Finite Group Databasebeta

← C47×#24454 #26064152

Subgroups — C47×#24454 #26064152

Order 12032.

1528 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#547C211yesmaximal, characteristic, complemented
2C2×C47×#468C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#449C211yesmaximal, characteristic, complemented
5C2×C47×#417C211yesmaximal, characteristic, complemented
6C47×#2416C211yesmaximal, characteristic, complemented
7C47×#2043C211yesmaximal, characteristic, complemented
8C47×#2036C211yesmaximal, characteristic, complemented
9C47×#2013C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1872C211yesmaximal, characteristic, complemented
13C47×#1870C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C22×M16×C47C2211yescharacteristic
22C47×#547—24no—
23C47×#547—24no—
24C2×C4⋊Q8×C47C2211yescharacteristic
25C2×#123×C47—21no—
26C2×#123×C47—21no—
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×C22⋊Q8×C47C2211yescharacteristic
29C2×#121×C47—21no—
30C2×#121×C47—21no—
31C2×#121×C47C2211yescharacteristic
32C2×#121×C47C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C2×C4×D4×C47C2211yescharacteristic
35C22×C4⋊C4×C47—21no—
36C22×C4⋊C4×C47C2211yescharacteristic
37C47×#468—24no—
38C47×#449—24no—
39C47×#449—24no—
40C2×#107×C47C2211yescharacteristic
41C47×#417—24no—
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#103×C47C2211yescharacteristic
45C2×#103×C47C2211yescharacteristic
46C2×#103×C47C2211yescharacteristic
47C2×#103×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×#102×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×#102×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C47×#396—21no—
56C47×#394—21no—
57C47×#390C2211yescharacteristic
58C47×#389C2211yescharacteristic
59C47×#386—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C47×#336C2211yescharacteristic
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47—41no—
76C2×#41×C47D414yescomplemented
77C22×Q8×C47C2311yescharacteristic
78C22×Q8×C47C2311yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47D411yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47—21no—
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×SD16×C47—22no—
93C2×SD16×C47—22no—
94C2×SD16×C47—22no—
95C2×SD16×C47—41no—
96C2×SD16×C47—41no—
97C2×SD16×C47—41no—
98C2×D8×C47—22no—
99C2×D8×C47—22no—
100C2×D8×C47—22no—
101C2×M16×C47—22no—
102C2×M16×C47—22no—
103C2×M16×C47—41no—
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C4⋊Q8×C47—22no—
109C4⋊Q8×C47—22no—
110#123×C47—28no—
111#123×C47—28no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47D414yescomplemented
116#121×C47—28no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—41no—
121#121×C47—44no—
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C2×C4⋊C4×C47—28no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—22no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—41no—
135C2×C4⋊C4×C47D411yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
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#107×C47—22no—
152#103×C47—22no—
153#103×C47—22no—
154#103×C47—22no—
155#103×C47—22no—
156#103×C47—22no—
157#103×C47—41no—
158#102×C47—22no—
159#102×C47—22no—
160#102×C47—22no—
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—21no—
169C24×C47C2×D411yescharacteristic
170C24×C47C2×D411yescharacteristic
171#41×C47—28no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175#41×C47—44no—
176#41×C47—44no—
177#41×C47—44no—
178#41×C47—44no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47C2×D412yes—
190C2×Q8×C47C2×D412yes—
191C2×D4×C47—24no—
192C2×D4×C47—22no—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
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—41no—
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×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—81no—
215C2×D4×C47C2×D412yes—
216C2×D4×C47C2×D412yes—
217C2×D4×C47#4112yes—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—24no—
223C22×C4×C47—24no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—24no—
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—42no—
245C22×C4×C47—81no—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D412yes—
250C22×C4×C47C2×D412yes—
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2411yescharacteristic
253SD16×C47—44no—
254SD16×C47—44no—
255D8×C47—44no—
256M16×C47—44no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
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×C47C2×D412yes—
269C4⋊C4×C47—24no—
270C4⋊C4×C47—24no—
271C4⋊C4×C47—24no—
272C4⋊C4×C47—22no—
273C4⋊C4×C47—24no—
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—42no—
281C4⋊C4×C47—42no—
282C4⋊C4×C47C2×D412yes—
283C4⋊C4×C47C2×D412yes—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—22no—
288C22⋊C4×C47—22no—
289C22⋊C4×C47—42no—
290C22⋊C4×C47—42no—
291C22⋊C4×C47—42no—
292C22⋊C4×C47—42no—
293C22⋊C4×C47—81no—
294C42×C47—21no—
295C42×C47—21no—
296C23×C47—22no—
297C23×C47—21no—
298C23×C47—22no—
299C23×C47—21no—
300C23×C47—22no—
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—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#12012yes—
324C23×C47C22×D411yescharacteristic
325Q8×C47—22no—
326Q8×C47—22no—
327Q8×C47—22no—
328Q8×C47—22no—
329Q8×C47—41no—
330Q8×C47—41no—
331Q8×C47—41no—
332Q8×C47—41no—
333D4×C47—22no—
334D4×C47—22no—
335D4×C47—22no—
336D4×C47—44no—
337D4×C47—48no—
338D4×C47—48no—
339D4×C47—41no—
340D4×C47—41no—
341D4×C47—41no—
342D4×C47—41no—
343D4×C47—84no—
344D4×C47—84no—
345D4×C47#12114yescomplemented
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—21no—
355C2×C4×C47—22no—
356C2×C4×C47—21no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—21no—
360C2×C4×C47—22no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—48no—
365C2×C4×C47—48no—
366C2×C4×C47—48no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
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—84no—
386C2×C4×C47#12012yes—
387C2×C4×C47AGL(1,ℤ/8)12yes—
388C2×C4×C47C22×D411yescharacteristic
389C2×C4×C47C22×D411yescharacteristic
390C2×C4×C47C22×D411yescharacteristic
391C2×C4×C47C2×#4111yescharacteristic
392C2×C4×C47H(5,𝔽2)11yescharacteristic
393C2×C4×C47H(5,𝔽2)11yescharacteristic
394C8×C47—22no—
395C8×C47—41no—
396C8×C47—41no—
397C8×C47—41no—
398#24454C4711yesmaximal, characteristic, direct product factor, Sylow
399C22×C47—22no—
400C22×C47—24no—
401C22×C47—22no—
402C22×C47—22no—
403C22×C47—41no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—41no—
408C22×C47—42no—
409C22×C47—41no—
410C22×C47—42no—
411C22×C47—41no—
412C22×C47—42no—
413C22×C47—41no—
414C22×C47—41no—
415C22×C47—41no—
416C22×C47—41no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—81no—
421C22×C47—81no—
422C22×C47—81no—
423C22×C47—81no—
424C22×C47—81no—
425C22×C47—81no—
426C22×C47—81no—
427C22×C47C2×#12011yescharacteristic
428C22×C47D4211yescharacteristic
429C22×C47#54611yescharacteristic
430C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C47#57511yescharacteristic
432C22×C47#57711yescharacteristic
433C22×C47#57811yescharacteristic
434C4×C47—22no—
435C4×C47—22no—
436C4×C47—41no—
437C4×C47—42no—
438C4×C47—42no—
439C4×C47—42no—
440C4×C47—41no—
441C4×C47—42no—
442C4×C47—81no—
443C4×C47—81no—
444C4×C47C2×#12111yescharacteristic
445C4×C47#53411yescharacteristic
446C4×C47D4211yescharacteristic
447C4×C47#54611yescharacteristic
448C2×#547C2×C4711yescharacteristic, complemented
449C2×#468C2×C4711yescharacteristic, complemented
450C2×#449C2×C4711yescharacteristic, complemented
451C2×#449C2×C4711yescharacteristic, complemented
452C2×#417C2×C4711yescharacteristic, complemented
453#2416C2×C4711yescharacteristic, complemented
454#2043C2×C4711yescharacteristic, complemented
455#2036C2×C4711yescharacteristic, complemented
456#2013C2×C4711yescharacteristic, complemented
457#2000C2×C4711yescharacteristic, complemented
458#1879C2×C4711yescharacteristic, complemented
459#1872C2×C4711yescharacteristic, complemented
460#1870C2×C4711yescharacteristic, complemented
461#1862C2×C4711yescharacteristic, complemented
462#1788C2×C4711yescharacteristic, complemented
463C2×C47—42no—
464C2×C47—44no—
465C2×C47—81no—
466C2×C47—161no—
467C2×C47#241011yescharacteristic
468C2×C47#300611yescharacteristic
469C2×C47#301311yescharacteristic
470C2×C47#326911yescharacteristic
471C2×C47#327211yescharacteristic
472C2×C47#330711yescharacteristic
473C2×C47#333011yescharacteristic
474C22×#41C22×C4711yescharacteristic
475C22×#41C22×C4711yescharacteristic
476C22×SD16C22×C4711yescharacteristic
477C22×SD16C22×C4711yescharacteristic
478C22×D8C22×C4711yescharacteristic
479C22×M16C22×C4711yescharacteristic
480#547—24no—
481#547—24no—
482C2×C4⋊Q8C22×C4711yescharacteristic
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C22×C4711yescharacteristic
486C2×C22⋊Q8C22×C4711yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C4711yescharacteristic
490C2×#121C22×C4711yescharacteristic
491C2×C4×D4C22×C4711yescharacteristic
492C2×C4×D4C22×C4711yescharacteristic
493C22×C4⋊C4—21no—
494C22×C4⋊C4C22×C4711yescharacteristic
495#468—24no—
496#449—24no—
497#449—24no—
498C2×#107C22×C4711yescharacteristic
499#417—24no—
500C2×#103C22×C4711yescharacteristic
501C2×#103C22×C4711yescharacteristic
502C2×#103C22×C4711yescharacteristic
503C2×#103C22×C4711yescharacteristic
504C2×#103C22×C4711yescharacteristic
505C2×#103C22×C4711yescharacteristic
506C2×#102C22×C4711yescharacteristic
507C2×#102C22×C4711yescharacteristic
508C2×#102C22×C4711yescharacteristic
509C2×#102C22×C4711yescharacteristic
510C2×C22⋊C8C22×C4711yescharacteristic
511C2×C22⋊C8C22×C4711yescharacteristic
512C2×C22⋊C8C22×C4711yescharacteristic
513#396—21no—
514#394—21no—
515#390C22×C4711yescharacteristic
516#389C22×C4711yescharacteristic
517#386—21no—
518#380C22×C4711yescharacteristic
519#340C22×C4711yescharacteristic
520#340C22×C4711yescharacteristic
521#336C22×C4711yescharacteristic
522#336C22×C4711yescharacteristic
523C47#2445411yescharacteristic, direct product factor, Sylow
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C4714yescomplemented
536C22×Q8C23×C4711yescharacteristic
537C22×Q8C23×C4711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C4711yescharacteristic
543C22×D4C23×C4711yescharacteristic
544C22×D4C23×C4711yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C4711yescharacteristic
550C23×C4C23×C4711yescharacteristic
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C4711yescharacteristic
564C22×C8C23×C4711yescharacteristic
565C22×C8C23×C4711yescharacteristic
566C22×C8C23×C4711yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569#123—28no—
570#123—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8D4×C4714yescomplemented
575#121—28no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—44no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4D4×C4711yescharacteristic
595C2×C4⋊C4C23×C4711yescharacteristic
596C2×C4⋊C4C23×C4711yescharacteristic
597C2×C4⋊C4C23×C4711yescharacteristic
598C2×C4⋊C4C23×C4711yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4D4×C4711yescharacteristic
608C2×C22⋊C4D4×C4711yescharacteristic
609C2×C42C23×C4711yescharacteristic
610#107—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102D4×C4714yescomplemented
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—21no—
628C24C2×D4×C4711yescharacteristic
629C24C2×D4×C4711yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C4712yes—
649C2×Q8C2×D4×C4712yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—81no—
674C2×D4C2×D4×C4712yes—
675C2×D4C2×D4×C4712yes—
676C2×D4#41×C4712yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4C2×D4×C4711yescharacteristic
706C22×C4C2×D4×C4711yescharacteristic
707C22×C4C2×D4×C4711yescharacteristic
708C22×C4C2×D4×C4712yes—
709C22×C4C2×D4×C4712yes—
710C22×C4C2×D4×C4711yescharacteristic
711C22×C4C24×C4711yescharacteristic
712SD16—44no—
713SD16—44no—
714D8—44no—
715M16—44no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8C2×D4×C4712yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4C2×D4×C4712yes—
742C4⋊C4C2×D4×C4712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C42—21no—
754C42—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#120×C4712yes—
783C23C22×D4×C4711yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804D4#121×C4714yescomplemented
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—48no—
824C2×C4—48no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C4712yes—
846C2×C4AGL(1,ℤ/8)×C4712yes—
847C2×C4C22×D4×C4711yescharacteristic
848C2×C4C22×D4×C4711yescharacteristic
849C2×C4C22×D4×C4711yescharacteristic
850C2×C4C2×#41×C4711yescharacteristic
851C2×C4H(5,𝔽2)×C4711yescharacteristic
852C2×C4H(5,𝔽2)×C4711yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C4711yescharacteristic
886C22D42×C4711yescharacteristic
887C22C47×#54611yescharacteristic
888C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
889C22C47×#57511yescharacteristic
890C22C47×#57711yescharacteristic
891C22C47×#57811yescharacteristic
892C4—22no—
893C4—22no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—41no—
899C4—42no—
900C4—81no—
901C4—81no—
902C4C2×#121×C4711yescharacteristic
903C4C47×#53411yescharacteristic
904C4D42×C4711yescharacteristic
905C4C47×#54611yescharacteristic
906C2—42no—
907C2—44no—
908C2—81no—
909C2—161no—
910C2C47×#241011yescharacteristic
911C2C47×#300611yescharacteristic
912C2C47×#301311yescharacteristic
913C2C47×#326911yescharacteristic
914C2C47×#327211yescharacteristic
915C2C47×#330711yescharacteristic
916C2C47×#333011yescharacteristic
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×#547C2semidirect
2. C2×C47×#468C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#449C2semidirect
5. C2×C47×#417C2semidirect
6. C47×#2416C2semidirect
7. C47×#2043C2semidirect
8. C47×#2036C2semidirect
9. C47×#2013C2semidirect
10. C47×#2000C2semidirect
11. C47×#1879C2semidirect
12. C47×#1872C2semidirect
13. C47×#1870C2semidirect
14. C47×#1862C2semidirect
15. C47×#1788C2semidirect
76. C2×#41×C47D4semidirect
115. C22⋊Q8×C47D4semidirect
161. #102×C47D4semidirect
345. D4×C47#121semidirect
398. #24454C47direct (N × H)
448. C2×#547C2×C47semidirect
449. C2×#468C2×C47semidirect
450. C2×#449C2×C47semidirect
451. C2×#449C2×C47semidirect
452. C2×#417C2×C47semidirect
453. #2416C2×C47semidirect
454. #2043C2×C47semidirect
455. #2036C2×C47semidirect
456. #2013C2×C47semidirect
457. #2000C2×C47semidirect
458. #1879C2×C47semidirect
459. #1872C2×C47semidirect
460. #1870C2×C47semidirect
461. #1862C2×C47semidirect
462. #1788C2×C47semidirect
523. C47#24454direct (N × H)
535. C2×#41D4×C47semidirect
574. C22⋊Q8D4×C47semidirect
620. #102D4×C47semidirect
804. 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×#5472
C2×C47×#4682
C2×C47×#4492
C2×C47×#4172
C47×#24162
C47×#20432
C47×#20362
C47×#20132
C47×#20002
C47×#18792
C47×#18722
C47×#18702
C47×#18622
C47×#17882
#2445447