Finite Group Databasebeta

← C47×#25088 #26064786

Subgroups — C47×#25088 #26064786

Order 12032.

1310 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#465C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#447C211yesmaximal, characteristic
4C22×#102×C47C211yesmaximal, characteristic, complemented
5C47×#2435C211yesmaximal, characteristic, complemented
6C47×#2361C211yesmaximal, characteristic, complemented
7C47×#2065C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1983C211yesmaximal, characteristic, complemented
12C47×#1926C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1872C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic, complemented
18C22×D8×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C23×C8×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47—21no—
26C2×C4×D4×C47C2211yescharacteristic, complemented
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#465—24no—
29C47×#463—24no—
30C47×#447—24no—
31C2×#106×C47C2211yescharacteristic, complemented
32C2×C4⋊C8×C47C2211yescharacteristic, complemented
33C2×C4⋊C8×C47C2211yescharacteristic, complemented
34C2×#103×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#102×C47—24no—
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic, complemented
45C2×C22⋊C8×C47C2211yescharacteristic
46C47×#394—21no—
47C47×#394—21no—
48C47×#390C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic, complemented
51C47×#389C2211yescharacteristic, complemented
52C47×#388—21no—
53C47×#386—21no—
54C47×#385—21no—
55C47×#379—21no—
56C47×#379—21no—
57C4×C4⋊C4×C47C2211yescharacteristic, complemented
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—22no—
69C22×D4×C47—21no—
70C22×D4×C47—22no—
71C22×D4×C47—41no—
72C22×D4×C47—41no—
73C22×D4×C47C2311yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47C2311yescharacteristic
79C2×SD16×C47—22no—
80C2×SD16×C47—22no—
81C2×SD16×C47—41no—
82C2×D8×C47—22no—
83C2×D8×C47—22no—
84C2×D8×C47—22no—
85C2×D8×C47—22no—
86C2×D8×C47—41no—
87C2×D8×C47—41no—
88C22×C8×C47—22no—
89C22×C8×C47—22no—
90C22×C8×C47—41no—
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95#124×C47—22no—
96#124×C47—22no—
97#124×C47—41no—
98#124×C47—41no—
99C22⋊Q8×C47—22no—
100C22⋊Q8×C47—22no—
101#121×C47—22no—
102#121×C47D414yes—
103C4×D4×C47—22no—
104C4×D4×C47—41no—
105C4×D4×C47—44no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—41no—
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133#106×C47—22no—
134C4⋊C8×C47—22no—
135C4⋊C8×C47—41no—
136#103×C47—22no—
137#103×C47—22no—
138#103×C47—41no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—22no—
144#102×C47—22no—
145#102×C47D414yescomplemented
146C22⋊C8×C47—22no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47D411yescharacteristic
150#95×C47D411yescharacteristic
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—42no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—81no—
160C24×C47—81no—
161C24×C47C2×D411yescharacteristic
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×D4×C47—28no—
169C2×D4×C47—24no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—44no—
186C2×D4×C47—44no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—44no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—42no—
193C2×D4×C47C2×D412yes—
194C2×D4×C47C2×D412yes—
195C2×D4×C47#4112yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—42no—
206C22×C4×C47—42no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—81no—
210C22×C4×C47—81no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47#4112yes—
218C22×C4×C47C2411yescharacteristic
219SD16×C47—44no—
220D8×C47—44no—
221D8×C47—44no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—44no—
234C2×C8×C47C2×D412yes—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—42no—
242C4⋊C4×C47—42no—
243C4⋊C4×C47—42no—
244C4⋊C4×C47C2×D412yes—
245C4⋊C4×C47C2×D412yes—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—24no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—81no—
257C22⋊C4×C47—81no—
258C22⋊C4×C47—81no—
259C22⋊C4×C47—81no—
260C22⋊C4×C47—81no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—42no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—48no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—84no—
293C23×C47—84no—
294C23×C47—84no—
295C23×C47—84no—
296C23×C47—84no—
297C23×C47—84no—
298C23×C47#12112yes—
299C23×C47#13512yes—
300C23×C47AGL(1,ℤ/8)12yes—
301C23×C47C22×D411yescharacteristic
302Q8×C47—41no—
303Q8×C47—41no—
304Q8×C47—41no—
305Q8×C47—41no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—48no—
313D4×C47—48no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—41no—
319D4×C47—41no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—22no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—84no—
354C2×C4×C47—84no—
355C2×C4×C47#12112yes—
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C2×#4111yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47H(5,𝔽2)11yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C8×C47—22no—
363C8×C47—41no—
364C8×C47—41no—
365C8×C47—41no—
366#25088C4711yesmaximal, characteristic, direct product factor, Sylow
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—816no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47#46314yescomplemented
396C22×C47C2×#12111yescharacteristic
397C22×C47D4211yescharacteristic
398C22×C47#54611yescharacteristic
399C22×C47C2×#13511yescharacteristic
400C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C47#57611yescharacteristic
402C22×C47#57711yescharacteristic
403C4×C47—22no—
404C4×C47—41no—
405C4×C47—42no—
406C4×C47—41no—
407C4×C47—42no—
408C4×C47—41no—
409C4×C47—41no—
410C4×C47—81no—
411C4×C47—81no—
412C4×C47—81no—
413C4×C47#52511yescharacteristic
414C4×C47#53811yescharacteristic
415C4×C47D4211yescharacteristic
416C4×C47#54611yescharacteristic
417C2×#465C2×C4711yescharacteristic, complemented
418C2×#463C2×C4711yescharacteristic, complemented
419C2×#447C2×C4711yescharacteristic
420C22×#102C2×C4711yescharacteristic, complemented
421#2435C2×C4711yescharacteristic, complemented
422#2361C2×C4711yescharacteristic, complemented
423#2065C2×C4711yescharacteristic, complemented
424#2054C2×C4711yescharacteristic, complemented
425#2042C2×C4711yescharacteristic, complemented
426#2012C2×C4711yescharacteristic, complemented
427#1983C2×C4711yescharacteristic, complemented
428#1926C2×C4711yescharacteristic, complemented
429#1879C2×C4711yescharacteristic, complemented
430#1872C2×C4711yescharacteristic, complemented
431#1850C2×C4711yescharacteristic, complemented
432C2×C47—24no—
433C2×C47—82no—
434C2×C47—82no—
435C2×C47—82no—
436C2×C47#242411yescharacteristic
437C2×C47C2×#46311yescharacteristic
438C2×C47#304511yescharacteristic
439C2×C47#326411yescharacteristic
440C2×C47#328211yescharacteristic
441C2×C47#329711yescharacteristic
442C2×C47#330611yescharacteristic
443C23×D4C22×C4711yescharacteristic
444C22×SD16C22×C4711yescharacteristic, complemented
445C22×D8C22×C4711yescharacteristic
446C22×D8C22×C4711yescharacteristic
447C23×C8C22×C4711yescharacteristic
448C2×#124C22×C4711yescharacteristic
449C2×#124C22×C4711yescharacteristic
450C2×C22⋊Q8C22×C4711yescharacteristic
451C2×#121C22×C4711yescharacteristic
452C2×C4×D4—21no—
453C2×C4×D4C22×C4711yescharacteristic, complemented
454C22×C4⋊C4C22×C4711yescharacteristic
455#465—24no—
456#463—24no—
457#447—24no—
458C2×#106C22×C4711yescharacteristic, complemented
459C2×C4⋊C8C22×C4711yescharacteristic, complemented
460C2×C4⋊C8C22×C4711yescharacteristic, complemented
461C2×#103C22×C4711yescharacteristic, complemented
462C2×#103C22×C4711yescharacteristic, complemented
463C2×#103C22×C4711yescharacteristic, complemented
464C2×#102—24no—
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic
467C2×#102C22×C4711yescharacteristic
468C2×#102C22×C4711yescharacteristic
469C2×#102C22×C4711yescharacteristic
470C2×#102C22×C4711yescharacteristic
471C2×#102C22×C4711yescharacteristic, complemented
472C2×C22⋊C8C22×C4711yescharacteristic
473#394—21no—
474#394—21no—
475#390C22×C4711yescharacteristic
476#390C22×C4711yescharacteristic
477#390C22×C4711yescharacteristic, complemented
478#389C22×C4711yescharacteristic, complemented
479#388—21no—
480#386—21no—
481#385—21no—
482#379—21no—
483#379—21no—
484C4×C4⋊C4C22×C4711yescharacteristic, complemented
485C4×C22⋊C4C22×C4711yescharacteristic
486#340C22×C4711yescharacteristic, complemented
487#340C22×C4711yescharacteristic, complemented
488#336C22×C4711yescharacteristic, complemented
489#336C22×C4711yescharacteristic, complemented
490C47#2508811yescharacteristic, direct product factor, Sylow
491C25—21no—
492C22×Q8C23×C4711yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C4711yescharacteristic
502C22×D4C23×C4711yescharacteristic
503C22×D4C23×C4711yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C4711yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—41no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8C23×C4711yescharacteristic
520C22×C8C23×C4711yescharacteristic
521C22×C8C23×C4711yescharacteristic
522C22×C8C23×C4711yescharacteristic
523#124—22no—
524#124—22no—
525#124—41no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529#121—22no—
530#121D4×C4714yes—
531C4×D4—22no—
532C4×D4—41no—
533C4×D4—44no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C4⋊C4C23×C4711yescharacteristic
542C2×C4⋊C4C23×C4711yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4D4×C4711yescharacteristic
557C2×C22⋊C4D4×C4711yescharacteristic
558C2×C42—21no—
559C2×C42C23×C4711yescharacteristic
560C2×C42C23×C4711yescharacteristic
561#106—22no—
562C4⋊C8—22no—
563C4⋊C8—41no—
564#103—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102D4×C4714yescomplemented
574C22⋊C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C4711yescharacteristic
578#95D4×C4711yescharacteristic
579C24—21no—
580C24—21no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C4711yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×D4—28no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C4712yes—
622C2×D4C2×D4×C4712yes—
623C2×D4#41×C4712yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4C2×D4×C4711yescharacteristic
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4C2×D4×C4711yescharacteristic
642C22×C4C2×D4×C4711yescharacteristic
643C22×C4C2×D4×C4711yescharacteristic
644C22×C4C2×D4×C4712yes—
645C22×C4#41×C4712yes—
646C22×C4C24×C4711yescharacteristic
647SD16—44no—
648D8—44no—
649D8—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8C2×D4×C4712yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C4712yes—
673C4⋊C4C2×D4×C4712yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—48no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C4712yes—
727C23#135×C4712yes—
728C23AGL(1,ℤ/8)×C4712yes—
729C23C22×D4×C4711yescharacteristic
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4#121×C4712yes—
784C2×C4C22×D4×C4711yescharacteristic
785C2×C4C22×D4×C4711yescharacteristic
786C2×C4C2×#41×C4711yescharacteristic
787C2×C4C2×#41×C4711yescharacteristic
788C2×C4H(5,𝔽2)×C4711yescharacteristic
789C2×C4H(5,𝔽2)×C4711yescharacteristic
790C8—22no—
791C8—41no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—816no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22C47×#46314yescomplemented
823C22C2×#121×C4711yescharacteristic
824C22D42×C4711yescharacteristic
825C22C47×#54611yescharacteristic
826C22C2×#135×C4711yescharacteristic
827C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
828C22C47×#57611yescharacteristic
829C22C47×#57711yescharacteristic
830C4—22no—
831C4—42no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C47×#52511yescharacteristic
841C4C47×#53811yescharacteristic
842C4D42×C4711yescharacteristic
843C4C47×#54611yescharacteristic
844C2—24no—
845C2—82no—
846C2—82no—
847C2—82no—
848C2C47×#242411yescharacteristic
849C2C2×C47×#46311yescharacteristic
850C2C47×#304511yescharacteristic
851C2C47×#326411yescharacteristic
852C2C47×#328211yescharacteristic
853C2C47×#329711yescharacteristic
854C2C47×#330611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#465C2semidirect
2. C2×C47×#463C2semidirect
4. C22×#102×C47C2semidirect
5. C47×#2435C2semidirect
6. C47×#2361C2semidirect
7. C47×#2065C2semidirect
8. C47×#2054C2semidirect
9. C47×#2042C2semidirect
10. C47×#2012C2semidirect
11. C47×#1983C2semidirect
12. C47×#1926C2semidirect
13. C47×#1879C2semidirect
14. C47×#1872C2semidirect
15. C47×#1850C2semidirect
17. C22×SD16×C47C22semidirect
26. C2×C4×D4×C47C22semidirect
31. C2×#106×C47C22semidirect
32. C2×C4⋊C8×C47C22semidirect
33. C2×C4⋊C8×C47C22semidirect
34. C2×#103×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
44. C2×#102×C47C22semidirect
50. C47×#390C22semidirect
51. C47×#389C22semidirect
57. C4×C4⋊C4×C47C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
145. #102×C47D4semidirect
366. #25088C47direct (N × H)
395. C22×C47#463semidirect
417. C2×#465C2×C47semidirect
418. C2×#463C2×C47semidirect
420. C22×#102C2×C47semidirect
421. #2435C2×C47semidirect
422. #2361C2×C47semidirect
423. #2065C2×C47semidirect
424. #2054C2×C47semidirect
425. #2042C2×C47semidirect
426. #2012C2×C47semidirect
427. #1983C2×C47semidirect
428. #1926C2×C47semidirect
429. #1879C2×C47semidirect
430. #1872C2×C47semidirect
431. #1850C2×C47semidirect
444. C22×SD16C22×C47semidirect
453. C2×C4×D4C22×C47semidirect
458. C2×#106C22×C47semidirect
459. C2×C4⋊C8C22×C47semidirect
460. C2×C4⋊C8C22×C47semidirect
461. C2×#103C22×C47semidirect
462. C2×#103C22×C47semidirect
463. C2×#103C22×C47semidirect
471. C2×#102C22×C47semidirect
477. #390C22×C47semidirect
478. #389C22×C47semidirect
484. C4×C4⋊C4C22×C47semidirect
486. #340C22×C47semidirect
487. #340C22×C47semidirect
488. #336C22×C47semidirect
489. #336C22×C47semidirect
490. C47#25088direct (N × H)
573. #102D4×C47semidirect
822. C22C47×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4652
C2×C47×#4632
C2×C47×#4472
C22×#102×C472
C47×#24352
C47×#23612
C47×#20652
C47×#20542
C47×#20422
C47×#20122
C47×#19832
C47×#19262
C47×#18792
C47×#18722
C47×#18502
#2508847