Finite Group Databasebeta

← C47×#25549 #26065247

Subgroups — C47×#25549 #26065247

Order 12032.

1390 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
1C2×C47×#547C211yesmaximal, characteristic, complemented
2C2×C47×#481C211yesmaximal, characteristic, complemented
3C2×C47×#469C211yesmaximal, characteristic, complemented
4C47×#2414C211yesmaximal, characteristic, complemented
5C47×#2058C211yesmaximal, characteristic, complemented
6C47×#2034C211yesmaximal, characteristic, complemented
7C47×#2023C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1879C211yesmaximal, characteristic, complemented
10C47×#1875C211yesmaximal, characteristic, complemented
11C47×#1874C211yesmaximal, characteristic, complemented
12C47×#1870C211yesmaximal, characteristic, complemented
13C47×#1864C211yesmaximal, characteristic, complemented
14C47×#1853C211yesmaximal, characteristic, complemented
15C47×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C47—21no—
17C22×D8×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C47×#547—24no—
20C47×#547—24no—
21C2×C4⋊Q8×C47C2211yescharacteristic
22C2×#123×C47—21no—
23C2×#123×C47—21no—
24C2×C22⋊Q8×C47—21no—
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×C4×D4×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C47×#481—24no—
35C47×#469—24no—
36C2×#106×C47C2211yescharacteristic
37C2×#106×C47C2211yescharacteristic
38C2×#106×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#394—21no—
49C47×#392—21no—
50C47×#390—21no—
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—28no—
64C2×#41×C47—44no—
65C2×#41×C47—44no—
66C22×Q8×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47D411yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C2×D8×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47—41no—
82C2×M16×C47—22no—
83C2×M16×C47—22no—
84C2×M16×C47—41no—
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C4⋊Q8×C47—22no—
90C4⋊Q8×C47—22no—
91#123×C47—28no—
92#123×C47—28no—
93C22⋊Q8×C47—28no—
94#121×C47—22no—
95#121×C47—22no—
96#121×C47—22no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—41no—
101#121×C47D414yescomplemented
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106#117×C47—22no—
107#117×C47—41no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—22no—
113C2×C4⋊C4×C47—22no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47D411yescharacteristic
116C2×C4⋊C4×C47D414yescomplemented
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C22⋊C4×C47D411yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136#106×C47—22no—
137#106×C47—22no—
138#106×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—22no—
144#102×C47—41no—
145C22⋊C8×C47—22no—
146C22⋊C8×C47—22no—
147C22⋊C8×C47—41no—
148#95×C47—21no—
149#95×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47C2×D411yescharacteristic
153C24×C47C2×D411yescharacteristic
154#41×C47—432no—
155C2×Q8×C47—24no—
156C2×Q8×C47—42no—
157C2×Q8×C47—42no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—24no—
161C2×D4×C47—24no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—42no—
175C2×D4×C47—42no—
176C2×D4×C47—42no—
177C2×D4×C47—42no—
178C2×D4×C47—42no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—81no—
182C2×D4×C47—81no—
183C2×D4×C47—81no—
184C2×D4×C47C2×D412yes—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—24no—
190C22×C4×C47—24no—
191C22×C4×C47—24no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
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—42no—
205C22×C4×C47—42no—
206C22×C4×C47—42no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—42no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2411yescharacteristic
217D8×C47—44no—
218M16×C47—44no—
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—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47#4112yescomplemented
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—22no—
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—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—81no—
244C4⋊C4×C47C2×D412yes—
245C4⋊C4×C47C2×D412yes—
246C4⋊C4×C47C2×D412yes—
247C4⋊C4×C47#4112yescomplemented
248C22⋊C4×C47—24no—
249C22⋊C4×C47—24no—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—24no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—81no—
258C22⋊C4×C47—81no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—42no—
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—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—22no—
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#12012yes—
289C23×C47AGL(1,ℤ/8)12yes—
290C23×C47C22×D411yescharacteristic
291Q8×C47—48no—
292D4×C47—28no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—48no—
296D4×C47—48no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—84no—
304D4×C47—84no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—48no—
324C2×C4×C47—48no—
325C2×C4×C47—48no—
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#12012yes—
345C2×C4×C47AGL(1,ℤ/8)12yes—
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C2×#4111yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47H(5,𝔽2)11yescharacteristic
351C2×C4×C472−1+411yescharacteristic
352C8×C47—22no—
353C8×C47—41no—
354C8×C47—41no—
355C8×C47—41no—
356#25549C4711yesmaximal, characteristic, direct product factor, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47C2×#12011yescharacteristic
386C22×C47#54611yescharacteristic
387C22×C47#54711yescharacteristic
388C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C47#57711yescharacteristic
391C22×C47#57711yescharacteristic
392C4×C47—22no—
393C4×C47—22no—
394C4×C47—41no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47—42no—
398C4×C47—41no—
399C4×C47—42no—
400C4×C47—81no—
401C4×C47—81no—
402C4×C47#53211yescharacteristic
403C4×C47#53711yescharacteristic
404C4×C47#54611yescharacteristic
405C4×C47#54711yescharacteristic
406C2×#547C2×C4711yescharacteristic, complemented
407C2×#481C2×C4711yescharacteristic, complemented
408C2×#469C2×C4711yescharacteristic, complemented
409#2414C2×C4711yescharacteristic, complemented
410#2058C2×C4711yescharacteristic, complemented
411#2034C2×C4711yescharacteristic, complemented
412#2023C2×C4711yescharacteristic, complemented
413#1999C2×C4711yescharacteristic, complemented
414#1879C2×C4711yescharacteristic, complemented
415#1875C2×C4711yescharacteristic, complemented
416#1874C2×C4711yescharacteristic, complemented
417#1870C2×C4711yescharacteristic, complemented
418#1864C2×C4711yescharacteristic, complemented
419#1853C2×C4711yescharacteristic, complemented
420#1736C2×C4711yescharacteristic, complemented
421C2×C47—42no—
422C2×C47—42no—
423C2×C47—82no—
424C2×C47—161no—
425C2×C47#243011yescharacteristic
426C2×C47#300311yescharacteristic
427C2×C47#301011yescharacteristic
428C2×C47#330611yescharacteristic
429C2×C47#333211yescharacteristic
430C2×C47#334511yescharacteristic
431C2×C47#335411yescharacteristic
432C22×#41—21no—
433C22×D8C22×C4711yescharacteristic
434C22×M16C22×C4711yescharacteristic
435#547—24no—
436#547—24no—
437C2×C4⋊Q8C22×C4711yescharacteristic
438C2×#123—21no—
439C2×#123—21no—
440C2×C22⋊Q8—21no—
441C2×#121C22×C4711yescharacteristic
442C2×#121C22×C4711yescharacteristic
443C2×#121C22×C4711yescharacteristic
444C2×#121C22×C4711yescharacteristic
445C2×C4×D4C22×C4711yescharacteristic
446C2×C4×D4C22×C4711yescharacteristic
447C2×#117C22×C4711yescharacteristic
448C22×C4⋊C4C22×C4711yescharacteristic
449C22×C4⋊C4C22×C4711yescharacteristic
450#481—24no—
451#469—24no—
452C2×#106C22×C4711yescharacteristic
453C2×#106C22×C4711yescharacteristic
454C2×#106C22×C4711yescharacteristic
455C2×#102C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×#102C22×C4711yescharacteristic
458C2×#102C22×C4711yescharacteristic
459C2×#102C22×C4711yescharacteristic
460C2×#102C22×C4711yescharacteristic
461C2×C22⋊C8C22×C4711yescharacteristic
462C2×C22⋊C8C22×C4711yescharacteristic
463C2×C22⋊C8C22×C4711yescharacteristic
464#394—21no—
465#392—21no—
466#390—21no—
467#390C22×C4711yescharacteristic
468#389C22×C4711yescharacteristic
469#388—21no—
470#380C22×C4711yescharacteristic
471#340C22×C4711yescharacteristic
472#340C22×C4711yescharacteristic
473#340C22×C4711yescharacteristic
474#340C22×C4711yescharacteristic
475#340C22×C4711yescharacteristic
476#340C22×C4711yescharacteristic
477#336C22×C4711yescharacteristic
478#336C22×C4711yescharacteristic
479C47#2554911yescharacteristic, direct product factor, Sylow
480C2×#41—28no—
481C2×#41—44no—
482C2×#41—44no—
483C22×Q8—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C4711yescharacteristic
489C22×D4C23×C4711yescharacteristic
490C22×D4C23×C4711yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C4711yescharacteristic
495C23×C4C23×C4711yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8C23×C4711yescharacteristic
503C22×C8C23×C4711yescharacteristic
504C22×C8C23×C4711yescharacteristic
505C22×C8C23×C4711yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508#123—28no—
509#123—28no—
510C22⋊Q8—28no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121D4×C4714yescomplemented
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C4711yescharacteristic
533C2×C4⋊C4D4×C4714yescomplemented
534C2×C4⋊C4C23×C4711yescharacteristic
535C2×C4⋊C4C23×C4711yescharacteristic
536C2×C4⋊C4C23×C4711yescharacteristic
537C2×C4⋊C4C23×C4711yescharacteristic
538C2×C4⋊C4C23×C4711yescharacteristic
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
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⋊C4D4×C4711yescharacteristic
550C2×C22⋊C4D4×C4711yescharacteristic
551C2×C42—21no—
552C2×C42C23×C4711yescharacteristic
553#106—22no—
554#106—22no—
555#106—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567C24—21no—
568C24—21no—
569C24C2×D4×C4711yescharacteristic
570C24C2×D4×C4711yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C4712yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C4711yescharacteristic
628C22×C4C2×D4×C4711yescharacteristic
629C22×C4C2×D4×C4711yescharacteristic
630C22×C4C2×D4×C4712yes—
631C22×C4C2×D4×C4712yes—
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C24×C4711yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C4712yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C4712yes—
662C4⋊C4C2×D4×C4712yes—
663C4⋊C4C2×D4×C4712yes—
664C4⋊C4#41×C4712yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23#120×C4712yes—
706C23AGL(1,ℤ/8)×C4712yes—
707C23C22×D4×C4711yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
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#120×C4712yes—
762C2×C4AGL(1,ℤ/8)×C4712yes—
763C2×C4C22×D4×C4711yescharacteristic
764C2×C4C22×D4×C4711yescharacteristic
765C2×C4C2×#41×C4711yescharacteristic
766C2×C4C2×#41×C4711yescharacteristic
767C2×C4H(5,𝔽2)×C4711yescharacteristic
768C2×C42−1+4×C4711yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#120×C4711yescharacteristic
802C22C47×#54611yescharacteristic
803C22C47×#54711yescharacteristic
804C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
805C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
806C22C47×#57711yescharacteristic
807C22C47×#57711yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4C47×#53211yescharacteristic
819C4C47×#53711yescharacteristic
820C4C47×#54611yescharacteristic
821C4C47×#54711yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C47×#243011yescharacteristic
827C2C47×#300311yescharacteristic
828C2C47×#301011yescharacteristic
829C2C47×#330611yescharacteristic
830C2C47×#333211yescharacteristic
831C2C47×#334511yescharacteristic
832C2C47×#335411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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×#547C2semidirect
2. C2×C47×#481C2semidirect
3. C2×C47×#469C2semidirect
4. C47×#2414C2semidirect
5. C47×#2058C2semidirect
6. C47×#2034C2semidirect
7. C47×#2023C2semidirect
8. C47×#1999C2semidirect
9. C47×#1879C2semidirect
10. C47×#1875C2semidirect
11. C47×#1874C2semidirect
12. C47×#1870C2semidirect
13. C47×#1864C2semidirect
14. C47×#1853C2semidirect
15. C47×#1736C2semidirect
101. #121×C47D4semidirect
116. C2×C4⋊C4×C47D4semidirect
230. C2×C8×C47#41semidirect
247. C4⋊C4×C47#41semidirect
356. #25549C47direct (N × H)
406. C2×#547C2×C47semidirect
407. C2×#481C2×C47semidirect
408. C2×#469C2×C47semidirect
409. #2414C2×C47semidirect
410. #2058C2×C47semidirect
411. #2034C2×C47semidirect
412. #2023C2×C47semidirect
413. #1999C2×C47semidirect
414. #1879C2×C47semidirect
415. #1875C2×C47semidirect
416. #1874C2×C47semidirect
417. #1870C2×C47semidirect
418. #1864C2×C47semidirect
419. #1853C2×C47semidirect
420. #1736C2×C47semidirect
479. C47#25549direct (N × H)
518. #121D4×C47semidirect
533. C2×C4⋊C4D4×C47semidirect
647. C2×C8#41×C47semidirect
664. C4⋊C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5472
C2×C47×#4812
C2×C47×#4692
C47×#24142
C47×#20582
C47×#20342
C47×#20232
C47×#19992
C47×#18792
C47×#18752
C47×#18742
C47×#18702
C47×#18642
C47×#18532
C47×#17362
#2554947