
213SD16×C47—44no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—42no—
239C4⋊C4×C47—42no—
240C4⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—42no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—42no—
246C22⋊C4×C47—42no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—44no—
272C23×C47—44no—
273C23×C47—44no—
274C23×C47—44no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47#13512yes—
286C23×C47AGL(1,ℤ/8)12yes—
287C23×C47#13712yes—
288C23×C47C22×D411yescharacteristic
289Q8×C47—41no—
290Q8×C47—41no—
291Q8×C47—41no—
292Q8×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—84no—
298D4×C47—84no—
299D4×C47—84no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
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—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47H(5,𝔽2)11yescharacteristic
346C2×C4×C47H(5,𝔽2)11yescharacteristic
347C2×C4×C47H(5,𝔽2)11yescharacteristic
348C2×C4×C47H(5,𝔽2)11yescharacteristic
349C2×C4×C47H(5,𝔽2)11yescharacteristic
350C2×C4×C47H(5,𝔽2)11yescharacteristic
351C8×C47—41no—
352C8×C47—41no—
353C8×C47—41no—
354C8×C47—41no—
355#32709C4711yesmaximal, characteristic, direct product factor, Sylow
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—416no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47#53411yescharacteristic
386C22×C47#53411yescharacteristic
387C22×C47#53411yescharacteristic
388C22×C47C2×#13511yescharacteristic
389C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C47C2×#13711yescharacteristic
391C22×C47#57511yescharacteristic
392C4×C47—41no—
393C4×C47—41no—
394C4×C47—41no—
395C4×C47—81no—
396C4×C47—81no—
397C4×C47—81no—
398C4×C47—81no—
399C4×C47—81no—
400C4×C47—81no—
401C4×C47—81no—
402C4×C47#56011yescharacteristic
403C4×C47#56011yescharacteristic
404C4×C47#56011yescharacteristic
405C4×C47H(3,𝔽4)11yescharacteristic
406#2848C2×C4711yescharacteristic, complemented
407#2847C2×C4711yescharacteristic
408#2077C2×C4711yescharacteristic, complemented
409#2076C2×C4711yescharacteristic, complemented
410#2075C2×C4711yescharacteristic, complemented
411#2036C2×C4711yescharacteristic, complemented
412#2036C2×C4711yescharacteristic, complemented
413#2035C2×C4711yescharacteristic, complemented
414#2034C2×C4711yescharacteristic, complemented
415#2033C2×C4711yescharacteristic, complemented
416#2033C2×C4711yescharacteristic, complemented
417#2000C2×C4711yescharacteristic, complemented
418#2000C2×C4711yescharacteristic, complemented
419#2000C2×C4711yescharacteristic, complemented
420#1779C2×C4711yescharacteristic, complemented
421C2×C47—42no—
422C2×C47—42no—
423C2×C47—42no—
424C2×C47—161no—
425C2×C47#281211yescharacteristic
426C2×C47#318811yescharacteristic
427C2×C47#319011yescharacteristic
428C2×C47#319111yescharacteristic
429C2×C47#319311yescharacteristic
430C2×C47#319411yescharacteristic
431C2×C47#319611yescharacteristic
432C24×C4C22×C4711yescharacteristic
433C22×SD16C22×C4711yescharacteristic, complemented
434C2×C22⋊Q8C22×C4711yescharacteristic
435C2×C22⋊Q8C22×C4711yescharacteristic
436C2×C22⋊Q8C22×C4711yescharacteristic
437C2×#121C22×C4711yescharacteristic
438C2×#121C22×C4711yescharacteristic
439C2×#121C22×C4711yescharacteristic
440C2×#120—21no—
441C2×#107C22×C4711yescharacteristic, complemented
442C2×#107C22×C4711yescharacteristic, complemented
443C2×#106C22×C4711yescharacteristic, complemented
444C2×#103C22×C4711yescharacteristic, complemented
445C2×#103C22×C4711yescharacteristic, complemented
446C2×#103C22×C4711yescharacteristic, complemented
447C2×#102C22×C4711yescharacteristic, complemented
448C2×#102C22×C4711yescharacteristic, complemented
449C2×#102C22×C4711yescharacteristic, complemented
450C2×C22⋊C8C22×C4711yescharacteristic
451C2×C22⋊C8C22×C4711yescharacteristic
452C2×C22⋊C8C22×C4711yescharacteristic
453C2×C22⋊C8C22×C4711yescharacteristic
454C2×C22⋊C8C22×C4711yescharacteristic
455C2×C22⋊C8C22×C4711yescharacteristic
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#380C22×C4711yescharacteristic
463#380C22×C4711yescharacteristic
464#380C22×C4711yescharacteristic
465#380C22×C4711yescharacteristic
466#380C22×C4711yescharacteristic
467#380C22×C4711yescharacteristic
468#379—21no—
469#340C22×C4711yescharacteristic, complemented
470#340C22×C4711yescharacteristic, complemented
471#340C22×C4711yescharacteristic, complemented
472#340C22×C4711yescharacteristic, complemented
473#340C22×C4711yescharacteristic, complemented
474#340C22×C4711yescharacteristic, complemented
475C47#3270911yescharacteristic, direct product factor, Sylow
476C25D4×C4711yescharacteristic
477C22×Q8C23×C4711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4C23×C4711yescharacteristic
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4D4×C4711yescharacteristic
489C23×C4D4×C4711yescharacteristic
490C23×C4D4×C4711yescharacteristic
491C23×C4C23×C4711yescharacteristic
492C23×C4C23×C4711yescharacteristic
493C23×C4C23×C4711yescharacteristic
494C2×SD16—41no—
495C2×SD16—41no—
496C2×SD16—41no—
497C22×C8C23×C4711yescharacteristic
498C22×C8C23×C4711yescharacteristic
499C22×C8C23×C4711yescharacteristic
500C22×C8C23×C4711yescharacteristic
501C22⋊Q8—41no—
502C22⋊Q8—41no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506C22⋊Q8—41no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—41no—
513#120—44no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4C23×C4711yescharacteristic
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4711yescharacteristic
520C2×C4⋊C4C23×C4711yescharacteristic
521C2×C4⋊C4C23×C4711yescharacteristic
522C2×C4⋊C4C23×C4711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535#107—41no—
536#107—41no—
537#106—41no—
538#103—41no—
539#103—41no—
540#103—41no—
541#102—41no—
542#102—41no—
543#102—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×D4×C4711yescharacteristic
565C24C2×D4×C4711yescharacteristic
566C24C2×D4×C4711yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C4711yescharacteristic
627C22×C4C2×D4×C4711yescharacteristic
628C22×C4C2×D4×C4711yescharacteristic
629C22×C4C24×C4711yescharacteristic
630SD16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#135×C4712yes—
703C23AGL(1,ℤ/8)×C4712yes—
704C23#137×C4712yes—
705C23C22×D4×C4711yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4H(5,𝔽2)×C4711yescharacteristic
763C2×C4H(5,𝔽2)×C4711yescharacteristic
764C2×C4H(5,𝔽2)×C4711yescharacteristic
765C2×C4H(5,𝔽2)×C4711yescharacteristic
766C2×C4H(5,𝔽2)×C4711yescharacteristic
767C2×C4H(5,𝔽2)×C4711yescharacteristic
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C47×#53411yescharacteristic
802C22C47×#53411yescharacteristic
803C22C47×#53411yescharacteristic
804C22C2×#135×C4711yescharacteristic
805C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
806C22C2×#137×C4711yescharacteristic
807C22C47×#57511yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C47×#56011yescharacteristic
819C4C47×#56011yescharacteristic
820C4C47×#56011yescharacteristic
821C4C47×H(3,𝔽4)11yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2C47×#281211yescharacteristic
827C2C47×#318811yescharacteristic
828C2C47×#319011yescharacteristic
829C2C47×#319111yescharacteristic
830C2C47×#319311yescharacteristic
831C2C47×#319411yescharacteristic
832C2C47×#319611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2848C2semidirect
3. C47×#2077C2semidirect
4. C47×#2076C2semidirect
5. C47×#2075C2semidirect
6. C47×#2036C2semidirect
7. C47×#2036C2semidirect
8. C47×#2035C2semidirect
9. C47×#2034C2semidirect
10. C47×#2033C2semidirect
11. C47×#2033C2semidirect
12. C47×#2000C2semidirect
13. C47×#2000C2semidirect
14. C47×#2000C2semidirect
15. C47×#1779C2semidirect
17. C22×SD16×C47C22semidirect
25. C2×#107×C47C22semidirect
26. C2×#107×C47C22semidirect
27. C2×#106×C47C22semidirect
28. C2×#103×C47C22semidirect
29. C2×#103×C47C22semidirect
30. C2×#103×C47C22semidirect
31. C2×#102×C47C22semidirect
32. C2×#102×C47C22semidirect
33. C2×#102×C47C22semidirect
53. C47×#340C22semidirect
54. C47×#340C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
355. #32709C47direct (N × H)
406. #2848C2×C47semidirect
408. #2077C2×C47semidirect
409. #2076C2×C47semidirect
410. #2075C2×C47semidirect
411. #2036C2×C47semidirect
412. #2036C2×C47semidirect
413. #2035C2×C47semidirect
414. #2034C2×C47semidirect
415. #2033C2×C47semidirect
416. #2033C2×C47semidirect
417. #2000C2×C47semidirect
418. #2000C2×C47semidirect
419. #2000C2×C47semidirect
420. #1779C2×C47semidirect
433. C22×SD16C22×C47semidirect
441. C2×#107C22×C47semidirect
442. C2×#107C22×C47semidirect
443. C2×#106C22×C47semidirect
444. C2×#103C22×C47semidirect
445. C2×#103C22×C47semidirect
446. C2×#103C22×C47semidirect
447. C2×#102C22×C47semidirect
448. C2×#102C22×C47semidirect
449. C2×#102C22×C47semidirect
469. #340C22×C47semidirect
470. #340C22×C47semidirect
471. #340C22×C47semidirect
472. #340C22×C47semidirect
473. #340C22×C47semidirect
474. #340C22×C47semidirect
475. C47#32709direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28482
C47×#28472
C47×#20772
C47×#20762
C47×#20752
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#20002
C47×#17792
#3270947