Finite Group Databasebeta

← C47×#23008 #26062706

Subgroups — C47×#23008 #26062706

Order 12032.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#459C211yesmaximal, characteristic
2C2×C47×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C47C211yesmaximal, characteristic, complemented
4C47×#2366C211yesmaximal, characteristic, complemented
5C47×#2349C211yesmaximal, characteristic, complemented
6C47×#1961C211yesmaximal, characteristic, complemented
7C47×#1949C211yesmaximal, characteristic, complemented
8C47×#1936C211yesmaximal, characteristic, complemented
9C47×#1934C211yesmaximal, characteristic, complemented
10C47×#1879C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1864C211yesmaximal, characteristic, complemented
13C47×#1862C211yesmaximal, characteristic, complemented
14C47×#1771C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×#127×C47C2211yescharacteristic
19C2×C4×D4×C47—21no—
20C2×C4×D4×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C47×#459C418yescomplemented
26C47×#442—24no—
27C4×D8×C47—24no—
28C2×#107×C47C2211yescharacteristic
29C2×#106×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
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×#97×C47C2211yescharacteristic
40C2×#97×C47C2211yescharacteristic
41C2×C4×C8×C47C2211yescharacteristic
42C47×#390—21no—
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#389C2211yescharacteristic
46C47×#389C2211yescharacteristic
47C47×#386—21no—
48C47×#386—21no—
49C47×#385—21no—
50C47×#385—21no—
51C47×#382C2211yescharacteristic
52C47×#380—21no—
53C4×C4⋊C4×C47C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C2×#95×C47—21no—
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47C2311yescharacteristic
65C22×D4×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47—21no—
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C2×D8×C47—22no—
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×D8×C47C2×C414yescomplemented
77C2×D8×C47C2×C414yescomplemented
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82#127×C47—22no—
83#127×C47C2×C414yescomplemented
84C4×D4×C47—22no—
85C4×D4×C47—22no—
86C4×D4×C47—22no—
87C4×D4×C47—22no—
88C4×D4×C47—22no—
89C4×D4×C47—41no—
90C4×D4×C47—41no—
91C4×D4×C47—41no—
92C4×D4×C47—41no—
93C4×D4×C47—44no—
94C4×D4×C47C2×C414yescomplemented
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C4⋊C4×C47D411yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
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×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117#107×C47—22no—
118#106×C47—22no—
119C4⋊C8×C47C2×C414yescomplemented
120#102×C47—22no—
121#102×C47—22no—
122#102×C47—22no—
123#102×C47—41no—
124#102×C47—41no—
125#102×C47C2×C414yescomplemented
126#102×C47C2×C414yescomplemented
127#102×C47D414yescomplemented
128#97×C47—22no—
129#97×C47—22no—
130C4×C8×C47—22no—
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47D411yescharacteristic
137#95×C47D411yescharacteristic
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C2×D4×C47—24no—
142C2×D4×C47—24no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—42no—
157C2×D4×C47—42no—
158C2×D4×C47—81no—
159C2×D4×C47—81no—
160C2×D4×C47C22×C412yes—
161C2×D4×C47C22×C412yes—
162C2×D4×C47C22×C412yes—
163C2×D4×C47C2×D412yes—
164C2×D4×C47#4112yes—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—24no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—42no—
172C22×C4×C47—42no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47—42no—
177C22×C4×C47—42no—
178C22×C4×C47—42no—
179C22×C4×C47—81no—
180C22×C4×C47—81no—
181C22×C4×C47—81no—
182C22×C4×C47—81no—
183C22×C4×C47—81no—
184C22×C4×C47—81no—
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2411yescharacteristic
192D8×C47—28no—
193D8×C47—28no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47C22×C412yes—
204C2×C8×C47C22×C412yes—
205C2×C8×C47C2×D412yes—
206C4⋊C4×C47—22no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—41no—
216C4⋊C4×C47—81no—
217C4⋊C4×C47—81no—
218C4⋊C4×C47C22×C412yes—
219C4⋊C4×C47C2×D412yes—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—42no—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—42no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—81no—
228C22⋊C4×C47—81no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47—42no—
234C42×C47C22×C412yes—
235C42×C47#4112yes—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47C22×D411yescharacteristic
258D4×C47—22no—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47—22no—
262D4×C47—22no—
263D4×C47—22no—
264D4×C47—22no—
265D4×C47—48no—
266D4×C47—41no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—41no—
270D4×C47—84no—
271D4×C47C4×D414yescomplemented
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—22no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—84no—
303C2×C4×C47—84no—
304C2×C4×C47—84no—
305C2×C4×C47—84no—
306C2×C4×C47—84no—
307C2×C4×C47C4×D412yes—
308C2×C4×C47C4×D412yes—
309C2×C4×C47AGL(1,ℤ/8)12yes—
310C2×C4×C47C23×C411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4111yescharacteristic
313C2×C4×C47C2×#4111yescharacteristic
314C2×C4×C47H(5,𝔽2)11yescharacteristic
315C2×C4×C472−1+411yescharacteristic
316C8×C47—22no—
317C8×C47—22no—
318C8×C47—22no—
319C8×C47—41no—
320#23008C4711yesmaximal, characteristic, direct product factor, Sylow
321C22×C47—24no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47—42no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—81no—
335C22×C47—81no—
336C22×C47—81no—
337C22×C47—81no—
338C22×C47—81no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47C2×C4×D411yescharacteristic
343C22×C47D4211yescharacteristic
344C22×C47#54811yescharacteristic
345C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C47#57511yescharacteristic
347C22×C47#57611yescharacteristic
348C22×C47#57611yescharacteristic
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—41no—
354C4×C47—42no—
355C4×C47—41no—
356C4×C47—41no—
357C4×C47—81no—
358C4×C47—81no—
359C4×C47—81no—
360C4×C47C2×C4×D411yescharacteristic
361C4×C47#52011yescharacteristic
362C4×C47#54711yescharacteristic
363C4×C47#55311yescharacteristic
364C2×#459C2×C4711yescharacteristic
365C2×#442C2×C4711yescharacteristic, complemented
366C2×C4×D8C2×C4711yescharacteristic, complemented
367#2366C2×C4711yescharacteristic, complemented
368#2349C2×C4711yescharacteristic, complemented
369#1961C2×C4711yescharacteristic, complemented
370#1949C2×C4711yescharacteristic, complemented
371#1936C2×C4711yescharacteristic, complemented
372#1934C2×C4711yescharacteristic, complemented
373#1879C2×C4711yescharacteristic, complemented
374#1879C2×C4711yescharacteristic, complemented
375#1864C2×C4711yescharacteristic, complemented
376#1862C2×C4711yescharacteristic, complemented
377#1771C2×C4711yescharacteristic, complemented
378#1762C2×C4711yescharacteristic, complemented
379C2×C47—44no—
380C2×C47—82no—
381C2×C47—82no—
382C2×C47#236111yescharacteristic
383C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C47#294811yescharacteristic
385C2×C47#326411yescharacteristic
386C2×C47#326811yescharacteristic
387C2×C47#336611yescharacteristic
388C2×C47#337011yescharacteristic
389C22×D8C22×C4711yescharacteristic
390C22×D8C22×C4711yescharacteristic
391C2×#127C22×C4711yescharacteristic
392C2×C4×D4—21no—
393C2×C4×D4C22×C4711yescharacteristic
394C2×C4×D4C22×C4711yescharacteristic
395C2×C4×D4C22×C4711yescharacteristic
396C2×C4×D4C22×C4711yescharacteristic
397C2×C4×D4C22×C4711yescharacteristic
398#459C4×C4718yescomplemented
399#442—24no—
400C4×D8—24no—
401C2×#107C22×C4711yescharacteristic
402C2×#106C22×C4711yescharacteristic
403C2×C4⋊C8C22×C4711yescharacteristic
404C2×#102C22×C4711yescharacteristic
405C2×#102C22×C4711yescharacteristic
406C2×#102C22×C4711yescharacteristic
407C2×#102C22×C4711yescharacteristic
408C2×#102C22×C4711yescharacteristic
409C2×#102C22×C4711yescharacteristic
410C2×#102C22×C4711yescharacteristic
411C2×#102C22×C4711yescharacteristic
412C2×#97C22×C4711yescharacteristic
413C2×#97C22×C4711yescharacteristic
414C2×C4×C8C22×C4711yescharacteristic
415#390—21no—
416#390C22×C4711yescharacteristic
417#390C22×C4711yescharacteristic
418#389C22×C4711yescharacteristic
419#389C22×C4711yescharacteristic
420#386—21no—
421#386—21no—
422#385—21no—
423#385—21no—
424#382C22×C4711yescharacteristic
425#380—21no—
426C4×C4⋊C4C22×C4711yescharacteristic
427C4×C4⋊C4C22×C4711yescharacteristic
428C2×#95—21no—
429#340C22×C4711yescharacteristic
430#340C22×C4711yescharacteristic
431#340C22×C4711yescharacteristic
432#340C22×C4711yescharacteristic
433#336C22×C4711yescharacteristic
434#336C22×C4711yescharacteristic
435C47#2300811yescharacteristic, direct product factor, Sylow
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C23×C4711yescharacteristic
439C22×D4C23×C4711yescharacteristic
440C22×D4C23×C4711yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8C2×C4×C4714yescomplemented
451C2×D8C2×C4×C4714yescomplemented
452C22×C8C23×C4711yescharacteristic
453C22×C8C23×C4711yescharacteristic
454C22×C8C23×C4711yescharacteristic
455C22×C8C23×C4711yescharacteristic
456#127—22no—
457#127C2×C4×C4714yescomplemented
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465C4×D4—41no—
466C4×D4—41no—
467C4×D4—44no—
468C4×D4C2×C4×C4714yescomplemented
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4D4×C4711yescharacteristic
472C2×C4⋊C4D4×C4711yescharacteristic
473C2×C4⋊C4C23×C4711yescharacteristic
474C2×C4⋊C4C23×C4711yescharacteristic
475C2×C4⋊C4C23×C4711yescharacteristic
476C2×C4⋊C4C23×C4711yescharacteristic
477C2×C4⋊C4C23×C4711yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42C23×C4711yescharacteristic
489C2×C42C23×C4711yescharacteristic
490C2×C42C23×C4711yescharacteristic
491#107—22no—
492#106—22no—
493C4⋊C8C2×C4×C4714yescomplemented
494#102—22no—
495#102—22no—
496#102—22no—
497#102—41no—
498#102—41no—
499#102C2×C4×C4714yescomplemented
500#102C2×C4×C4714yescomplemented
501#102D4×C4714yescomplemented
502#97—22no—
503#97—22no—
504C4×C8—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95D4×C4711yescharacteristic
511#95D4×C4711yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4C22×C4×C4712yes—
535C2×D4C22×C4×C4712yes—
536C2×D4C22×C4×C4712yes—
537C2×D4C2×D4×C4712yes—
538C2×D4#41×C4712yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×D4×C4711yescharacteristic
560C22×C4C2×D4×C4711yescharacteristic
561C22×C4C2×D4×C4711yescharacteristic
562C22×C4C2×D4×C4711yescharacteristic
563C22×C4C2×D4×C4711yescharacteristic
564C22×C4C2×D4×C4711yescharacteristic
565C22×C4C24×C4711yescharacteristic
566D8—28no—
567D8—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8C22×C4×C4712yes—
578C2×C8C22×C4×C4712yes—
579C2×C8C2×D4×C4712yes—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—41no—
590C4⋊C4—81no—
591C4⋊C4—81no—
592C4⋊C4C22×C4×C4712yes—
593C4⋊C4C2×D4×C4712yes—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42C22×C4×C4712yes—
609C42#41×C4712yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C22×D4×C4711yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4C4×D4×C4714yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4C4×D4×C4712yes—
682C2×C4C4×D4×C4712yes—
683C2×C4AGL(1,ℤ/8)×C4712yes—
684C2×C4C23×C4×C4711yescharacteristic
685C2×C4C22×D4×C4711yescharacteristic
686C2×C4C2×#41×C4711yescharacteristic
687C2×C4C2×#41×C4711yescharacteristic
688C2×C4H(5,𝔽2)×C4711yescharacteristic
689C2×C42−1+4×C4711yescharacteristic
690C8—22no—
691C8—22no—
692C8—22no—
693C8—41no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×C4×D4×C4711yescharacteristic
716C22D42×C4711yescharacteristic
717C22C47×#54811yescharacteristic
718C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
719C22C47×#57511yescharacteristic
720C22C47×#57611yescharacteristic
721C22C47×#57611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—41no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4C2×C4×D4×C4711yescharacteristic
734C4C47×#52011yescharacteristic
735C4C47×#54711yescharacteristic
736C4C47×#55311yescharacteristic
737C2—44no—
738C2—82no—
739C2—82no—
740C2C47×#236111yescharacteristic
741C2C4×AGL(1,ℤ/8)×C4711yescharacteristic
742C2C47×#294811yescharacteristic
743C2C47×#326411yescharacteristic
744C2C47×#326811yescharacteristic
745C2C47×#336611yescharacteristic
746C2C47×#337011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#442C2semidirect
3. C2×C4×D8×C47C2semidirect
4. C47×#2366C2semidirect
5. C47×#2349C2semidirect
6. C47×#1961C2semidirect
7. C47×#1949C2semidirect
8. C47×#1936C2semidirect
9. C47×#1934C2semidirect
10. C47×#1879C2semidirect
11. C47×#1879C2semidirect
12. C47×#1864C2semidirect
13. C47×#1862C2semidirect
14. C47×#1771C2semidirect
15. C47×#1762C2semidirect
25. C47×#459C4semidirect
76. C2×D8×C47C2×C4semidirect
77. C2×D8×C47C2×C4semidirect
83. #127×C47C2×C4semidirect
94. C4×D4×C47C2×C4semidirect
119. C4⋊C8×C47C2×C4semidirect
125. #102×C47C2×C4semidirect
126. #102×C47C2×C4semidirect
127. #102×C47D4semidirect
271. D4×C47C4×D4semidirect
320. #23008C47direct (N × H)
365. C2×#442C2×C47semidirect
366. C2×C4×D8C2×C47semidirect
367. #2366C2×C47semidirect
368. #2349C2×C47semidirect
369. #1961C2×C47semidirect
370. #1949C2×C47semidirect
371. #1936C2×C47semidirect
372. #1934C2×C47semidirect
373. #1879C2×C47semidirect
374. #1879C2×C47semidirect
375. #1864C2×C47semidirect
376. #1862C2×C47semidirect
377. #1771C2×C47semidirect
378. #1762C2×C47semidirect
398. #459C4×C47semidirect
435. C47#23008direct (N × H)
450. C2×D8C2×C4×C47semidirect
451. C2×D8C2×C4×C47semidirect
457. #127C2×C4×C47semidirect
468. C4×D4C2×C4×C47semidirect
493. C4⋊C8C2×C4×C47semidirect
499. #102C2×C4×C47semidirect
500. #102C2×C4×C47semidirect
501. #102D4×C47semidirect
645. D4C4×D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4592
C2×C47×#4422
C2×C4×D8×C472
C47×#23662
C47×#23492
C47×#19612
C47×#19492
C47×#19362
C47×#19342
C47×#18792
C47×#18642
C47×#18622
C47×#17712
C47×#17622
#2300847