Finite Group Databasebeta

← C47×#18046 #26057744

Subgroups — C47×#18046 #26057744

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2970C211yesmaximal, characteristic, complemented
2C4×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic
3D4×M16×C47C211yesmaximal, characteristic, complemented
4C47×#1592C211yesmaximal, characteristic, complemented
5C47×#1590C211yesmaximal, characteristic, complemented
6C47×#1586C211yesmaximal, characteristic, complemented
7C47×#1585C211yesmaximal, characteristic, complemented
8C47×#1582C211yesmaximal, characteristic, complemented
9C47×#1581C211yesmaximal, characteristic, complemented
10C47×#1580C211yesmaximal, characteristic, complemented
11C8×D8×C47C211yesmaximal, characteristic, complemented
12C47×#1569C211yesmaximal, characteristic, complemented
13C47×#1490C211yesmaximal, characteristic, complemented
14C47×#1489C211yesmaximal, characteristic, complemented
15C47×#1455C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C47C411yescharacteristic
17C22×M16×C47—21no—
18C4×#41×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C47×#446C2211yescharacteristic, complemented
21C47×#446C2211yescharacteristic, complemented
22C47×#442C411yescharacteristic
23C47×#442C411yescharacteristic
24C47×#440C411yescharacteristic
25C47×#440C411yescharacteristic
26C4×SD16×C47C2211yescharacteristic
27C4×SD16×C47C2211yescharacteristic
28C4×D8×C47C2211yescharacteristic
29C4×D8×C47C2211yescharacteristic
30C47×#436C2211yescharacteristic
31C47×#436C2211yescharacteristic
32C47×#435—21no—
33C47×#435—21no—
34C47×#435—21no—
35C47×#435—21no—
36C8×D4×C47C2211yescharacteristic
37C8×D4×C47C2211yescharacteristic
38C8×D4×C47C2211yescharacteristic, complemented
39C8×D4×C47C2211yescharacteristic, complemented
40C47×#432—21no—
41C47×#432C2211yescharacteristic
42C47×#428C411yescharacteristic
43C47×#423C2211yescharacteristic
44C47×#418C411yescharacteristic
45C47×#417C411yescharacteristic
46C47×#407—21no—
47C4×M16×C47C2211yescharacteristic
48C4×M16×C47C2211yescharacteristic
49C4×M16×C47C2211yescharacteristic
50C2×#97×C47—21no—
51C47×#335C2211yescharacteristic, complemented
52C47×#335C2211yescharacteristic, complemented
53C47×#334C2211yescharacteristic, complemented
54C47×#334C2211yescharacteristic, complemented
55C47×Q8⋊C8C2211yescharacteristic, complemented
56C47×Q8⋊C8C2211yescharacteristic, complemented
57C47×D4⋊C8C2211yescharacteristic
58C47×D4⋊C8C2211yescharacteristic
59C47×D4⋊C8C2211yescharacteristic
60C47×D4⋊C8C2211yescharacteristic
61C47×D4⋊C8C2211yescharacteristic, complemented
62C47×D4⋊C8C2211yescharacteristic, complemented
63C47×#322C2211yescharacteristic, complemented
64C47×#322C2211yescharacteristic, complemented
65C47×#322C2211yescharacteristic, complemented
66C82×C47C2211yescharacteristic, complemented
67C2×#41×C47C2×C411yescharacteristic
68C22×D4×C47C2×C411yescharacteristic
69C23×C4×C47—21no—
70AGL(1,ℤ/8)×C47—24no—
71C2×SD16×C47C2×C411yescharacteristic
72C2×SD16×C47C2×C411yescharacteristic
73C2×D8×C47C2×C411yescharacteristic
74C2×D8×C47C2×C411yescharacteristic
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—44no—
80C2×M16×C47C2×C411yescharacteristic
81C2×M16×C47C2×C411yescharacteristic
82C2×M16×C47D411yescharacteristic
83C2×M16×C47D411yescharacteristic
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C4×Q8×C47C2×C411yescharacteristic
89C4×Q8×C47C2311yescharacteristic
90C4×D4×C47—21no—
91C4×D4×C47—21no—
92C4×D4×C47—21no—
93C4×D4×C47—21no—
94C4×D4×C47C2×C411yescharacteristic
95C4×D4×C47C2×C411yescharacteristic
96C4×D4×C47C2×C411yescharacteristic
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
101#117×C47C2×C411yescharacteristic
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C22⋊C4×C47—21no—
104C2×C42×C47—21no—
105C2×C42×C47C2311yescharacteristic
106#107×C47C2×C411yescharacteristic
107#107×C47C2×C411yescharacteristic
108#106×C47C2×C411yescharacteristic
109#106×C47C2×C411yescharacteristic
110C4⋊C8×C47—21no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117#103×C47C2×C411yescharacteristic
118#103×C47C2×C411yescharacteristic
119#102×C47C2×C411yescharacteristic
120#102×C47C2×C411yescharacteristic
121#102×C47C2×C411yescharacteristic
122#102×C47C2×C411yescharacteristic
123#102×C47C2×C411yescharacteristic
124#102×C47C2×C411yescharacteristic
125C22⋊C8×C47—21no—
126C22⋊C8×C47—21no—
127C22⋊C8×C47—21no—
128C22⋊C8×C47—21no—
129C22⋊C8×C47—21no—
130C22⋊C8×C47—21no—
131C22⋊C8×C47—21no—
132#97×C47—21no—
133#97×C47—21no—
134#97×C47—21no—
135#97×C47—21no—
136#97×C47C2×C411yescharacteristic
137#97×C47C2×C411yescharacteristic
138#97×C47D411yescharacteristic
139#97×C47D411yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C4×C8×C47C2311yescharacteristic
146C24×C47—21no—
147#41×C47—22no—
148#41×C47—41no—
149C2×Q8×C47C22×C411yescharacteristic
150C2×D4×C47—22no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—41no—
154C2×D4×C47C22×C411yescharacteristic
155C2×D4×C47C22×C411yescharacteristic
156C2×D4×C47C22×C411yescharacteristic
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—42no—
166C22×C4×C47—42no—
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47#4111yescharacteristic
170SD16×C47—22no—
171SD16×C47—22no—
172D8×C47—22no—
173D8×C47M1614yescomplemented
174M16×C47—22no—
175M16×C47—22no—
176M16×C47—41no—
177M16×C47—41no—
178M16×C47—42no—
179M16×C47—42no—
180M16×C47—42no—
181M16×C47—42no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—42no—
189C2×C8×C47—42no—
190C2×C8×C47—42no—
191C2×C8×C47—42no—
192C2×C8×C47C22×C411yescharacteristic
193C2×C8×C47C22×C411yescharacteristic
194C2×C8×C47C22×C411yescharacteristic
195C2×C8×C47C22×C411yescharacteristic
196C2×C8×C47C2×D411yescharacteristic
197C2×C8×C47C2×D411yescharacteristic
198C2×C8×C47C2×D411yescharacteristic
199C2×C8×C47C2×D411yescharacteristic
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47C22×C411yescharacteristic
204C4⋊C4×C47C22×C411yescharacteristic
205C4⋊C4×C47C22×C411yescharacteristic
206C4⋊C4×C47C22×C411yescharacteristic
207C22⋊C4×C47—21no—
208C22⋊C4×C47—21no—
209C22⋊C4×C47—21no—
210C22⋊C4×C47—21no—
211C22⋊C4×C47—21no—
212C22⋊C4×C47—21no—
213C22⋊C4×C47—21no—
214C42×C47—21no—
215C42×C47—21no—
216C42×C47—21no—
217C42×C47C22×C411yescharacteristic
218C42×C47C2×D411yescharacteristic
219C42×C47#4111yescharacteristic
220C42×C47C2411yescharacteristic
221C23×C47—21no—
222C23×C47—21no—
223C23×C47—21no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—81no—
227C23×C47C4×D411yescharacteristic
228Q8×C47—21no—
229Q8×C47—21no—
230D4×C47—21no—
231D4×C47—21no—
232D4×C47—21no—
233D4×C47—21no—
234D4×C47—42no—
235D4×C47—42no—
236D4×C47C2×M1612yes—
237D4×C47C2×M1612yescomplemented
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—41no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—81no—
259C2×C4×C47C4×D411yescharacteristic
260C2×C4×C47C4×D411yescharacteristic
261C2×C4×C47C4×D411yescharacteristic
262C2×C4×C47C23×C411yescharacteristic
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C8×C47—22no—
266C8×C47—21no—
267C8×C47—21no—
268C8×C47—21no—
269C8×C47—21no—
270C8×C47—21no—
271C8×C47—21no—
272C8×C47—41no—
273C8×C47—41no—
274C8×C47—41no—
275C8×C47—41no—
276C8×C47—41no—
277C8×C47C2×M1612yescomplemented
278C8×C47AGL(1,ℤ/8)12yescomplemented
279#18046C4711yesmaximal, characteristic, direct product factor, Sylow
280C22×C47—21no—
281C22×C47—22no—
282C22×C47—22no—
283C22×C47—21no—
284C22×C47—21no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47—84no—
293C22×C47C2×C4×D411yescharacteristic
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—41no—
299C4×C47—41no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47C22×M1611yescharacteristic
304C4×C47#56811yescharacteristic
305C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C47#57511yescharacteristic
307#2970C2×C4711yescharacteristic, complemented
308C4×AGL(1,ℤ/8)C2×C4711yescharacteristic
309D4×M16C2×C4711yescharacteristic, complemented
310#1592C2×C4711yescharacteristic, complemented
311#1590C2×C4711yescharacteristic, complemented
312#1586C2×C4711yescharacteristic, complemented
313#1585C2×C4711yescharacteristic, complemented
314#1582C2×C4711yescharacteristic, complemented
315#1581C2×C4711yescharacteristic, complemented
316#1580C2×C4711yescharacteristic, complemented
317C8×D8C2×C4711yescharacteristic, complemented
318#1569C2×C4711yescharacteristic, complemented
319#1490C2×C4711yescharacteristic, complemented
320#1489C2×C4711yescharacteristic, complemented
321#1455C2×C4711yescharacteristic, complemented
322C2×C47—41no—
323C2×C47—42no—
324C2×C47—42no—
325C2×C47—81no—
326C2×C47D4×M1611yescharacteristic
327C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
328C2×C47#295611yescharacteristic
329C2×AGL(1,ℤ/8)C4×C4711yescharacteristic
330C22×M16—21no—
331C4×#41C22×C4711yescharacteristic
332C2×C4×D4C22×C4711yescharacteristic
333#446C22×C4711yescharacteristic, complemented
334#446C22×C4711yescharacteristic, complemented
335#442C4×C4711yescharacteristic
336#442C4×C4711yescharacteristic
337#440C4×C4711yescharacteristic
338#440C4×C4711yescharacteristic
339C4×SD16C22×C4711yescharacteristic
340C4×SD16C22×C4711yescharacteristic
341C4×D8C22×C4711yescharacteristic
342C4×D8C22×C4711yescharacteristic
343#436C22×C4711yescharacteristic
344#436C22×C4711yescharacteristic
345#435—21no—
346#435—21no—
347#435—21no—
348#435—21no—
349C8×D4C22×C4711yescharacteristic
350C8×D4C22×C4711yescharacteristic
351C8×D4C22×C4711yescharacteristic, complemented
352C8×D4C22×C4711yescharacteristic, complemented
353#432—21no—
354#432C22×C4711yescharacteristic
355#428C4×C4711yescharacteristic
356#423C22×C4711yescharacteristic
357#418C4×C4711yescharacteristic
358#417C4×C4711yescharacteristic
359#407—21no—
360C4×M16C22×C4711yescharacteristic
361C4×M16C22×C4711yescharacteristic
362C4×M16C22×C4711yescharacteristic
363C2×#97—21no—
364#335C22×C4711yescharacteristic, complemented
365#335C22×C4711yescharacteristic, complemented
366#334C22×C4711yescharacteristic, complemented
367#334C22×C4711yescharacteristic, complemented
368Q8⋊C8C22×C4711yescharacteristic, complemented
369Q8⋊C8C22×C4711yescharacteristic, complemented
370D4⋊C8C22×C4711yescharacteristic
371D4⋊C8C22×C4711yescharacteristic
372D4⋊C8C22×C4711yescharacteristic
373D4⋊C8C22×C4711yescharacteristic
374D4⋊C8C22×C4711yescharacteristic, complemented
375D4⋊C8C22×C4711yescharacteristic, complemented
376#322C22×C4711yescharacteristic, complemented
377#322C22×C4711yescharacteristic, complemented
378#322C22×C4711yescharacteristic, complemented
379C82C22×C4711yescharacteristic, complemented
380C47#1804611yescharacteristic, direct product factor, Sylow
381C2×#41C2×C4×C4711yescharacteristic
382C22×D4C2×C4×C4711yescharacteristic
383C23×C4—21no—
384AGL(1,ℤ/8)—24no—
385C2×SD16C2×C4×C4711yescharacteristic
386C2×SD16C2×C4×C4711yescharacteristic
387C2×D8C2×C4×C4711yescharacteristic
388C2×D8C2×C4×C4711yescharacteristic
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—44no—
394C2×M16C2×C4×C4711yescharacteristic
395C2×M16C2×C4×C4711yescharacteristic
396C2×M16D4×C4711yescharacteristic
397C2×M16D4×C4711yescharacteristic
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C4×Q8C2×C4×C4711yescharacteristic
403C4×Q8C23×C4711yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C2×C4×C4711yescharacteristic
409C4×D4C2×C4×C4711yescharacteristic
410C4×D4C2×C4×C4711yescharacteristic
411C4×D4C23×C4711yescharacteristic
412C4×D4C23×C4711yescharacteristic
413C4×D4C23×C4711yescharacteristic
414#117—21no—
415#117C2×C4×C4711yescharacteristic
416C2×C4⋊C4C2×C4×C4711yescharacteristic
417C2×C22⋊C4—21no—
418C2×C42—21no—
419C2×C42C23×C4711yescharacteristic
420#107C2×C4×C4711yescharacteristic
421#107C2×C4×C4711yescharacteristic
422#106C2×C4×C4711yescharacteristic
423#106C2×C4×C4711yescharacteristic
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8—21no—
427C4⋊C8C23×C4711yescharacteristic
428C4⋊C8C23×C4711yescharacteristic
429C4⋊C8C23×C4711yescharacteristic
430C4⋊C8C23×C4711yescharacteristic
431#103C2×C4×C4711yescharacteristic
432#103C2×C4×C4711yescharacteristic
433#102C2×C4×C4711yescharacteristic
434#102C2×C4×C4711yescharacteristic
435#102C2×C4×C4711yescharacteristic
436#102C2×C4×C4711yescharacteristic
437#102C2×C4×C4711yescharacteristic
438#102C2×C4×C4711yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447#97—21no—
448#97—21no—
449#97—21no—
450#97C2×C4×C4711yescharacteristic
451#97C2×C4×C4711yescharacteristic
452#97D4×C4711yescharacteristic
453#97D4×C4711yescharacteristic
454C4×C8C23×C4711yescharacteristic
455C4×C8C23×C4711yescharacteristic
456C4×C8C23×C4711yescharacteristic
457C4×C8C23×C4711yescharacteristic
458C4×C8C23×C4711yescharacteristic
459C4×C8C23×C4711yescharacteristic
460C24—21no—
461#41—22no—
462#41—41no—
463C2×Q8C22×C4×C4711yescharacteristic
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4C22×C4×C4711yescharacteristic
469C2×D4C22×C4×C4711yescharacteristic
470C2×D4C22×C4×C4711yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4C22×C4×C4711yescharacteristic
482C22×C4C2×D4×C4711yescharacteristic
483C22×C4#41×C4711yescharacteristic
484SD16—22no—
485SD16—22no—
486D8—22no—
487D8M16×C4714yescomplemented
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—42no—
493M16—42no—
494M16—42no—
495M16—42no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—42no—
503C2×C8—42no—
504C2×C8—42no—
505C2×C8—42no—
506C2×C8C22×C4×C4711yescharacteristic
507C2×C8C22×C4×C4711yescharacteristic
508C2×C8C22×C4×C4711yescharacteristic
509C2×C8C22×C4×C4711yescharacteristic
510C2×C8C2×D4×C4711yescharacteristic
511C2×C8C2×D4×C4711yescharacteristic
512C2×C8C2×D4×C4711yescharacteristic
513C2×C8C2×D4×C4711yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4C22×C4×C4711yescharacteristic
518C4⋊C4C22×C4×C4711yescharacteristic
519C4⋊C4C22×C4×C4711yescharacteristic
520C4⋊C4C22×C4×C4711yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42C22×C4×C4711yescharacteristic
532C42C2×D4×C4711yescharacteristic
533C42#41×C4711yescharacteristic
534C42C24×C4711yescharacteristic
535C23—21no—
536C23—21no—
537C23—21no—
538C23—42no—
539C23—42no—
540C23—81no—
541C23C4×D4×C4711yescharacteristic
542Q8—21no—
543Q8—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—42no—
550D4C2×M16×C4712yes—
551D4C2×M16×C4712yescomplemented
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4C4×D4×C4711yescharacteristic
574C2×C4C4×D4×C4711yescharacteristic
575C2×C4C4×D4×C4711yescharacteristic
576C2×C4C23×C4×C4711yescharacteristic
577C2×C4C22×D4×C4711yescharacteristic
578C2×C4C2×#41×C4711yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8C2×M16×C4712yescomplemented
592C8AGL(1,ℤ/8)×C4712yescomplemented
593C22—21no—
594C22—22no—
595C22—22no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—84no—
606C22C2×C4×D4×C4711yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4C22×M16×C4711yescharacteristic
617C4C47×#56811yescharacteristic
618C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
619C4C47×#57511yescharacteristic
620C2—41no—
621C2—42no—
622C2—42no—
623C2—81no—
624C2D4×M16×C4711yescharacteristic
625C2C4×AGL(1,ℤ/8)×C4711yescharacteristic
626C2C47×#295611yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC42C24×C47
socleC22×C47C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×C47C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C4×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2970C2semidirect
3. D4×M16×C47C2semidirect
4. C47×#1592C2semidirect
5. C47×#1590C2semidirect
6. C47×#1586C2semidirect
7. C47×#1585C2semidirect
8. C47×#1582C2semidirect
9. C47×#1581C2semidirect
10. C47×#1580C2semidirect
11. C8×D8×C47C2semidirect
12. C47×#1569C2semidirect
13. C47×#1490C2semidirect
14. C47×#1489C2semidirect
15. C47×#1455C2semidirect
20. C47×#446C22semidirect
21. C47×#446C22semidirect
38. C8×D4×C47C22semidirect
39. C8×D4×C47C22semidirect
51. C47×#335C22semidirect
52. C47×#335C22semidirect
53. C47×#334C22semidirect
54. C47×#334C22semidirect
55. C47×Q8⋊C8C22semidirect
56. C47×Q8⋊C8C22semidirect
61. C47×D4⋊C8C22semidirect
62. C47×D4⋊C8C22semidirect
63. C47×#322C22semidirect
64. C47×#322C22semidirect
65. C47×#322C22semidirect
66. C82×C47C22semidirect
173. D8×C47M16semidirect
237. D4×C47C2×M16semidirect
277. C8×C47C2×M16semidirect
278. C8×C47AGL(1,ℤ/8)semidirect
279. #18046C47direct (N × H)
307. #2970C2×C47semidirect
309. D4×M16C2×C47semidirect
310. #1592C2×C47semidirect
311. #1590C2×C47semidirect
312. #1586C2×C47semidirect
313. #1585C2×C47semidirect
314. #1582C2×C47semidirect
315. #1581C2×C47semidirect
316. #1580C2×C47semidirect
317. C8×D8C2×C47semidirect
318. #1569C2×C47semidirect
319. #1490C2×C47semidirect
320. #1489C2×C47semidirect
321. #1455C2×C47semidirect
333. #446C22×C47semidirect
334. #446C22×C47semidirect
351. C8×D4C22×C47semidirect
352. C8×D4C22×C47semidirect
364. #335C22×C47semidirect
365. #335C22×C47semidirect
366. #334C22×C47semidirect
367. #334C22×C47semidirect
368. Q8⋊C8C22×C47semidirect
369. Q8⋊C8C22×C47semidirect
374. D4⋊C8C22×C47semidirect
375. D4⋊C8C22×C47semidirect
376. #322C22×C47semidirect
377. #322C22×C47semidirect
378. #322C22×C47semidirect
379. C82C22×C47semidirect
380. C47#18046direct (N × H)
487. D8M16×C47semidirect
551. D4C2×M16×C47semidirect
591. C8C2×M16×C47semidirect
592. C8AGL(1,ℤ/8)×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#29702
C4×AGL(1,ℤ/8)×C472
D4×M16×C472
C47×#15922
C47×#15902
C47×#15862
C47×#15852
C47×#15822
C47×#15812
C47×#15802
C8×D8×C472
C47×#15692
C47×#14902
C47×#14892
C47×#14552
#1804647