Finite Group Databasebeta

← C47×#24865 #26064563

Subgroups — C47×#24865 #26064563

Order 12032.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#481C211yesmaximal, characteristic, complemented
2C22×#102×C47C211yesmaximal, characteristic, complemented
3C47×#2408C211yesmaximal, characteristic
4D4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
5C47×#2094C211yesmaximal, characteristic, complemented
6C47×#2071C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#1926C211yesmaximal, characteristic, complemented
10C47×#1926C211yesmaximal, characteristic, complemented
11C47×#1874C211yesmaximal, characteristic, complemented
12C47×#1869C211yesmaximal, characteristic, complemented
13C47×#1853C211yesmaximal, characteristic, complemented
14C47×#1807C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×#121×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×#120×C47—21no—
21C2×C4×D4×C47—21no—
22C2×C4×D4×C47C2211yescharacteristic
23C22×C4⋊C4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic, complemented
25C47×#481—24no—
26C2×#106×C47C2211yescharacteristic, complemented
27C2×#106×C47C2211yescharacteristic, complemented
28C2×#106×C47C2211yescharacteristic, complemented
29C2×#106×C47C2211yescharacteristic, complemented
30C2×#102×C47—24no—
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×C22⋊C8×C47C2211yescharacteristic, complemented
41C2×C22⋊C8×C47C2211yescharacteristic, complemented
42C47×#394—21no—
43C47×#392—21no—
44C47×#390C2211yescharacteristic
45C47×#390C2211yescharacteristic
46C47×#389—21no—
47C47×#385—21no—
48C47×#385—21no—
49C47×#384C2211yescharacteristic, complemented
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic, complemented
53C47×#379—21no—
54C4×C4⋊C4×C47C2211yescharacteristic, complemented
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C25×C47—21no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—22no—
68C22×D4×C47—22no—
69C22×D4×C47—41no—
70C22×D4×C47—41no—
71C22×D4×C47D411yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C22×C8×C47—22no—
79C22×C8×C47—22no—
80C22×C8×C47—41no—
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85#121×C47—22no—
86#121×C47—22no—
87#121×C47—41no—
88#121×C47—41no—
89#120×C47—44no—
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C4×D4×C47—44no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×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—41no—
100C2×C4⋊C4×C47—41no—
101C2×C4⋊C4×C47D411yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
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×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121#106×C47—22no—
122#106×C47—22no—
123#106×C47—41no—
124#106×C47—41no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—22no—
129#102×C47—22no—
130#102×C47—41no—
131#102×C47—41no—
132#102×C47D414yescomplemented
133C22⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135C22⋊C8×C47—41no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—42no—
143C24×C47—42no—
144C24×C47—42no—
145C24×C47—42no—
146C24×C47—42no—
147C24×C47—81no—
148C24×C47—81no—
149C24×C47C2×D411yescharacteristic
150C24×C47C2×D411yescharacteristic
151C2×D4×C47—22no—
152C2×D4×C47—22no—
153C2×D4×C47—28no—
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—21no—
164C2×D4×C47—44no—
165C2×D4×C47—44no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47—44no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—42no—
174C2×D4×C47—81no—
175C2×D4×C47—81no—
176C2×D4×C47SD1614yes—
177C2×D4×C47C2×D412yes—
178C2×D4×C47#4112yes—
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—42no—
196C22×C4×C47—42no—
197C22×C4×C47—42no—
198C22×C4×C47—42no—
199C22×C4×C47—81no—
200C22×C4×C47—81no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47#4112yes—
206C22×C4×C47#4112yes—
207C22×C4×C47C2411yescharacteristic
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—44no—
220C2×C8×C47C2×D412yes—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×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—42no—
234C4⋊C4×C47—42no—
235C4⋊C4×C47—42no—
236C4⋊C4×C47—81no—
237C4⋊C4×C47C2×D412yes—
238C22⋊C4×C47—22no—
239C22⋊C4×C47—22no—
240C22⋊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—81no—
248C22⋊C4×C47—81no—
249C42×C47—21no—
250C42×C47—21no—
251C42×C47—42no—
252C23×C47—21no—
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—22no—
263C23×C47—22no—
264C23×C47—48no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—84no—
278C23×C47—84no—
279C23×C47—84no—
280C23×C47—84no—
281C23×C47—84no—
282C23×C47—84no—
283C23×C47#12312yes—
284C23×C47C2×SD1612yes—
285C23×C47C2×SD1612yes—
286C23×C47AGL(1,ℤ/8)12yes—
287C23×C47C22×D411yescharacteristic
288D4×C47—28no—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—48no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
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—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—22no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
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—84no—
337C2×C4×C47—84no—
338C2×C4×C47#12312yes—
339C2×C4×C47C2×SD1612yes—
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C2×#4111yescharacteristic
342C2×C4×C47C2×#4111yescharacteristic
343C2×C4×C47C2×#4111yescharacteristic
344C2×C4×C47H(5,𝔽2)11yescharacteristic
345C2×C4×C47H(5,𝔽2)11yescharacteristic
346C8×C47—22no—
347C8×C47—41no—
348C8×C47—41no—
349C8×C47—41no—
350#24865C4711yesmaximal, characteristic, direct product factor, Sylow
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—816no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47#48114yescomplemented
380C22×C47C2×#12311yescharacteristic
381C22×C47D4211yescharacteristic
382C22×C47#54611yescharacteristic
383C22×C47C22×SD1611yescharacteristic
384C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C47#57611yescharacteristic
386C22×C47#57711yescharacteristic
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—41no—
390C4×C47—41no—
391C4×C47—42no—
392C4×C47—81no—
393C4×C47—81no—
394C4×C47—81no—
395C4×C47—81no—
396C4×C47—81no—
397C4×C47#52511yescharacteristic
398C4×C47#53811yescharacteristic
399C4×C47#54611yescharacteristic
400C4×C47#55111yescharacteristic
401C2×#481C2×C4711yescharacteristic, complemented
402C22×#102C2×C4711yescharacteristic, complemented
403#2408C2×C4711yescharacteristic
404D4×C4⋊C4C2×C4711yescharacteristic, complemented
405#2094C2×C4711yescharacteristic, complemented
406#2071C2×C4711yescharacteristic, complemented
407#2034C2×C4711yescharacteristic, complemented
408#2034C2×C4711yescharacteristic, complemented
409#1926C2×C4711yescharacteristic, complemented
410#1926C2×C4711yescharacteristic, complemented
411#1874C2×C4711yescharacteristic, complemented
412#1869C2×C4711yescharacteristic, complemented
413#1853C2×C4711yescharacteristic, complemented
414#1807C2×C4711yescharacteristic, complemented
415#1786C2×C4711yescharacteristic, complemented
416C2×C47—24no—
417C2×C47—42no—
418C2×C47—82no—
419C2×C47—82no—
420C2×C47#241811yescharacteristic
421C2×C47C2×#48111yescharacteristic
422C2×C47#309611yescharacteristic
423C2×C47#326411yescharacteristic
424C2×C47D4×SD1611yescharacteristic
425C2×C47#329511yescharacteristic
426C2×C47#330611yescharacteristic
427C23×D4C22×C4711yescharacteristic
428C23×C8C22×C4711yescharacteristic
429C2×#121C22×C4711yescharacteristic
430C2×#121C22×C4711yescharacteristic
431C2×#120—21no—
432C2×C4×D4—21no—
433C2×C4×D4C22×C4711yescharacteristic
434C22×C4⋊C4C22×C4711yescharacteristic
435C22×C4⋊C4C22×C4711yescharacteristic, complemented
436#481—24no—
437C2×#106C22×C4711yescharacteristic, complemented
438C2×#106C22×C4711yescharacteristic, complemented
439C2×#106C22×C4711yescharacteristic, complemented
440C2×#106C22×C4711yescharacteristic, complemented
441C2×#102—24no—
442C2×#102C22×C4711yescharacteristic
443C2×#102C22×C4711yescharacteristic
444C2×#102C22×C4711yescharacteristic
445C2×#102C22×C4711yescharacteristic
446C2×#102C22×C4711yescharacteristic
447C2×#102C22×C4711yescharacteristic
448C2×#102C22×C4711yescharacteristic
449C2×#102C22×C4711yescharacteristic
450C2×C22⋊C8C22×C4711yescharacteristic
451C2×C22⋊C8C22×C4711yescharacteristic, complemented
452C2×C22⋊C8C22×C4711yescharacteristic, complemented
453#394—21no—
454#392—21no—
455#390C22×C4711yescharacteristic
456#390C22×C4711yescharacteristic
457#389—21no—
458#385—21no—
459#385—21no—
460#384C22×C4711yescharacteristic, complemented
461#380C22×C4711yescharacteristic
462#380C22×C4711yescharacteristic
463#380C22×C4711yescharacteristic, complemented
464#379—21no—
465C4×C4⋊C4C22×C4711yescharacteristic, complemented
466#340C22×C4711yescharacteristic, complemented
467#340C22×C4711yescharacteristic, complemented
468#340C22×C4711yescharacteristic, complemented
469#340C22×C4711yescharacteristic, complemented
470#336C22×C4711yescharacteristic, complemented
471#336C22×C4711yescharacteristic, complemented
472C47#2486511yescharacteristic, direct product factor, Sylow
473C25—21no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4D4×C4711yescharacteristic
484C22×D4C23×C4711yescharacteristic
485C22×D4C23×C4711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C4711yescharacteristic
489C23×C4C23×C4711yescharacteristic
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—41no—
493C22×C8C23×C4711yescharacteristic
494C22×C8C23×C4711yescharacteristic
495C22×C8C23×C4711yescharacteristic
496C22×C8C23×C4711yescharacteristic
497#121—22no—
498#121—22no—
499#121—41no—
500#121—41no—
501#120—44no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—44no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4D4×C4711yescharacteristic
514C2×C4⋊C4C23×C4711yescharacteristic
515C2×C4⋊C4C23×C4711yescharacteristic
516C2×C4⋊C4C23×C4711yescharacteristic
517C2×C4⋊C4C23×C4711yescharacteristic
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
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⋊C4D4×C4711yescharacteristic
530C2×C22⋊C4D4×C4711yescharacteristic
531C2×C42—21no—
532C2×C42C23×C4711yescharacteristic
533#106—22no—
534#106—22no—
535#106—41no—
536#106—41no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—41no—
543#102—41no—
544#102D4×C4714yescomplemented
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×D4×C4711yescharacteristic
562C24C2×D4×C4711yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—28no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4SD16×C4714yes—
589C2×D4C2×D4×C4712yes—
590C2×D4#41×C4712yes—
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—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C4711yescharacteristic
614C22×C4C2×D4×C4711yescharacteristic
615C22×C4C2×D4×C4711yescharacteristic
616C22×C4C2×D4×C4711yescharacteristic
617C22×C4#41×C4712yes—
618C22×C4#41×C4712yes—
619C22×C4C24×C4711yescharacteristic
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8C2×D4×C4712yes—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4C2×D4×C4712yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#123×C4712yes—
696C23C2×SD16×C4712yes—
697C23C2×SD16×C4712yes—
698C23AGL(1,ℤ/8)×C4712yes—
699C23C22×D4×C4711yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
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—84no—
749C2×C4—84no—
750C2×C4#123×C4712yes—
751C2×C4C2×SD16×C4712yes—
752C2×C4C22×D4×C4711yescharacteristic
753C2×C4C2×#41×C4711yescharacteristic
754C2×C4C2×#41×C4711yescharacteristic
755C2×C4C2×#41×C4711yescharacteristic
756C2×C4H(5,𝔽2)×C4711yescharacteristic
757C2×C4H(5,𝔽2)×C4711yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C47×#48114yescomplemented
791C22C2×#123×C4711yescharacteristic
792C22D42×C4711yescharacteristic
793C22C47×#54611yescharacteristic
794C22C22×SD16×C4711yescharacteristic
795C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
796C22C47×#57611yescharacteristic
797C22C47×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4C47×#52511yescharacteristic
809C4C47×#53811yescharacteristic
810C4C47×#54611yescharacteristic
811C4C47×#55111yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2C47×#241811yescharacteristic
817C2C2×C47×#48111yescharacteristic
818C2C47×#309611yescharacteristic
819C2C47×#326411yescharacteristic
820C2D4×SD16×C4711yescharacteristic
821C2C47×#329511yescharacteristic
822C2C47×#330611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#481C2semidirect
2. C22×#102×C47C2semidirect
4. D4×C4⋊C4×C47C2semidirect
5. C47×#2094C2semidirect
6. C47×#2071C2semidirect
7. C47×#2034C2semidirect
8. C47×#2034C2semidirect
9. C47×#1926C2semidirect
10. C47×#1926C2semidirect
11. C47×#1874C2semidirect
12. C47×#1869C2semidirect
13. C47×#1853C2semidirect
14. C47×#1807C2semidirect
15. C47×#1786C2semidirect
24. C22×C4⋊C4×C47C22semidirect
26. C2×#106×C47C22semidirect
27. C2×#106×C47C22semidirect
28. C2×#106×C47C22semidirect
29. C2×#106×C47C22semidirect
40. C2×C22⋊C8×C47C22semidirect
41. C2×C22⋊C8×C47C22semidirect
49. C47×#384C22semidirect
52. C47×#380C22semidirect
54. C4×C4⋊C4×C47C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
132. #102×C47D4semidirect
350. #24865C47direct (N × H)
379. C22×C47#481semidirect
401. C2×#481C2×C47semidirect
402. C22×#102C2×C47semidirect
404. D4×C4⋊C4C2×C47semidirect
405. #2094C2×C47semidirect
406. #2071C2×C47semidirect
407. #2034C2×C47semidirect
408. #2034C2×C47semidirect
409. #1926C2×C47semidirect
410. #1926C2×C47semidirect
411. #1874C2×C47semidirect
412. #1869C2×C47semidirect
413. #1853C2×C47semidirect
414. #1807C2×C47semidirect
415. #1786C2×C47semidirect
435. C22×C4⋊C4C22×C47semidirect
437. C2×#106C22×C47semidirect
438. C2×#106C22×C47semidirect
439. C2×#106C22×C47semidirect
440. C2×#106C22×C47semidirect
451. C2×C22⋊C8C22×C47semidirect
452. C2×C22⋊C8C22×C47semidirect
460. #384C22×C47semidirect
463. #380C22×C47semidirect
465. C4×C4⋊C4C22×C47semidirect
466. #340C22×C47semidirect
467. #340C22×C47semidirect
468. #340C22×C47semidirect
469. #340C22×C47semidirect
470. #336C22×C47semidirect
471. #336C22×C47semidirect
472. C47#24865direct (N × H)
544. #102D4×C47semidirect
790. C22C47×#481semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4812
C22×#102×C472
C47×#24082
D4×C4⋊C4×C472
C47×#20942
C47×#20712
C47×#20342
C47×#19262
C47×#18742
C47×#18692
C47×#18532
C47×#18072
C47×#17862
#2486547