Finite Group Databasebeta

← C47×#24839 #26064537

Subgroups — C47×#24839 #26064537

Order 12032.

944 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#478C211yesmaximal, characteristic, complemented
2C22×C4⋊C8×C47C211yesmaximal, characteristic, complemented
3C47×#2851C211yesmaximal, characteristic, complemented
4C4×#121×C47C211yesmaximal, characteristic
5C47×#2088C211yesmaximal, characteristic, complemented
6C47×#2087C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#1989C211yesmaximal, characteristic, complemented
10C47×#1949C211yesmaximal, characteristic, complemented
11C47×#1893C211yesmaximal, characteristic
12C47×#1893C211yesmaximal, characteristic
13C47×#1808C211yesmaximal, characteristic, complemented
14C47×#1807C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C23×C8×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×#125×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×C4×D4×C47—21no—
21C2×C4×D4×C47C2211yescharacteristic
22C22×C42×C47C2211yescharacteristic
23C47×#478—24no—
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C2×#106×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C2×C4⋊C8×C47—24no—
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C47×#390C2211yescharacteristic
38C47×#389C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#389C2211yescharacteristic
41C47×#388—21no—
42C47×#387—21no—
43C47×#387—21no—
44C47×#386—21no—
45C47×#385—21no—
46C47×#385—21no—
47C47×#382C2211yescharacteristic
48C47×#380C2211yescharacteristic
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C4×C4⋊C4×C47C2211yescharacteristic
52C4×C22⋊C4×C47—21no—
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C22×D4×C47—21no—
62C22×D4×C47C2311yescharacteristic
63C23×C4×C47—21no—
64C23×C4×C47D411yescharacteristic
65C23×C4×C47D411yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C22×C8×C47—22no—
68C22×C8×C47—22no—
69C22×C8×C47—22no—
70C22×C8×C47—22no—
71C22×C8×C47—41no—
72C22×C8×C47—41no—
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77#125×C47—22no—
78#125×C47—22no—
79#121×C47—22no—
80#121×C47Q814yes—
81C4×D4×C47—22no—
82C4×D4×C47—22no—
83C4×D4×C47—44no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C22⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C42×C47—22no—
104C2×C42×C47—22no—
105C2×C42×C47—21no—
106C2×C42×C47D411yescharacteristic
107C2×C42×C47D411yescharacteristic
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110#107×C47—22no—
111#107×C47—41no—
112#106×C47—22no—
113#106×C47—41no—
114C4⋊C8×C47—22no—
115C4⋊C8×C47—22no—
116C4⋊C8×C47—22no—
117C4⋊C8×C47D414yescomplemented
118#102×C47—22no—
119#102×C47—22no—
120#102×C47—41no—
121#102×C47—41no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131C24×C47—21no—
132C24×C47C2×D411yescharacteristic
133C2×D4×C47—24no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47—42no—
140C2×D4×C47—42no—
141C2×D4×C47C2×Q812yes—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—41no—
159C22×C4×C47—42no—
160C22×C4×C47—42no—
161C22×C4×C47—42no—
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×Q812yes—
168C22×C4×C47#4112yes—
169C22×C4×C47C2411yescharacteristic
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—44no—
181C2×C8×C47—44no—
182C2×C8×C47C2×D412yes—
183C2×C8×C47C2×D412yes—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—42no—
198C4⋊C4×C47—42no—
199C4⋊C4×C47—42no—
200C4⋊C4×C47—42no—
201C4⋊C4×C47—42no—
202C4⋊C4×C47C2×Q812yes—
203C22⋊C4×C47—24no—
204C22⋊C4×C47—42no—
205C22⋊C4×C47—42no—
206C22⋊C4×C47—42no—
207C22⋊C4×C47—42no—
208C22⋊C4×C47—42no—
209C22⋊C4×C47—42no—
210C42×C47—22no—
211C42×C47—22no—
212C42×C47—21no—
213C42×C47—21no—
214C42×C47—42no—
215C42×C47C2×D412yes—
216C42×C47#4112yes—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—22no—
222C23×C47—41no—
223C23×C47—41no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47C22⋊Q812yes—
229C23×C47#13512yes—
230C23×C47AGL(1,ℤ/8)12yes—
231C23×C47C22×D411yescharacteristic
232D4×C47—22no—
233D4×C47—22no—
234D4×C47—48no—
235D4×C47—41no—
236D4×C47—41no—
237C2×C4×C47—28no—
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—22no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—21no—
251C2×C4×C47—22no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—44no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—84no—
276C2×C4×C47#12112yes—
277C2×C4×C47#12112yes—
278C2×C4×C47C22⋊Q812yes—
279C2×C4×C47#13512yes—
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C22×Q811yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47H(5,𝔽2)11yescharacteristic
285C2×C4×C472−1+411yescharacteristic
286C8×C47—22no—
287C8×C47—22no—
288C8×C47—41no—
289C8×C47—41no—
290#24839C4711yesmaximal, characteristic, direct product factor, Sylow
291C22×C47—22no—
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—22no—
295C22×C47—22no—
296C22×C47—22no—
297C22×C47—42no—
298C22×C47—42no—
299C22×C47—42no—
300C22×C47—81no—
301C22×C47—81no—
302C22×C47—81no—
303C22×C47—81no—
304C22×C47#47814yescomplemented
305C22×C47C2×#12111yescharacteristic
306C22×C47C2×C22⋊Q811yescharacteristic
307C22×C47#53711yescharacteristic
308C22×C47C2×#13511yescharacteristic
309C22×C47C2×#13511yescharacteristic
310C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C47#57511yescharacteristic
312C4×C47—22no—
313C4×C47—22no—
314C4×C47—22no—
315C4×C47—22no—
316C4×C47—42no—
317C4×C47—41no—
318C4×C47—81no—
319C4×C47—81no—
320C4×C47—81no—
321C4×C47—81no—
322C4×C47—81no—
323C4×C47—81no—
324C4×C47#54611yescharacteristic
325C4×C47D4×Q811yescharacteristic
326C4×C47#55211yescharacteristic
327C4×C47#55411yescharacteristic
328C2×#478C2×C4711yescharacteristic, complemented
329C22×C4⋊C8C2×C4711yescharacteristic, complemented
330#2851C2×C4711yescharacteristic, complemented
331C4×#121C2×C4711yescharacteristic
332#2088C2×C4711yescharacteristic, complemented
333#2087C2×C4711yescharacteristic, complemented
334#2067C2×C4711yescharacteristic, complemented
335#2065C2×C4711yescharacteristic, complemented
336#1989C2×C4711yescharacteristic, complemented
337#1949C2×C4711yescharacteristic, complemented
338#1893C2×C4711yescharacteristic
339#1893C2×C4711yescharacteristic
340#1808C2×C4711yescharacteristic, complemented
341#1807C2×C4711yescharacteristic, complemented
342#1804C2×C4711yescharacteristic, complemented
343C2×C47—24no—
344C2×C47—82no—
345C2×C47#241711yescharacteristic
346C2×C47#305011yescharacteristic
347C2×C47#305511yescharacteristic
348C2×C47C2×#47811yescharacteristic
349C2×C47#307611yescharacteristic
350C2×C47#324711yescharacteristic
351C2×C47#325011yescharacteristic
352C23×C8C22×C4711yescharacteristic
353C23×C8C22×C4711yescharacteristic
354C2×#125C22×C4711yescharacteristic
355C2×#121C22×C4711yescharacteristic
356C2×C4×D4—21no—
357C2×C4×D4C22×C4711yescharacteristic
358C22×C42C22×C4711yescharacteristic
359#478—24no—
360C2×#107C22×C4711yescharacteristic
361C2×#107C22×C4711yescharacteristic
362C2×#106C22×C4711yescharacteristic
363C2×#106C22×C4711yescharacteristic
364C2×C4⋊C8—24no—
365C2×C4⋊C8C22×C4711yescharacteristic
366C2×C4⋊C8C22×C4711yescharacteristic
367C2×C4⋊C8C22×C4711yescharacteristic
368C2×C4⋊C8C22×C4711yescharacteristic
369C2×#102C22×C4711yescharacteristic
370C2×#102C22×C4711yescharacteristic
371C2×#102C22×C4711yescharacteristic
372C2×#102C22×C4711yescharacteristic
373#390C22×C4711yescharacteristic
374#389C22×C4711yescharacteristic
375#389C22×C4711yescharacteristic
376#389C22×C4711yescharacteristic
377#388—21no—
378#387—21no—
379#387—21no—
380#386—21no—
381#385—21no—
382#385—21no—
383#382C22×C4711yescharacteristic
384#380C22×C4711yescharacteristic
385#380C22×C4711yescharacteristic
386#380C22×C4711yescharacteristic
387C4×C4⋊C4C22×C4711yescharacteristic
388C4×C22⋊C4—21no—
389#340C22×C4711yescharacteristic
390#340C22×C4711yescharacteristic
391#340C22×C4711yescharacteristic
392#340C22×C4711yescharacteristic
393#340C22×C4711yescharacteristic
394#340C22×C4711yescharacteristic
395#340C22×C4711yescharacteristic
396#340C22×C4711yescharacteristic
397C47#2483911yescharacteristic, direct product factor, Sylow
398C22×D4—21no—
399C22×D4C23×C4711yescharacteristic
400C23×C4—21no—
401C23×C4D4×C4711yescharacteristic
402C23×C4D4×C4711yescharacteristic
403C23×C4C23×C4711yescharacteristic
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8—41no—
409C22×C8—41no—
410C22×C8C23×C4711yescharacteristic
411C22×C8C23×C4711yescharacteristic
412C22×C8C23×C4711yescharacteristic
413C22×C8C23×C4711yescharacteristic
414#125—22no—
415#125—22no—
416#121—22no—
417#121Q8×C4714yes—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—44no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4C23×C4711yescharacteristic
427C2×C4⋊C4C23×C4711yescharacteristic
428C2×C4⋊C4C23×C4711yescharacteristic
429C2×C4⋊C4C23×C4711yescharacteristic
430C2×C4⋊C4C23×C4711yescharacteristic
431C2×C4⋊C4C23×C4711yescharacteristic
432C2×C4⋊C4C23×C4711yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—21no—
443C2×C42D4×C4711yescharacteristic
444C2×C42D4×C4711yescharacteristic
445C2×C42C23×C4711yescharacteristic
446C2×C42C23×C4711yescharacteristic
447#107—22no—
448#107—41no—
449#106—22no—
450#106—41no—
451C4⋊C8—22no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454C4⋊C8D4×C4714yescomplemented
455#102—22no—
456#102—22no—
457#102—41no—
458#102—41no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468C24—21no—
469C24C2×D4×C4711yescharacteristic
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4C2×Q8×C4712yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4C2×D4×C4711yescharacteristic
500C22×C4C2×D4×C4711yescharacteristic
501C22×C4C2×D4×C4711yescharacteristic
502C22×C4C2×D4×C4711yescharacteristic
503C22×C4C2×D4×C4711yescharacteristic
504C22×C4C2×Q8×C4712yes—
505C22×C4#41×C4712yes—
506C22×C4C24×C4711yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—44no—
518C2×C8—44no—
519C2×C8C2×D4×C4712yes—
520C2×C8C2×D4×C4712yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4C2×Q8×C4712yes—
540C22⋊C4—24no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C42—22no—
548C42—22no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42C2×D4×C4712yes—
553C42#41×C4712yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C22⋊Q8×C4712yes—
566C23#135×C4712yes—
567C23AGL(1,ℤ/8)×C4712yes—
568C23C22×D4×C4711yescharacteristic
569D4—22no—
570D4—22no—
571D4—48no—
572D4—41no—
573D4—41no—
574C2×C4—28no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—44no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4#121×C4712yes—
614C2×C4#121×C4712yes—
615C2×C4C22⋊Q8×C4712yes—
616C2×C4#135×C4712yes—
617C2×C4C22×D4×C4711yescharacteristic
618C2×C4C22×Q8×C4711yescharacteristic
619C2×C4C2×#41×C4711yescharacteristic
620C2×C4C2×#41×C4711yescharacteristic
621C2×C4H(5,𝔽2)×C4711yescharacteristic
622C2×C42−1+4×C4711yescharacteristic
623C8—22no—
624C8—22no—
625C8—41no—
626C8—41no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22C47×#47814yescomplemented
641C22C2×#121×C4711yescharacteristic
642C22C2×C22⋊Q8×C4711yescharacteristic
643C22C47×#53711yescharacteristic
644C22C2×#135×C4711yescharacteristic
645C22C2×#135×C4711yescharacteristic
646C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
647C22C47×#57511yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—41no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4C47×#54611yescharacteristic
661C4D4×Q8×C4711yescharacteristic
662C4C47×#55211yescharacteristic
663C4C47×#55411yescharacteristic
664C2—24no—
665C2—82no—
666C2C47×#241711yescharacteristic
667C2C47×#305011yescharacteristic
668C2C47×#305511yescharacteristic
669C2C2×C47×#47811yescharacteristic
670C2C47×#307611yescharacteristic
671C2C47×#324711yescharacteristic
672C2C47×#325011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#478C2semidirect
2. C22×C4⋊C8×C47C2semidirect
3. C47×#2851C2semidirect
5. C47×#2088C2semidirect
6. C47×#2087C2semidirect
7. C47×#2067C2semidirect
8. C47×#2065C2semidirect
9. C47×#1989C2semidirect
10. C47×#1949C2semidirect
13. C47×#1808C2semidirect
14. C47×#1807C2semidirect
15. C47×#1804C2semidirect
117. C4⋊C8×C47D4semidirect
290. #24839C47direct (N × H)
304. C22×C47#478semidirect
328. C2×#478C2×C47semidirect
329. C22×C4⋊C8C2×C47semidirect
330. #2851C2×C47semidirect
332. #2088C2×C47semidirect
333. #2087C2×C47semidirect
334. #2067C2×C47semidirect
335. #2065C2×C47semidirect
336. #1989C2×C47semidirect
337. #1949C2×C47semidirect
340. #1808C2×C47semidirect
341. #1807C2×C47semidirect
342. #1804C2×C47semidirect
397. C47#24839direct (N × H)
454. C4⋊C8D4×C47semidirect
640. C22C47×#478semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4782
C22×C4⋊C8×C472
C47×#28512
C4×#121×C472
C47×#20882
C47×#20872
C47×#20672
C47×#20652
C47×#19892
C47×#19492
C47×#18932
C47×#18082
C47×#18072
C47×#18042
#2483947