Finite Group Databasebeta

← C47×#24444 #26064142

Subgroups — C47×#24444 #26064142

Order 12032.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#546C211yesmaximal, characteristic, complemented
2C2×C47×#469C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#447C211yesmaximal, characteristic, complemented
5C2×C47×#417C211yesmaximal, characteristic, complemented
6C47×#2416C211yesmaximal, characteristic, complemented
7C47×#2042C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2012C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1870C211yesmaximal, characteristic, complemented
14C47×#1864C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic, complemented
19C22×D8×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C22×M16×C47C2211yescharacteristic, complemented
22C47×#546—24no—
23C47×#546—24no—
24C2×#124×C47C2211yescharacteristic
25C2×#123×C47—21no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×#121×C47—21no—
28C2×#121×C47—21no—
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×#121×C47C2211yescharacteristic, complemented
32C2×#120×C47—21no—
33C2×C4×D4×C47C2211yescharacteristic
34C2×C4×D4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic, complemented
36C22×C22⋊C4×C47—21no—
37C47×#469—24no—
38C47×#449—24no—
39C47×#447—24no—
40C2×#106×C47C2211yescharacteristic, complemented
41C47×#417—24no—
42C2×#103×C47C2211yescharacteristic, complemented
43C2×#103×C47C2211yescharacteristic, complemented
44C2×#103×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×#102×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×#102×C47C2211yescharacteristic, complemented
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic, complemented
55C47×#396—21no—
56C47×#394—21no—
57C47×#390C2211yescharacteristic, complemented
58C47×#389C2211yescharacteristic, complemented
59C47×#386—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47—21no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47D414yescomplemented
72C22×Q8×C47C2311yescharacteristic
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—22no—
76C22×D4×C47—22no—
77C22×D4×C47—22no—
78C22×D4×C47—22no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—41no—
83C22×D4×C47—41no—
84C22×D4×C47D411yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C22×D4×C47C2311yescharacteristic
88C23×C4×C47—21no—
89C23×C4×C47—21no—
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C2×SD16×C47—22no—
94C2×SD16×C47—41no—
95C2×SD16×C47—41no—
96C2×D8×C47—22no—
97C2×D8×C47—22no—
98C2×D8×C47—22no—
99C2×D8×C47—22no—
100C2×D8×C47—22no—
101C2×D8×C47—41no—
102C2×M16×C47—22no—
103C2×M16×C47—22no—
104C2×M16×C47—41no—
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109#124×C47—22no—
110#124×C47—22no—
111#123×C47—28no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114#121×C47—28no—
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—41no—
120#121×C47—44no—
121#121×C47D414yescomplemented
122#120×C47—28no—
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—22no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—41no—
132C2×C4⋊C4×C47D411yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C22⋊C4×C47—28no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47—21no—
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C22⋊C4×C47D411yescharacteristic
150C2×C42×C47C2311yescharacteristic
151#106×C47—22no—
152#103×C47—22no—
153#103×C47—22no—
154#103×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—22no—
158#102×C47—22no—
159#102×C47—22no—
160#102×C47—41no—
161#102×C47D414yescomplemented
162C22⋊C8×C47—22no—
163C22⋊C8×C47—22no—
164C22⋊C8×C47—41no—
165#95×C47—21no—
166#95×C47—21no—
167C24×C47—21no—
168C24×C47—24no—
169C24×C47—21no—
170C24×C47—21no—
171C24×C47—42no—
172C24×C47—42no—
173C24×C47—42no—
174C24×C47—42no—
175C24×C47—81no—
176C24×C47—81no—
177C24×C47C2×D411yescharacteristic
178C24×C47C2×D411yescharacteristic
179#41×C47—28no—
180#41×C47—44no—
181#41×C47—44no—
182#41×C47—44no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47C2×D412yes—
189C2×D4×C47—24no—
190C2×D4×C47—22no—
191C2×D4×C47—24no—
192C2×D4×C47—22no—
193C2×D4×C47—24no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—41no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—44no—
213C2×D4×C47—44no—
214C2×D4×C47—44no—
215C2×D4×C47—42no—
216C2×D4×C47—42no—
217C2×D4×C47—44no—
218C2×D4×C47—42no—
219C2×D4×C47—42no—
220C2×D4×C47—42no—
221C2×D4×C47—42no—
222C2×D4×C47—81no—
223C2×D4×C47—81no—
224C2×D4×C47—81no—
225C2×D4×C47C2×D412yes—
226C2×D4×C47C2×D412yes—
227C2×D4×C47C2×D412yes—
228C2×D4×C47#4112yes—
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—24no—
237C22×C4×C47—24no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—42no—
247C22×C4×C47—42no—
248C22×C4×C47—42no—
249C22×C4×C47—42no—
250C22×C4×C47—81no—
251C22×C4×C47—81no—
252C22×C4×C47—81no—
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D412yes—
258C22×C4×C47C2×D412yes—
259C22×C4×C47C2411yescharacteristic
260SD16×C47—44no—
261D8×C47—44no—
262D8×C47—44no—
263M16×C47—44no—
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—
271C2×C8×C47—21no—
272C2×C8×C47—21no—
273C2×C8×C47—21no—
274C2×C8×C47—21no—
275C2×C8×C47C2×D412yes—
276C4⋊C4×C47—24no—
277C4⋊C4×C47—22no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—42no—
285C4⋊C4×C47—42no—
286C4⋊C4×C47C2×D412yes—
287C4⋊C4×C47C2×D412yes—
288C22⋊C4×C47—24no—
289C22⋊C4×C47—24no—
290C22⋊C4×C47—24no—
291C22⋊C4×C47—24no—
292C22⋊C4×C47—22no—
293C22⋊C4×C47—22no—
294C22⋊C4×C47—24no—
295C22⋊C4×C47—42no—
296C22⋊C4×C47—42no—
297C22⋊C4×C47—42no—
298C22⋊C4×C47—42no—
299C22⋊C4×C47—81no—
300C42×C47—21no—
301C42×C47—21no—
302C23×C47—21no—
303C23×C47—22no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—22no—
307C23×C47—21no—
308C23×C47—21no—
309C23×C47—22no—
310C23×C47—21no—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—21no—
314C23×C47—21no—
315C23×C47—21no—
316C23×C47—21no—
317C23×C47—22no—
318C23×C47—48no—
319C23×C47—48no—
320C23×C47—41no—
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—41no—
335C23×C47—41no—
336C23×C47—41no—
337C23×C47—84no—
338C23×C47—84no—
339C23×C47—84no—
340C23×C47—84no—
341C23×C47—84no—
342C23×C47#12012yes—
343C23×C47AGL(1,ℤ/8)12yes—
344C23×C47C22×D411yescharacteristic
345Q8×C47—22no—
346Q8×C47—22no—
347Q8×C47—41no—
348Q8×C47—41no—
349D4×C47—22no—
350D4×C47—22no—
351D4×C47—22no—
352D4×C47—22no—
353D4×C47—22no—
354D4×C47—44no—
355D4×C47—48no—
356D4×C47—48no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47—41no—
362D4×C47—41no—
363D4×C47—84no—
364D4×C47—84no—
365D4×C47—84no—
366D4×C47#12114yescomplemented
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—21no—
374C2×C4×C47—21no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—21no—
378C2×C4×C47—21no—
379C2×C4×C47—22no—
380C2×C4×C47—21no—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—21no—
385C2×C4×C47—48no—
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—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—84no—
403C2×C4×C47—84no—
404C2×C4×C47#12012yes—
405C2×C4×C47C22×D411yescharacteristic
406C2×C4×C47C22×D411yescharacteristic
407C2×C4×C47C22×D411yescharacteristic
408C2×C4×C47C2×#4111yescharacteristic
409C2×C4×C47H(5,𝔽2)11yescharacteristic
410C2×C4×C47H(5,𝔽2)11yescharacteristic
411C8×C47—22no—
412C8×C47—41no—
413C8×C47—41no—
414C8×C47—41no—
415#24444C4711yesmaximal, characteristic, direct product factor, Sylow
416C22×C47—22no—
417C22×C47—24no—
418C22×C47—22no—
419C22×C47—22no—
420C22×C47—22no—
421C22×C47—22no—
422C22×C47—22no—
423C22×C47—41no—
424C22×C47—42no—
425C22×C47—41no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—41no—
429C22×C47—41no—
430C22×C47—41no—
431C22×C47—42no—
432C22×C47—41no—
433C22×C47—42no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—816no—
441C22×C47—81no—
442C22×C47—81no—
443C22×C47—81no—
444C22×C47—81no—
445C22×C47—81no—
446C22×C47—81no—
447C22×C47—81no—
448C22×C47—81no—
449C22×C47—81no—
450C22×C47—81no—
451C22×C47—81no—
452C22×C47C2×#12011yescharacteristic
453C22×C47D4211yescharacteristic
454C22×C47#54611yescharacteristic
455C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C47#57511yescharacteristic
457C22×C47#57611yescharacteristic
458C22×C47#57711yescharacteristic
459C4×C47—22no—
460C4×C47—41no—
461C4×C47—42no—
462C4×C47—41no—
463C4×C47—42no—
464C4×C47—41no—
465C4×C47—42no—
466C4×C47—81no—
467C4×C47—81no—
468C4×C47C2×#12111yescharacteristic
469C4×C47#53411yescharacteristic
470C4×C47D4211yescharacteristic
471C4×C47#54611yescharacteristic
472C2×#546C2×C4711yescharacteristic, complemented
473C2×#469C2×C4711yescharacteristic, complemented
474C2×#449C2×C4711yescharacteristic, complemented
475C2×#447C2×C4711yescharacteristic, complemented
476C2×#417C2×C4711yescharacteristic, complemented
477#2416C2×C4711yescharacteristic, complemented
478#2042C2×C4711yescharacteristic, complemented
479#2035C2×C4711yescharacteristic, complemented
480#2012C2×C4711yescharacteristic, complemented
481#2000C2×C4711yescharacteristic, complemented
482#1879C2×C4711yescharacteristic, complemented
483#1874C2×C4711yescharacteristic, complemented
484#1870C2×C4711yescharacteristic, complemented
485#1864C2×C4711yescharacteristic, complemented
486#1786C2×C4711yescharacteristic, complemented
487C2×C47—42no—
488C2×C47—42no—
489C2×C47—44no—
490C2×C47—82no—
491C2×C47—161no—
492C2×C47#241011yescharacteristic
493C2×C47#300611yescharacteristic
494C2×C47#301211yescharacteristic
495C2×C47#326411yescharacteristic
496C2×C47#327511yescharacteristic
497C2×C47#330611yescharacteristic
498C2×C47#332211yescharacteristic
499C22×#41C22×C4711yescharacteristic
500C23×D4C22×C4711yescharacteristic
501C22×SD16C22×C4711yescharacteristic, complemented
502C22×D8C22×C4711yescharacteristic
503C22×D8C22×C4711yescharacteristic
504C22×M16C22×C4711yescharacteristic, complemented
505#546—24no—
506#546—24no—
507C2×#124C22×C4711yescharacteristic
508C2×#123—21no—
509C2×C22⋊Q8C22×C4711yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C4711yescharacteristic
513C2×#121C22×C4711yescharacteristic
514C2×#121C22×C4711yescharacteristic, complemented
515C2×#120—21no—
516C2×C4×D4C22×C4711yescharacteristic
517C2×C4×D4C22×C4711yescharacteristic
518C22×C4⋊C4C22×C4711yescharacteristic, complemented
519C22×C22⋊C4—21no—
520#469—24no—
521#449—24no—
522#447—24no—
523C2×#106C22×C4711yescharacteristic, complemented
524#417—24no—
525C2×#103C22×C4711yescharacteristic, complemented
526C2×#103C22×C4711yescharacteristic, complemented
527C2×#103C22×C4711yescharacteristic, complemented
528C2×#102C22×C4711yescharacteristic
529C2×#102C22×C4711yescharacteristic
530C2×#102C22×C4711yescharacteristic
531C2×#102C22×C4711yescharacteristic
532C2×#102C22×C4711yescharacteristic
533C2×#102C22×C4711yescharacteristic
534C2×#102C22×C4711yescharacteristic, complemented
535C2×C22⋊C8C22×C4711yescharacteristic
536C2×C22⋊C8C22×C4711yescharacteristic
537C2×C22⋊C8C22×C4711yescharacteristic, complemented
538#396—21no—
539#394—21no—
540#390C22×C4711yescharacteristic, complemented
541#389C22×C4711yescharacteristic, complemented
542#386—21no—
543#380C22×C4711yescharacteristic
544#340C22×C4711yescharacteristic, complemented
545#340C22×C4711yescharacteristic, complemented
546#336C22×C4711yescharacteristic, complemented
547#336C22×C4711yescharacteristic, complemented
548C47#2444411yescharacteristic, direct product factor, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C4714yescomplemented
556C22×Q8C23×C4711yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4D4×C4711yescharacteristic
569C22×D4C23×C4711yescharacteristic
570C22×D4C23×C4711yescharacteristic
571C22×D4C23×C4711yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C4711yescharacteristic
576C23×C4C23×C4711yescharacteristic
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—41no—
589C22×C8C23×C4711yescharacteristic
590C22×C8C23×C4711yescharacteristic
591C22×C8C23×C4711yescharacteristic
592C22×C8C23×C4711yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—44no—
605#121D4×C4714yescomplemented
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C4711yescharacteristic
617C2×C4⋊C4C23×C4711yescharacteristic
618C2×C4⋊C4C23×C4711yescharacteristic
619C2×C4⋊C4C23×C4711yescharacteristic
620C2×C4⋊C4C23×C4711yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C4711yescharacteristic
633C2×C22⋊C4D4×C4711yescharacteristic
634C2×C42C23×C4711yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645#102D4×C4714yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—24no—
653C24—21no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C4711yescharacteristic
662C24C2×D4×C4711yescharacteristic
663#41—28no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C4712yes—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C4712yes—
710C2×D4C2×D4×C4712yes—
711C2×D4C2×D4×C4712yes—
712C2×D4#41×C4712yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C4711yescharacteristic
738C22×C4C2×D4×C4711yescharacteristic
739C22×C4C2×D4×C4711yescharacteristic
740C22×C4C2×D4×C4711yescharacteristic
741C22×C4C2×D4×C4712yes—
742C22×C4C2×D4×C4712yes—
743C22×C4C24×C4711yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747M16—44no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8C2×D4×C4712yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C4712yes—
771C4⋊C4C2×D4×C4712yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23#120×C4712yes—
827C23AGL(1,ℤ/8)×C4712yes—
828C23C22×D4×C4711yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C4714yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C4712yes—
889C2×C4C22×D4×C4711yescharacteristic
890C2×C4C22×D4×C4711yescharacteristic
891C2×C4C22×D4×C4711yescharacteristic
892C2×C4C2×#41×C4711yescharacteristic
893C2×C4H(5,𝔽2)×C4711yescharacteristic
894C2×C4H(5,𝔽2)×C4711yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—24no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—816no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22C2×#120×C4711yescharacteristic
936C22D42×C4711yescharacteristic
937C22C47×#54611yescharacteristic
938C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
939C22C47×#57511yescharacteristic
940C22C47×#57611yescharacteristic
941C22C47×#57711yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C4711yescharacteristic
952C4C47×#53411yescharacteristic
953C4D42×C4711yescharacteristic
954C4C47×#54611yescharacteristic
955C2—42no—
956C2—42no—
957C2—44no—
958C2—82no—
959C2—161no—
960C2C47×#241011yescharacteristic
961C2C47×#300611yescharacteristic
962C2C47×#301211yescharacteristic
963C2C47×#326411yescharacteristic
964C2C47×#327511yescharacteristic
965C2C47×#330611yescharacteristic
966C2C47×#332211yescharacteristic
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×#546C2semidirect
2. C2×C47×#469C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#447C2semidirect
5. C2×C47×#417C2semidirect
6. C47×#2416C2semidirect
7. C47×#2042C2semidirect
8. C47×#2035C2semidirect
9. C47×#2012C2semidirect
10. C47×#2000C2semidirect
11. C47×#1879C2semidirect
12. C47×#1874C2semidirect
13. C47×#1870C2semidirect
14. C47×#1864C2semidirect
15. C47×#1786C2semidirect
18. C22×SD16×C47C22semidirect
21. C22×M16×C47C22semidirect
31. C2×#121×C47C22semidirect
35. C22×C4⋊C4×C47C22semidirect
40. C2×#106×C47C22semidirect
42. C2×#103×C47C22semidirect
43. C2×#103×C47C22semidirect
44. C2×#103×C47C22semidirect
51. C2×#102×C47C22semidirect
54. C2×C22⋊C8×C47C22semidirect
57. C47×#390C22semidirect
58. C47×#389C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
71. C2×#41×C47D4semidirect
121. #121×C47D4semidirect
161. #102×C47D4semidirect
366. D4×C47#121semidirect
415. #24444C47direct (N × H)
472. C2×#546C2×C47semidirect
473. C2×#469C2×C47semidirect
474. C2×#449C2×C47semidirect
475. C2×#447C2×C47semidirect
476. C2×#417C2×C47semidirect
477. #2416C2×C47semidirect
478. #2042C2×C47semidirect
479. #2035C2×C47semidirect
480. #2012C2×C47semidirect
481. #2000C2×C47semidirect
482. #1879C2×C47semidirect
483. #1874C2×C47semidirect
484. #1870C2×C47semidirect
485. #1864C2×C47semidirect
486. #1786C2×C47semidirect
501. C22×SD16C22×C47semidirect
504. C22×M16C22×C47semidirect
514. C2×#121C22×C47semidirect
518. C22×C4⋊C4C22×C47semidirect
523. C2×#106C22×C47semidirect
525. C2×#103C22×C47semidirect
526. C2×#103C22×C47semidirect
527. C2×#103C22×C47semidirect
534. C2×#102C22×C47semidirect
537. C2×C22⋊C8C22×C47semidirect
540. #390C22×C47semidirect
541. #389C22×C47semidirect
544. #340C22×C47semidirect
545. #340C22×C47semidirect
546. #336C22×C47semidirect
547. #336C22×C47semidirect
548. C47#24444direct (N × H)
555. C2×#41D4×C47semidirect
605. #121D4×C47semidirect
645. #102D4×C47semidirect
850. D4#121×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5462
C2×C47×#4692
C2×C47×#4492
C2×C47×#4472
C2×C47×#4172
C47×#24162
C47×#20422
C47×#20352
C47×#20122
C47×#20002
C47×#18792
C47×#18742
C47×#18702
C47×#18642
C47×#17862
#2444447