Finite Group Databasebeta

← C47×#29600 #26069298

Subgroups — C47×#29600 #26069298

Order 12032.

1540 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#525C211yesmaximal, characteristic, complemented
2C2×C47×#482C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C47×#2847C211yesmaximal, characteristic, complemented
5C47×#2036C211yesmaximal, characteristic, complemented
6C47×#2035C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#2000C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1999C211yesmaximal, characteristic, complemented
12C47×#1999C211yesmaximal, characteristic, complemented
13C47×#1825C211yesmaximal, characteristic, complemented
14C47×#1788C211yesmaximal, characteristic, complemented
15C47×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C24×C4×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic, complemented
19C22×D8×C47C2211yescharacteristic, complemented
20C47×#525—24no—
21C47×#525—24no—
22C2×#123×C47—21no—
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×#120×C47—21no—
31C2×#120×C47—21no—
32C2×C4×D4×C47—21no—
33C2×C4×D4×C47—21no—
34C2×#117×C47C2211yescharacteristic
35C47×#482—24no—
36C47×#449—24no—
37C2×#107×C47C2211yescharacteristic, complemented
38C2×#106×C47C2211yescharacteristic, complemented
39C2×#103×C47C2211yescharacteristic, complemented
40C2×#103×C47C2211yescharacteristic, complemented
41C2×#103×C47C2211yescharacteristic, complemented
42C2×#102×C47C2211yescharacteristic, complemented
43C2×#102×C47C2211yescharacteristic, complemented
44C2×#102×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic, complemented
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic
50C2×C22⋊C8×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C47×#386—21no—
54C47×#386—21no—
55C47×#386—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C25×C47D411yescharacteristic
64C2×#41×C47—22no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C2×#41×C47D414yescomplemented
70C22×Q8×C47C2311yescharacteristic
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47C2311yescharacteristic
78C22×D4×C47C2311yescharacteristic
79C23×C4×C47—21no—
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—41no—
83C23×C4×C47—41no—
84C23×C4×C47—41no—
85C23×C4×C47—41no—
86C23×C4×C47D411yescharacteristic
87C23×C4×C47D411yescharacteristic
88C23×C4×C47D411yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×SD16×C47—22no—
93C2×SD16×C47—41no—
94C2×SD16×C47—41no—
95C2×D8×C47—22no—
96C2×D8×C47—41no—
97C2×D8×C47—41no—
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100C22×C8×C47C2311yescharacteristic
101C22×C8×C47C2311yescharacteristic
102#123×C47—28no—
103C22⋊Q8×C47—22no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—22no—
107#121×C47—22no—
108#121×C47—22no—
109#121×C47—22no—
110#121×C47—22no—
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—41no—
114#121×C47—41no—
115#121×C47—41no—
116#121×C47—41no—
117#120×C47—28no—
118#120×C47—44no—
119C4×D4×C47—28no—
120C4×D4×C47—28no—
121#117×C47—22no—
122#117×C47D414yescomplemented
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C42×C47—21no—
142#107×C47—22no—
143#106×C47—22no—
144#103×C47—22no—
145#103×C47—41no—
146#103×C47—41no—
147#102×C47—22no—
148#102×C47—22no—
149#102×C47—22no—
150#102×C47—41no—
151#102×C47—41no—
152C22⋊C8×C47—22no—
153C22⋊C8×C47—22no—
154C22⋊C8×C47—41no—
155C22⋊C8×C47—41no—
156C22⋊C8×C47—41no—
157C22⋊C8×C47—41no—
158#95×C47—21no—
159#95×C47—21no—
160#95×C47—21no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—21no—
165C24×C47—21no—
166C24×C47—41no—
167C24×C47—41no—
168C24×C47—41no—
169C24×C47—41no—
170C24×C47C2×D411yescharacteristic
171C24×C47C2×D411yescharacteristic
172C24×C47C2×D411yescharacteristic
173#41×C47—44no—
174#41×C47—44no—
175#41×C47—44no—
176#41×C47—44no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47C2×D412yes—
183C2×D4×C47—24no—
184C2×D4×C47—24no—
185C2×D4×C47—24no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—42no—
202C2×D4×C47—42no—
203C2×D4×C47—42no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47—42no—
207C2×D4×C47—42no—
208C2×D4×C47—42no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47C2×D412yes—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—22no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—24no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—41no—
240C22×C4×C47—41no—
241C22×C4×C47—41no—
242C22×C4×C47—41no—
243C22×C4×C47—41no—
244C22×C4×C47—41no—
245C22×C4×C47—44no—
246C22×C4×C47—44no—
247C22×C4×C47—44no—
248C22×C4×C47—44no—
249C22×C4×C47—42no—
250C22×C4×C47—42no—
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D412yes—
255C22×C4×C47C2×D412yes—
256C22×C4×C47C2411yescharacteristic
257SD16×C47—44no—
258D8×C47—44no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C4⋊C4×C47—24no—
272C4⋊C4×C47—24no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47C2×D412yes—
282C4⋊C4×C47C2×D412yes—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—42no—
289C22⋊C4×C47—42no—
290C22⋊C4×C47—42no—
291C22⋊C4×C47—42no—
292C22⋊C4×C47—42no—
293C22⋊C4×C47—42no—
294C42×C47—24no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—21no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—21no—
307C23×C47—21no—
308C23×C47—21no—
309C23×C47—21no—
310C23×C47—21no—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—22no—
314C23×C47—44no—
315C23×C47—44no—
316C23×C47—44no—
317C23×C47—44no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47—41no—
322C23×C47—41no—
323C23×C47—41no—
324C23×C47—41no—
325C23×C47—41no—
326C23×C47—41no—
327C23×C47—41no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—41no—
333C23×C47—41no—
334C23×C47#12012yes—
335C23×C47#13512yes—
336C23×C47AGL(1,ℤ/8)12yes—
337C23×C47C22×D411yescharacteristic
338Q8×C47—22no—
339Q8×C47—22no—
340Q8×C47—41no—
341Q8×C47—41no—
342D4×C47—22no—
343D4×C47—22no—
344D4×C47—48no—
345D4×C47—48no—
346D4×C47—48no—
347D4×C47—41no—
348D4×C47—41no—
349D4×C47—41no—
350D4×C47—41no—
351D4×C47—41no—
352D4×C47—41no—
353D4×C47—84no—
354D4×C47—84no—
355D4×C47—84no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—22no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—44no—
372C2×C4×C47—44no—
373C2×C4×C47—48no—
374C2×C4×C47—44no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47#12012yes—
399C2×C4×C47C22×D411yescharacteristic
400C2×C4×C47C22×D411yescharacteristic
401C2×C4×C47H(5,𝔽2)11yescharacteristic
402C2×C4×C47H(5,𝔽2)11yescharacteristic
403C2×C4×C47H(5,𝔽2)11yescharacteristic
404C2×C4×C47H(5,𝔽2)11yescharacteristic
405C8×C47—41no—
406C8×C47—41no—
407C8×C47—41no—
408C8×C47—41no—
409#29600C4711yesmaximal, characteristic, direct product factor, Sylow
410C22×C47—22no—
411C22×C47—22no—
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—22no—
417C22×C47—22no—
418C22×C47—22no—
419C22×C47—416no—
420C22×C47—41no—
421C22×C47—41no—
422C22×C47—41no—
423C22×C47—41no—
424C22×C47—41no—
425C22×C47—41no—
426C22×C47—41no—
427C22×C47—41no—
428C22×C47—41no—
429C22×C47—41no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—42no—
435C22×C47—81no—
436C22×C47—81no—
437C22×C47—81no—
438C22×C47—81no—
439C22×C47—81no—
440C22×C47—81no—
441C22×C47—81no—
442C22×C47—81no—
443C22×C47—81no—
444C22×C47—81no—
445C22×C47—81no—
446C22×C47C2×#12011yescharacteristic
447C22×C47#53411yescharacteristic
448C22×C47#53411yescharacteristic
449C22×C47C2×#13511yescharacteristic
450C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C47#57511yescharacteristic
452C22×C47#57511yescharacteristic
453C4×C47—22no—
454C4×C47—41no—
455C4×C47—41no—
456C4×C47—42no—
457C4×C47—42no—
458C4×C47—42no—
459C4×C47—81no—
460C4×C47—81no—
461C4×C47—81no—
462C4×C47#53411yescharacteristic
463C4×C47#53411yescharacteristic
464C4×C47#53511yescharacteristic
465C4×C47#53511yescharacteristic
466C2×#525C2×C4711yescharacteristic, complemented
467C2×#482C2×C4711yescharacteristic, complemented
468C2×#449C2×C4711yescharacteristic, complemented
469#2847C2×C4711yescharacteristic, complemented
470#2036C2×C4711yescharacteristic, complemented
471#2035C2×C4711yescharacteristic, complemented
472#2034C2×C4711yescharacteristic, complemented
473#2033C2×C4711yescharacteristic, complemented
474#2000C2×C4711yescharacteristic, complemented
475#2000C2×C4711yescharacteristic, complemented
476#1999C2×C4711yescharacteristic, complemented
477#1999C2×C4711yescharacteristic, complemented
478#1825C2×C4711yescharacteristic, complemented
479#1788C2×C4711yescharacteristic, complemented
480#1779C2×C4711yescharacteristic, complemented
481C2×C47—42no—
482C2×C47—42no—
483C2×C47—42no—
484C2×C47—82no—
485C2×C47—161no—
486C2×C47#261311yescharacteristic
487C2×C47#300211yescharacteristic
488C2×C47#300611yescharacteristic
489C2×C47#318811yescharacteristic
490C2×C47#319111yescharacteristic
491C2×C47#319411yescharacteristic
492C2×C47#319711yescharacteristic
493C22×#41C22×C4711yescharacteristic
494C24×C4C22×C4711yescharacteristic
495C22×SD16C22×C4711yescharacteristic, complemented
496C22×D8C22×C4711yescharacteristic, complemented
497#525—24no—
498#525—24no—
499C2×#123—21no—
500C2×C22⋊Q8C22×C4711yescharacteristic
501C2×C22⋊Q8C22×C4711yescharacteristic
502C2×#121C22×C4711yescharacteristic
503C2×#121C22×C4711yescharacteristic
504C2×#121C22×C4711yescharacteristic
505C2×#121C22×C4711yescharacteristic
506C2×#121C22×C4711yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4—21no—
510C2×C4×D4—21no—
511C2×#117C22×C4711yescharacteristic
512#482—24no—
513#449—24no—
514C2×#107C22×C4711yescharacteristic, complemented
515C2×#106C22×C4711yescharacteristic, complemented
516C2×#103C22×C4711yescharacteristic, complemented
517C2×#103C22×C4711yescharacteristic, complemented
518C2×#103C22×C4711yescharacteristic, complemented
519C2×#102C22×C4711yescharacteristic, complemented
520C2×#102C22×C4711yescharacteristic, complemented
521C2×#102C22×C4711yescharacteristic, complemented
522C2×#102C22×C4711yescharacteristic, complemented
523C2×#102C22×C4711yescharacteristic, complemented
524C2×C22⋊C8C22×C4711yescharacteristic
525C2×C22⋊C8C22×C4711yescharacteristic
526C2×C22⋊C8C22×C4711yescharacteristic
527C2×C22⋊C8C22×C4711yescharacteristic
528C2×C22⋊C8C22×C4711yescharacteristic
529C2×C22⋊C8C22×C4711yescharacteristic
530#386—21no—
531#386—21no—
532#386—21no—
533#380C22×C4711yescharacteristic
534#380C22×C4711yescharacteristic
535#380C22×C4711yescharacteristic
536#340C22×C4711yescharacteristic, complemented
537#340C22×C4711yescharacteristic, complemented
538#340C22×C4711yescharacteristic, complemented
539#340C22×C4711yescharacteristic, complemented
540C47#2960011yescharacteristic, direct product factor, Sylow
541C25D4×C4711yescharacteristic
542C2×#41—22no—
543C2×#41—41no—
544C2×#41—41no—
545C2×#41—41no—
546C2×#41—41no—
547C2×#41D4×C4714yescomplemented
548C22×Q8C23×C4711yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4C23×C4711yescharacteristic
556C22×D4C23×C4711yescharacteristic
557C23×C4—21no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4D4×C4711yescharacteristic
565C23×C4D4×C4711yescharacteristic
566C23×C4D4×C4711yescharacteristic
567C23×C4C23×C4711yescharacteristic
568C23×C4C23×C4711yescharacteristic
569C23×C4C23×C4711yescharacteristic
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C22×C8C23×C4711yescharacteristic
577C22×C8C23×C4711yescharacteristic
578C22×C8C23×C4711yescharacteristic
579C22×C8C23×C4711yescharacteristic
580#123—28no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#120—28no—
596#120—44no—
597C4×D4—28no—
598C4×D4—28no—
599#117—22no—
600#117D4×C4714yescomplemented
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C23×C4711yescharacteristic
604C2×C4⋊C4C23×C4711yescharacteristic
605C2×C4⋊C4C23×C4711yescharacteristic
606C2×C4⋊C4C23×C4711yescharacteristic
607C2×C4⋊C4C23×C4711yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C42—21no—
620#107—22no—
621#106—22no—
622#103—22no—
623#103—41no—
624#103—41no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—41no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—41no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—41no—
645C24—41no—
646C24—41no—
647C24—41no—
648C24C2×D4×C4711yescharacteristic
649C24C2×D4×C4711yescharacteristic
650C24C2×D4×C4711yescharacteristic
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C4712yes—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4C2×D4×C4712yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4C2×D4×C4711yescharacteristic
730C22×C4C2×D4×C4711yescharacteristic
731C22×C4C2×D4×C4711yescharacteristic
732C22×C4C2×D4×C4712yes—
733C22×C4C2×D4×C4712yes—
734C22×C4C24×C4711yescharacteristic
735SD16—44no—
736D8—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4C2×D4×C4712yes—
760C4⋊C4C2×D4×C4712yes—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C42—24no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—22no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23#120×C4712yes—
813C23#135×C4712yes—
814C23AGL(1,ℤ/8)×C4712yes—
815C23C22×D4×C4711yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—41no—
819Q8—41no—
820D4—22no—
821D4—22no—
822D4—48no—
823D4—48no—
824D4—48no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—84no—
832D4—84no—
833D4—84no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4#120×C4712yes—
877C2×C4C22×D4×C4711yescharacteristic
878C2×C4C22×D4×C4711yescharacteristic
879C2×C4H(5,𝔽2)×C4711yescharacteristic
880C2×C4H(5,𝔽2)×C4711yescharacteristic
881C2×C4H(5,𝔽2)×C4711yescharacteristic
882C2×C4H(5,𝔽2)×C4711yescharacteristic
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—416no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#120×C4711yescharacteristic
924C22C47×#53411yescharacteristic
925C22C47×#53411yescharacteristic
926C22C2×#135×C4711yescharacteristic
927C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
928C22C47×#57511yescharacteristic
929C22C47×#57511yescharacteristic
930C4—22no—
931C4—41no—
932C4—41no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C47×#53411yescharacteristic
940C4C47×#53411yescharacteristic
941C4C47×#53511yescharacteristic
942C4C47×#53511yescharacteristic
943C2—42no—
944C2—42no—
945C2—42no—
946C2—82no—
947C2—161no—
948C2C47×#261311yescharacteristic
949C2C47×#300211yescharacteristic
950C2C47×#300611yescharacteristic
951C2C47×#318811yescharacteristic
952C2C47×#319111yescharacteristic
953C2C47×#319411yescharacteristic
954C2C47×#319711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#525C2semidirect
2. C2×C47×#482C2semidirect
3. C2×C47×#449C2semidirect
4. C47×#2847C2semidirect
5. C47×#2036C2semidirect
6. C47×#2035C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#2000C2semidirect
10. C47×#2000C2semidirect
11. C47×#1999C2semidirect
12. C47×#1999C2semidirect
13. C47×#1825C2semidirect
14. C47×#1788C2semidirect
15. C47×#1779C2semidirect
18. C22×SD16×C47C22semidirect
19. C22×D8×C47C22semidirect
37. C2×#107×C47C22semidirect
38. C2×#106×C47C22semidirect
39. C2×#103×C47C22semidirect
40. C2×#103×C47C22semidirect
41. C2×#103×C47C22semidirect
42. C2×#102×C47C22semidirect
43. C2×#102×C47C22semidirect
44. C2×#102×C47C22semidirect
45. C2×#102×C47C22semidirect
46. C2×#102×C47C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
69. C2×#41×C47D4semidirect
122. #117×C47D4semidirect
409. #29600C47direct (N × H)
466. C2×#525C2×C47semidirect
467. C2×#482C2×C47semidirect
468. C2×#449C2×C47semidirect
469. #2847C2×C47semidirect
470. #2036C2×C47semidirect
471. #2035C2×C47semidirect
472. #2034C2×C47semidirect
473. #2033C2×C47semidirect
474. #2000C2×C47semidirect
475. #2000C2×C47semidirect
476. #1999C2×C47semidirect
477. #1999C2×C47semidirect
478. #1825C2×C47semidirect
479. #1788C2×C47semidirect
480. #1779C2×C47semidirect
495. C22×SD16C22×C47semidirect
496. C22×D8C22×C47semidirect
514. C2×#107C22×C47semidirect
515. C2×#106C22×C47semidirect
516. C2×#103C22×C47semidirect
517. C2×#103C22×C47semidirect
518. C2×#103C22×C47semidirect
519. C2×#102C22×C47semidirect
520. C2×#102C22×C47semidirect
521. C2×#102C22×C47semidirect
522. C2×#102C22×C47semidirect
523. C2×#102C22×C47semidirect
536. #340C22×C47semidirect
537. #340C22×C47semidirect
538. #340C22×C47semidirect
539. #340C22×C47semidirect
540. C47#29600direct (N × H)
547. C2×#41D4×C47semidirect
600. #117D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5252
C2×C47×#4822
C2×C47×#4492
C47×#28472
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#20002
C47×#19992
C47×#18252
C47×#17882
C47×#17792
#2960047