Finite Group Databasebeta

← C47×#24366 #26064064

Subgroups — C47×#24366 #26064064

Order 12032.

1662 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
1C22×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#459C211yesmaximal, characteristic, complemented
4C2×C47×#447C211yesmaximal, characteristic, complemented
5C47×#2431C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2055C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2012C211yesmaximal, characteristic, complemented
10C47×#2011C211yesmaximal, characteristic, complemented
11C47×#1895C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic, complemented
14C47×#1851C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47—24no—
19C2×AGL(1,ℤ/8)×C47—24no—
20C2×AGL(1,ℤ/8)×C47—24no—
21C22×SD16×C47C2211yescharacteristic
22C22×SD16×C47C2211yescharacteristic
23C22×D8×C47C2211yescharacteristic
24C22×D8×C47C2211yescharacteristic
25C22×D8×C47C2211yescharacteristic
26C22×D8×C47C2211yescharacteristic
27C22×M16×C47C2211yescharacteristic
28C2×#127×C47C2211yescharacteristic, complemented
29C2×#124×C47C2211yescharacteristic, complemented
30C2×#121×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C22×C22⋊C4×C47—21no—
34C47×#463—24no—
35C47×#459—24no—
36C47×#447—24no—
37C2×C4⋊C8×C47C2211yescharacteristic, complemented
38C2×C4⋊C8×C47C2211yescharacteristic, complemented
39C2×#103×C47C2211yescharacteristic, complemented
40C2×#103×C47C2211yescharacteristic, complemented
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic, complemented
44C2×#102×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic, complemented
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#392—21no—
49C47×#392—21no—
50C47×#391C2211yescharacteristic, complemented
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#390C2211yescharacteristic, complemented
54C47×#386—21no—
55C47×#386—21no—
56C47×#386—21no—
57C47×#386—21no—
58C47×#380C2211yescharacteristic
59C47×#379—21no—
60C4×C22⋊C4×C47C2211yescharacteristic
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—22no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C22×Q8×C47C2311yescharacteristic
73C22×D4×C47—22no—
74C22×D4×C47—22no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—22no—
81C22×D4×C47—41no—
82C22×D4×C47—41no—
83C22×D4×C47D414yescomplemented
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C22×D4×C47C2311yescharacteristic
88C23×C4×C47—21no—
89C23×C4×C47—21no—
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92AGL(1,ℤ/8)×C47—232no—
93C2×SD16×C47—22no—
94C2×SD16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47D414yescomplemented
99C2×D8×C47—22no—
100C2×D8×C47—22no—
101C2×D8×C47—22no—
102C2×D8×C47—22no—
103C2×D8×C47—22no—
104C2×D8×C47—22no—
105C2×D8×C47—22no—
106C2×D8×C47—22no—
107C2×D8×C47—22no—
108C2×D8×C47—41no—
109C2×D8×C47—41no—
110C2×D8×C47D414yescomplemented
111C2×M16×C47—22no—
112C2×M16×C47—22no—
113C2×M16×C47—22no—
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118#127×C47—22no—
119#127×C47—41no—
120#124×C47—22no—
121#124×C47—41no—
122#121×C47—22no—
123#121×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—41no—
127C4×D4×C47—41no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
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×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—44no—
144C2×C22⋊C4×C47D411yescharacteristic
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148C4⋊C8×C47—22no—
149C4⋊C8×C47—22no—
150#103×C47—22no—
151#103×C47—41no—
152#102×C47—22no—
153#102×C47—22no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—41no—
158C22⋊C8×C47—22no—
159#95×C47—21no—
160#95×C47—21no—
161#95×C47—21no—
162#95×C47D411yescharacteristic
163#95×C47D411yescharacteristic
164C24×C47—21no—
165C24×C47—21no—
166C24×C47—21no—
167C24×C47—24no—
168C24×C47—21no—
169C24×C47—42no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47—42no—
173C24×C47—81no—
174C24×C47—81no—
175C24×C47C2×D411yescharacteristic
176#41×C47—28no—
177#41×C47—44no—
178#41×C47—44no—
179#41×C47—44no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47C2×D412yes—
186C2×D4×C47—28no—
187C2×D4×C47—24no—
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—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—44no—
208C2×D4×C47—44no—
209C2×D4×C47—44no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—42no—
215C2×D4×C47—42no—
216C2×D4×C47—42no—
217C2×D4×C47—42no—
218C2×D4×C47—42no—
219C2×D4×C47—42no—
220C2×D4×C47—81no—
221C2×D4×C47—81no—
222C2×D4×C47—81no—
223C2×D4×C47—81no—
224C2×D4×C47C2×D412yes—
225C2×D4×C47C2×D412yes—
226C2×D4×C47C2×D412yes—
227C2×D4×C47C2×D412yes—
228C2×D4×C47C2×D412yes—
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—42no—
238C22×C4×C47—42no—
239C22×C4×C47—42no—
240C22×C4×C47—42no—
241C22×C4×C47—42no—
242C22×C4×C47—42no—
243C22×C4×C47—42no—
244C22×C4×C47—81no—
245C22×C4×C47—81no—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D412yes—
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47#4112yes—
253C22×C4×C47C2411yescharacteristic
254SD16×C47—28no—
255SD16×C47—28no—
256D8×C47—28no—
257D8×C47—28no—
258D8×C47—44no—
259D8×C47—44no—
260M16×C47—28no—
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—
271C2×C8×C47C2×D412yes—
272C2×C8×C47C2×D412yes—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C22⋊C4×C47—22no—
280C22⋊C4×C47—41no—
281C22⋊C4×C47—42no—
282C22⋊C4×C47—42no—
283C22⋊C4×C47—42no—
284C22⋊C4×C47—42no—
285C22⋊C4×C47—42no—
286C22⋊C4×C47—42no—
287C22⋊C4×C47—42no—
288C22⋊C4×C47—42no—
289C22⋊C4×C47—81no—
290C22⋊C4×C47—81no—
291C22⋊C4×C47—81no—
292C22⋊C4×C47—81no—
293C42×C47—21no—
294C42×C47—21no—
295C42×C47—21no—
296C42×C47—21no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—21no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—48no—
309C23×C47—48no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
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—84no—
334C23×C47—84no—
335C23×C47—84no—
336C23×C47—84no—
337C23×C47—84no—
338C23×C47#12112yes—
339C23×C47C22×D411yescharacteristic
340Q8×C47—22no—
341Q8×C47—22no—
342Q8×C47—41no—
343Q8×C47—41no—
344D4×C47—22no—
345D4×C47—22no—
346D4×C47—22no—
347D4×C47—22no—
348D4×C47—22no—
349D4×C47—22no—
350D4×C47—22no—
351D4×C47—48no—
352D4×C47—48no—
353D4×C47—41no—
354D4×C47—41no—
355D4×C47—41no—
356D4×C47—41no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47—84no—
362D4×C47—84no—
363D4×C47—84no—
364D4×C47#12014yes—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
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—21no—
376C2×C4×C47—22no—
377C2×C4×C47—21no—
378C2×C4×C47—21no—
379C2×C4×C47—21no—
380C2×C4×C47—21no—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—48no—
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—84no—
396C2×C4×C47—84no—
397C2×C4×C47#12112yes—
398C2×C4×C47AGL(1,ℤ/8)12yescomplemented
399C2×C4×C47C22×D411yescharacteristic
400C2×C4×C47C22×D411yescharacteristic
401C2×C4×C47C22×D411yescharacteristic
402C2×C4×C47C2×#4111yescharacteristic
403C2×C4×C47H(5,𝔽2)11yescharacteristic
404C2×C4×C47H(5,𝔽2)11yescharacteristic
405C8×C47—22no—
406C8×C47—22no—
407C8×C47—41no—
408C8×C47—41no—
409#24366C4711yesmaximal, characteristic, direct product factor, Sylow
410C22×C47—22no—
411C22×C47—24no—
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—42no—
415C22×C47—41no—
416C22×C47—41no—
417C22×C47—42no—
418C22×C47—41no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—41no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—42no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—816no—
431C22×C47—81no—
432C22×C47—81no—
433C22×C47—81no—
434C22×C47—81no—
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×#12111yescharacteristic
447C22×C47D4211yescharacteristic
448C22×C47D4211yescharacteristic
449C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C47#57511yescharacteristic
451C22×C47#57611yescharacteristic
452C22×C47#57611yescharacteristic
453C4×C47—22no—
454C4×C47—22no—
455C4×C47—42no—
456C4×C47—41no—
457C4×C47—41no—
458C4×C47—41no—
459C4×C47—81no—
460C4×C47—81no—
461C4×C47—81no—
462C4×C47C2×#12011yescharacteristic
463C4×C47#53411yescharacteristic
464C4×C47#54611yescharacteristic
465C4×C47#54611yescharacteristic
466C22×AGL(1,ℤ/8)C2×C4711yescharacteristic, complemented
467C2×#463C2×C4711yescharacteristic, complemented
468C2×#459C2×C4711yescharacteristic, complemented
469C2×#447C2×C4711yescharacteristic, complemented
470#2431C2×C4711yescharacteristic, complemented
471D4×C22⋊C4C2×C4711yescharacteristic, complemented
472#2055C2×C4711yescharacteristic, complemented
473#2054C2×C4711yescharacteristic, complemented
474#2012C2×C4711yescharacteristic, complemented
475#2011C2×C4711yescharacteristic, complemented
476#1895C2×C4711yescharacteristic, complemented
477#1879C2×C4711yescharacteristic, complemented
478#1877C2×C4711yescharacteristic, complemented
479#1851C2×C4711yescharacteristic, complemented
480#1788C2×C4711yescharacteristic, complemented
481C2×C47—42no—
482C2×C47—44no—
483C2×C47—82no—
484C2×C47—82no—
485C2×C47—161no—
486C2×C47#241011yescharacteristic
487C2×C47#303611yescharacteristic
488C2×C47#304111yescharacteristic
489C2×C47#326411yescharacteristic
490C2×C47#326811yescharacteristic
491C2×C47#327311yescharacteristic
492C2×C47#327411yescharacteristic
493C22×#41C22×C4711yescharacteristic
494C23×D4C22×C4711yescharacteristic
495C2×AGL(1,ℤ/8)—24no—
496C2×AGL(1,ℤ/8)—24no—
497C2×AGL(1,ℤ/8)—24no—
498C22×SD16C22×C4711yescharacteristic
499C22×SD16C22×C4711yescharacteristic
500C22×D8C22×C4711yescharacteristic
501C22×D8C22×C4711yescharacteristic
502C22×D8C22×C4711yescharacteristic
503C22×D8C22×C4711yescharacteristic
504C22×M16C22×C4711yescharacteristic
505C2×#127C22×C4711yescharacteristic, complemented
506C2×#124C22×C4711yescharacteristic, complemented
507C2×#121C22×C4711yescharacteristic
508C2×C4×D4C22×C4711yescharacteristic
509C2×C4×D4C22×C4711yescharacteristic
510C22×C22⋊C4—21no—
511#463—24no—
512#459—24no—
513#447—24no—
514C2×C4⋊C8C22×C4711yescharacteristic, complemented
515C2×C4⋊C8C22×C4711yescharacteristic, complemented
516C2×#103C22×C4711yescharacteristic, complemented
517C2×#103C22×C4711yescharacteristic, complemented
518C2×#102C22×C4711yescharacteristic
519C2×#102C22×C4711yescharacteristic
520C2×#102C22×C4711yescharacteristic, complemented
521C2×#102C22×C4711yescharacteristic, complemented
522C2×#102C22×C4711yescharacteristic, complemented
523C2×#102C22×C4711yescharacteristic, complemented
524C2×C22⋊C8C22×C4711yescharacteristic
525#392—21no—
526#392—21no—
527#391C22×C4711yescharacteristic, complemented
528#390C22×C4711yescharacteristic
529#390C22×C4711yescharacteristic
530#390C22×C4711yescharacteristic, complemented
531#386—21no—
532#386—21no—
533#386—21no—
534#386—21no—
535#380C22×C4711yescharacteristic
536#379—21no—
537C4×C22⋊C4C22×C4711yescharacteristic
538#340C22×C4711yescharacteristic, complemented
539#340C22×C4711yescharacteristic, complemented
540#336C22×C4711yescharacteristic, complemented
541#336C22×C4711yescharacteristic, complemented
542C47#2436611yescharacteristic, direct product factor, Sylow
543C25—21no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C22×Q8C23×C4711yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4D4×C4714yescomplemented
562C22×D4C23×C4711yescharacteristic
563C22×D4C23×C4711yescharacteristic
564C22×D4C23×C4711yescharacteristic
565C22×D4C23×C4711yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C4711yescharacteristic
570AGL(1,ℤ/8)—232no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16D4×C4714yescomplemented
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8D4×C4714yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C4711yescharacteristic
593C22×C8C23×C4711yescharacteristic
594C22×C8C23×C4711yescharacteristic
595C22×C8C23×C4711yescharacteristic
596#127—22no—
597#127—41no—
598#124—22no—
599#124—41no—
600#121—22no—
601#121—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C2×C4⋊C4C23×C4711yescharacteristic
607C2×C4⋊C4C23×C4711yescharacteristic
608C2×C4⋊C4C23×C4711yescharacteristic
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×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4D4×C4711yescharacteristic
623C2×C22⋊C4D4×C4711yescharacteristic
624C2×C42C23×C4711yescharacteristic
625C2×C42C23×C4711yescharacteristic
626C4⋊C8—22no—
627C4⋊C8—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95D4×C4711yescharacteristic
641#95D4×C4711yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C4711yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C4712yes—
664C2×D4—28no—
665C2×D4—24no—
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—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C4712yes—
703C2×D4C2×D4×C4712yes—
704C2×D4C2×D4×C4712yes—
705C2×D4C2×D4×C4712yes—
706C2×D4C2×D4×C4712yes—
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—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C4711yescharacteristic
725C22×C4C2×D4×C4711yescharacteristic
726C22×C4C2×D4×C4711yescharacteristic
727C22×C4C2×D4×C4711yescharacteristic
728C22×C4C2×D4×C4712yes—
729C22×C4C2×D4×C4711yescharacteristic
730C22×C4#41×C4712yes—
731C22×C4C24×C4711yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
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—
749C2×C8C2×D4×C4712yes—
750C2×C8C2×D4×C4712yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
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—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23#121×C4712yes—
817C23C22×D4×C4711yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#120×C4714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
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—84no—
874C2×C4—84no—
875C2×C4#121×C4712yes—
876C2×C4AGL(1,ℤ/8)×C4712yescomplemented
877C2×C4C22×D4×C4711yescharacteristic
878C2×C4C22×D4×C4711yescharacteristic
879C2×C4C22×D4×C4711yescharacteristic
880C2×C4C2×#41×C4711yescharacteristic
881C2×C4H(5,𝔽2)×C4711yescharacteristic
882C2×C4H(5,𝔽2)×C4711yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#121×C4711yescharacteristic
924C22D42×C4711yescharacteristic
925C22D42×C4711yescharacteristic
926C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
927C22C47×#57511yescharacteristic
928C22C47×#57611yescharacteristic
929C22C47×#57611yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×#120×C4711yescharacteristic
940C4C47×#53411yescharacteristic
941C4C47×#54611yescharacteristic
942C4C47×#54611yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C47×#241011yescharacteristic
949C2C47×#303611yescharacteristic
950C2C47×#304111yescharacteristic
951C2C47×#326411yescharacteristic
952C2C47×#326811yescharacteristic
953C2C47×#327311yescharacteristic
954C2C47×#327411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C47C2semidirect
2. C2×C47×#463C2semidirect
3. C2×C47×#459C2semidirect
4. C2×C47×#447C2semidirect
5. C47×#2431C2semidirect
6. D4×C22⋊C4×C47C2semidirect
7. C47×#2055C2semidirect
8. C47×#2054C2semidirect
9. C47×#2012C2semidirect
10. C47×#2011C2semidirect
11. C47×#1895C2semidirect
12. C47×#1879C2semidirect
13. C47×#1877C2semidirect
14. C47×#1851C2semidirect
15. C47×#1788C2semidirect
28. C2×#127×C47C22semidirect
29. C2×#124×C47C22semidirect
37. C2×C4⋊C8×C47C22semidirect
38. C2×C4⋊C8×C47C22semidirect
39. C2×#103×C47C22semidirect
40. C2×#103×C47C22semidirect
43. C2×#102×C47C22semidirect
44. C2×#102×C47C22semidirect
45. C2×#102×C47C22semidirect
46. C2×#102×C47C22semidirect
50. C47×#391C22semidirect
53. C47×#390C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
83. C22×D4×C47D4semidirect
98. C2×SD16×C47D4semidirect
110. C2×D8×C47D4semidirect
398. C2×C4×C47AGL(1,ℤ/8)semidirect
409. #24366C47direct (N × H)
466. C22×AGL(1,ℤ/8)C2×C47semidirect
467. C2×#463C2×C47semidirect
468. C2×#459C2×C47semidirect
469. C2×#447C2×C47semidirect
470. #2431C2×C47semidirect
471. D4×C22⋊C4C2×C47semidirect
472. #2055C2×C47semidirect
473. #2054C2×C47semidirect
474. #2012C2×C47semidirect
475. #2011C2×C47semidirect
476. #1895C2×C47semidirect
477. #1879C2×C47semidirect
478. #1877C2×C47semidirect
479. #1851C2×C47semidirect
480. #1788C2×C47semidirect
505. C2×#127C22×C47semidirect
506. C2×#124C22×C47semidirect
514. C2×C4⋊C8C22×C47semidirect
515. C2×C4⋊C8C22×C47semidirect
516. C2×#103C22×C47semidirect
517. C2×#103C22×C47semidirect
520. C2×#102C22×C47semidirect
521. C2×#102C22×C47semidirect
522. C2×#102C22×C47semidirect
523. C2×#102C22×C47semidirect
527. #391C22×C47semidirect
530. #390C22×C47semidirect
538. #340C22×C47semidirect
539. #340C22×C47semidirect
540. #336C22×C47semidirect
541. #336C22×C47semidirect
542. C47#24366direct (N × H)
561. C22×D4D4×C47semidirect
576. C2×SD16D4×C47semidirect
588. C2×D8D4×C47semidirect
876. C2×C4AGL(1,ℤ/8)×C47semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C472
C2×C47×#4632
C2×C47×#4592
C2×C47×#4472
C47×#24312
D4×C22⋊C4×C472
C47×#20552
C47×#20542
C47×#20122
C47×#20112
C47×#18952
C47×#18792
C47×#18772
C47×#18512
C47×#17882
#2436647