Finite Group Databasebeta

← C47×#23412 #26063110

Subgroups — C47×#23412 #26063110

Order 12032.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#575C211yesmaximal, characteristic, complemented
2C2×C47×#575C211yesmaximal, characteristic, complemented
3C47×#3449C211yesmaximal, characteristic, complemented
4C2×C47×#421C211yesmaximal, characteristic, complemented
5C47×#2896C211yesmaximal, characteristic, complemented
6C2×C47×#410C211yesmaximal, characteristic, complemented
7C47×#2009C214yesmaximal, complemented
8C47×#2008C214yesmaximal, complemented
9C2×C47×#344C211yesmaximal, characteristic, complemented
10C22×#41×C47C2211yescharacteristic
11C22×#41×C47C2211yescharacteristic
12C22×#41×C47C2211yescharacteristic
13C47×#575—22no—
14C47×#575—22no—
15C47×#575—22no—
16C47×#575—22no—
17C47×#575—22no—
18C47×#575—22no—
19C47×#575—22no—
20C47×#575C2214yes—
21C2×#137×C47—21no—
22C2×#137×C47—21no—
23C2×#137×C47—21no—
24C2×#137×C47C2212yescomplemented
25C2×AGL(1,ℤ/8)×C47—21no—
26C2×AGL(1,ℤ/8)×C47—21no—
27C2×AGL(1,ℤ/8)×C47—21no—
28C2×AGL(1,ℤ/8)×C47C2212yescomplemented
29C2×#135×C47—22no—
30C2×#135×C47—22no—
31C22×M16×C47C2211yescharacteristic
32C22×M16×C47C2211yescharacteristic
33C47×#537—22no—
34C47×#536—21no—
35C47×#536C2212yescomplemented
36C47×#535—21no—
37C47×#535C2212yescomplemented
38C47×#534—22no—
39C47×#532—22no—
40C47×#525—22no—
41C47×#525—22no—
42C2×#117×C47C2211yescharacteristic
43C2×#117×C47C2211yescharacteristic
44C47×#421—22no—
45C47×#421C2214yescomplemented
46C2×#104×C47—22no—
47C47×#419C2212yescomplemented
48C47×#418C2212yescomplemented
49C47×#417—22no—
50C47×#416—22no—
51C47×#410—22no—
52C47×#410C2214yescomplemented
53C2×#99×C47—22no—
54C47×#344C2214yescomplemented
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C2×#41×C47—21no—
58C2×#41×C47—21no—
59C2×#41×C47—21no—
60C2×#41×C47—21no—
61C2×#41×C47—21no—
62C2×#41×C47—21no—
63C2×#41×C47—21no—
64C2×#41×C47—21no—
65C2×#41×C47—21no—
66C2×#41×C47—21no—
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47—21no—
70C2×#41×C47—21no—
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—21no—
84C2×#41×C47—21no—
85C2×#41×C47D412yes—
86C2×#41×C47D412yes—
87C2×#41×C47D412yes—
88C2×#41×C47D412yescomplemented
89C2×#41×C47C2312yes—
90C2×#41×C47C2312yes—
91C22×Q8×C47D411yescharacteristic
92C22×Q8×C47D411yescharacteristic, complemented
93C22×Q8×C47C2311yescharacteristic
94C22×D4×C47—21no—
95C22×D4×C47—21no—
96C22×D4×C47—21no—
97C22×D4×C47D411yescharacteristic
98C22×D4×C47D411yescharacteristic, complemented
99C22×D4×C47C2311yescharacteristic
100C23×C4×C47—21no—
101C23×C4×C47—21no—
102C23×C4×C47—21no—
103C23×C4×C47C2311yescharacteristic
104#137×C47—24no—
105#137×C47—24no—
106#137×C47—24no—
107#137×C47—24no—
108#137×C47—24no—
109#137×C47—24no—
110#137×C47—24no—
111#137×C47—24no—
112AGL(1,ℤ/8)×C47—24no—
113AGL(1,ℤ/8)×C47—24no—
114AGL(1,ℤ/8)×C47—24no—
115AGL(1,ℤ/8)×C47—24no—
116AGL(1,ℤ/8)×C47—24no—
117AGL(1,ℤ/8)×C47—24no—
118AGL(1,ℤ/8)×C47—24no—
119AGL(1,ℤ/8)×C47—24no—
120#135×C47—28no—
121#135×C47—28no—
122#135×C47—28no—
123#135×C47—28no—
124C2×Q16×C47—22no—
125C2×Q16×C47—22no—
126C2×SD16×C47—22no—
127C2×SD16×C47—22no—
128C2×SD16×C47—22no—
129C2×SD16×C47—22no—
130C2×D8×C47—22no—
131C2×D8×C47—22no—
132C2×M16×C47—21no—
133C2×M16×C47—21no—
134C2×M16×C47—21no—
135C2×M16×C47—21no—
136C2×M16×C47—21no—
137C2×M16×C47—21no—
138C2×M16×C47—21no—
139C2×M16×C47D412yescomplemented
140C2×M16×C47D412yescomplemented
141C2×M16×C47D412yescomplemented
142C2×M16×C47C2312yes—
143C2×M16×C47C2312yes—
144C22×C8×C47—21no—
145C22×C8×C47D412yescomplemented
146C4⋊Q8×C47—22no—
147#127×C47—22no—
148#124×C47—22no—
149#124×C47—22no—
150#123×C47—24no—
151#123×C47—24no—
152C22⋊Q8×C47—24no—
153C22⋊Q8×C47—24no—
154#121×C47—24no—
155#121×C47—28no—
156#121×C47—24no—
157#120×C47—24no—
158#120×C47—24no—
159C4×D4×C47—28no—
160#117×C47—21no—
161#117×C47—21no—
162#117×C47—21no—
163#117×C47—21no—
164#117×C47—21no—
165#117×C47D412yes—
166#117×C47C2312yes—
167#117×C47C2312yes—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47D412yes—
172C2×C42×C47—21no—
173C2×C42×C47—21no—
174#104×C47—28no—
175#103×C47—24no—
176#102×C47—24no—
177#99×C47—28no—
178C24×C47—21no—
179C24×C47—21no—
180C24×C47—21no—
181C24×C47C2×D411yescharacteristic
182#41×C47—22no—
183#41×C47—22no—
184#41×C47—22no—
185#41×C47—22no—
186#41×C47—22no—
187#41×C47—22no—
188#41×C47—22no—
189#41×C47—22no—
190#41×C47—22no—
191#41×C47—22no—
192#41×C47—22no—
193#41×C47—22no—
194#41×C47—22no—
195#41×C47—22no—
196#41×C47—22no—
197#41×C47—22no—
198#41×C47—22no—
199#41×C47—22no—
200#41×C47—22no—
201#41×C47—22no—
202#41×C47—22no—
203#41×C47—22no—
204#41×C47—22no—
205#41×C47—22no—
206#41×C47—41no—
207#41×C47—41no—
208#41×C47—41no—
209#41×C47—41no—
210#41×C47—41no—
211#41×C47—41no—
212#41×C47—41no—
213#41×C47—41no—
214#41×C47—41no—
215#41×C47—41no—
216#41×C47—41no—
217#41×C47—41no—
218#41×C47—41no—
219#41×C47—41no—
220#41×C47—41no—
221#41×C47—41no—
222#41×C47—41no—
223#41×C47—41no—
224#41×C47—41no—
225#41×C47—41no—
226#41×C47—41no—
227#41×C47—41no—
228#41×C47—41no—
229#41×C47—41no—
230C2×Q8×C47—21no—
231C2×Q8×C47—21no—
232C2×Q8×C47—21no—
233C2×Q8×C47—21no—
234C2×Q8×C47—21no—
235C2×Q8×C47—21no—
236C2×Q8×C47—21no—
237C2×Q8×C47—21no—
238C2×Q8×C47—21no—
239C2×Q8×C47—21no—
240C2×Q8×C47—21no—
241C2×Q8×C47—21no—
242C2×Q8×C47—21no—
243C2×Q8×C47—21no—
244C2×Q8×C47—21no—
245C2×Q8×C47C2×D412yes—
246C2×Q8×C47C2×D412yes—
247C2×Q8×C47C2×D412yes—
248C2×D4×C47—22no—
249C2×D4×C47—22no—
250C2×D4×C47—22no—
251C2×D4×C47—22no—
252C2×D4×C47—22no—
253C2×D4×C47—22no—
254C2×D4×C47—28no—
255C2×D4×C47—21no—
256C2×D4×C47—21no—
257C2×D4×C47—21no—
258C2×D4×C47—21no—
259C2×D4×C47—21no—
260C2×D4×C47—21no—
261C2×D4×C47—21no—
262C2×D4×C47—21no—
263C2×D4×C47—21no—
264C2×D4×C47—21no—
265C2×D4×C47—21no—
266C2×D4×C47—21no—
267C2×D4×C47—21no—
268C2×D4×C47—21no—
269C2×D4×C47—21no—
270C2×D4×C47—41no—
271C2×D4×C47—41no—
272C2×D4×C47—41no—
273C2×D4×C47—41no—
274C2×D4×C47—41no—
275C2×D4×C47—41no—
276C2×D4×C47—41no—
277C2×D4×C47—41no—
278C2×D4×C47—41no—
279C2×D4×C47—41no—
280C2×D4×C47—41no—
281C2×D4×C47—41no—
282C2×D4×C47C2×D412yes—
283C2×D4×C47C2×D412yes—
284C2×D4×C47C2×D412yes—
285C22×C4×C47—21no—
286C22×C4×C47—21no—
287C22×C4×C47—21no—
288C22×C4×C47—22no—
289C22×C4×C47—22no—
290C22×C4×C47—22no—
291C22×C4×C47—22no—
292C22×C4×C47—22no—
293C22×C4×C47—22no—
294C22×C4×C47—22no—
295C22×C4×C47—41no—
296C22×C4×C47—41no—
297C22×C4×C47—41no—
298C22×C4×C47—41no—
299C22×C4×C47—41no—
300C22×C4×C47—41no—
301C22×C4×C47—41no—
302C22×C4×C47—41no—
303C22×C4×C47—41no—
304C22×C4×C47—41no—
305C22×C4×C47—41no—
306C22×C4×C47—41no—
307C22×C4×C47—41no—
308C22×C4×C47C2×D411yescharacteristic
309C22×C4×C47C2×D411yescharacteristic
310C22×C4×C47C2×D411yescharacteristic
311C22×C4×C47C2×D411yescharacteristic
312C22×C4×C47C2×D411yescharacteristic
313C22×C4×C47C2×D411yescharacteristic
314C22×C4×C47C2×D411yescharacteristic
315C22×C4×C47C2×D411yescharacteristic
316C22×C4×C47C2×D411yescharacteristic
317C22×C4×C47C2×D411yescharacteristic
318C22×C4×C47C2×D411yescharacteristic
319C22×C4×C47#4111yescharacteristic
320C22×C4×C47#4111yescharacteristic
321C22×C4×C47C2411yescharacteristic
322Q16×C47—28no—
323Q16×C47—28no—
324SD16×C47—28no—
325SD16×C47—28no—
326SD16×C47—28no—
327SD16×C47—28no—
328D8×C47—28no—
329D8×C47—28no—
330M16×C47—22no—
331M16×C47—22no—
332M16×C47—22no—
333M16×C47—22no—
334M16×C47—22no—
335M16×C47—22no—
336M16×C47—22no—
337M16×C47C2×D414yes—
338C2×C8×C47—22no—
339C2×C8×C47—22no—
340C2×C8×C47—22no—
341C2×C8×C47—22no—
342C2×C8×C47—22no—
343C2×C8×C47C2×D414yes—
344C4⋊C4×C47—28no—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
347C4⋊C4×C47—22no—
348C4⋊C4×C47—41no—
349C22⋊C4×C47—28no—
350C22⋊C4×C47—28no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—22no—
353C22⋊C4×C47—41no—
354C22⋊C4×C47C2×D414yes—
355C42×C47—22no—
356C42×C47—22no—
357C42×C47—22no—
358C42×C47—41no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—41no—
363C23×C47—41no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—41no—
367C23×C47—41no—
368C23×C47—81no—
369C23×C47—82no—
370C23×C47—82no—
371C23×C47—82no—
372C23×C47#12011yescharacteristic
373C23×C47#12011yescharacteristic
374C23×C47#12111yescharacteristic
375C23×C47#12111yescharacteristic
376C23×C47#12711yescharacteristic
377C23×C47#12711yescharacteristic
378C23×C47C22×D411yescharacteristic
379Q8×C47—22no—
380Q8×C47—22no—
381Q8×C47—22no—
382Q8×C47—22no—
383Q8×C47—22no—
384Q8×C47—22no—
385Q8×C47—41no—
386Q8×C47—41no—
387Q8×C47—41no—
388Q8×C47—41no—
389Q8×C47—41no—
390Q8×C47—41no—
391D4×C47—22no—
392D4×C47—22no—
393D4×C47—22no—
394D4×C47—22no—
395D4×C47—22no—
396D4×C47—22no—
397D4×C47—42no—
398D4×C47—42no—
399D4×C47—42no—
400D4×C47—42no—
401D4×C47—42no—
402D4×C47—42no—
403D4×C47—42no—
404D4×C47—42no—
405D4×C47—42no—
406D4×C47—42no—
407D4×C47—42no—
408D4×C47—42no—
409D4×C47—41no—
410D4×C47—41no—
411D4×C47—41no—
412D4×C47—41no—
413D4×C47—41no—
414D4×C47—41no—
415D4×C47—88no—
416C2×C4×C47—24no—
417C2×C4×C47—22no—
418C2×C4×C47—22no—
419C2×C4×C47—22no—
420C2×C4×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—42no—
427C2×C4×C47—42no—
428C2×C4×C47—42no—
429C2×C4×C47—42no—
430C2×C4×C47—42no—
431C2×C4×C47—42no—
432C2×C4×C47—42no—
433C2×C4×C47—42no—
434C2×C4×C47—42no—
435C2×C4×C47—42no—
436C2×C4×C47—42no—
437C2×C4×C47—42no—
438C2×C4×C47—42no—
439C2×C4×C47—82no—
440C2×C4×C47—82no—
441C2×C4×C47#12011yescharacteristic
442C2×C4×C47#12011yescharacteristic
443C2×C4×C47#12011yescharacteristic
444C2×C4×C47#12011yescharacteristic
445C2×C4×C47#12011yescharacteristic
446C2×C4×C47#12011yescharacteristic
447C2×C4×C47#12011yescharacteristic
448C2×C4×C47#12011yescharacteristic
449C2×C4×C47#12011yescharacteristic
450C2×C4×C47#12011yescharacteristic
451C2×C4×C47#12111yescharacteristic
452C2×C4×C47#12111yescharacteristic
453C2×C4×C47#12111yescharacteristic
454C2×C4×C47#12111yescharacteristic
455C2×C4×C47#12111yescharacteristic
456C2×C4×C47#12111yescharacteristic
457C2×C4×C47#12111yescharacteristic
458C2×C4×C47#12111yescharacteristic
459C2×C4×C47#12111yescharacteristic
460C2×C4×C47#12111yescharacteristic
461C2×C4×C47#12711yescharacteristic
462C2×C4×C47#12711yescharacteristic
463C2×C4×C47C22×D411yescharacteristic
464C2×C4×C47C22×D411yescharacteristic
465C2×C4×C47C22×D411yescharacteristic
466C2×C4×C47C22×D411yescharacteristic
467C2×C4×C47C22×D411yescharacteristic
468C2×C4×C47C2×#4111yescharacteristic
469C8×C47—24no—
470C8×C47—24no—
471#23412C4711yesmaximal, characteristic, direct product factor, Sylow
472C22×C47—41no—
473C22×C47—41no—
474C22×C47—41no—
475C22×C47—41no—
476C22×C47—41no—
477C22×C47—41no—
478C22×C47—41no—
479C22×C47—44no—
480C22×C47—44no—
481C22×C47—42no—
482C22×C47—42no—
483C22×C47—42no—
484C22×C47—82no—
485C22×C47—82no—
486C22×C47—82no—
487C22×C47—82no—
488C22×C47—82no—
489C22×C47—82no—
490C22×C47—82no—
491C22×C47#39211yescharacteristic
492C22×C47#39211yescharacteristic
493C22×C47#39211yescharacteristic
494C22×C47#39211yescharacteristic
495C22×C47C2×#12011yescharacteristic
496C22×C47C2×#12111yescharacteristic
497C22×C47C2×#12711yescharacteristic
498C4×C47—44no—
499C4×C47—42no—
500C4×C47—42no—
501C4×C47—42no—
502C4×C47—82no—
503C4×C47#39211yescharacteristic
504C4×C47#39211yescharacteristic
505C4×C47#39211yescharacteristic
506C4×C47#39211yescharacteristic
507C4×C47C2×#12011yescharacteristic
508C4×C47C2×#12011yescharacteristic
509C4×C47C2×#12111yescharacteristic
510C4×C47C2×#12111yescharacteristic
511C2×#575C2×C4711yescharacteristic, complemented
512C2×#575C2×C4711yescharacteristic, complemented
513#3449C2×C4711yescharacteristic, complemented
514C2×#421C2×C4711yescharacteristic, complemented
515#2896C2×C4711yescharacteristic, complemented
516C2×#410C2×C4711yescharacteristic, complemented
517#2009C2×C4714yescomplemented
518#2008C2×C4714yescomplemented
519C2×#344C2×C4711yescharacteristic, complemented
520C2×C47—21no—
521C2×C47—21no—
522C2×C47—21no—
523C2×C47—21no—
524C2×C47—21no—
525C2×C47—21no—
526C2×C47—21no—
527C2×C47—82no—
528C2×C47—82no—
529C2×C47—82no—
530C2×C47C2×#39211yescharacteristic
531C22×#41C22×C4711yescharacteristic
532C22×#41C22×C4711yescharacteristic
533C22×#41C22×C4711yescharacteristic
534#575—22no—
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575C22×C4714yes—
542C2×#137—21no—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137C22×C4712yescomplemented
546C2×AGL(1,ℤ/8)—21no—
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)C22×C4712yescomplemented
550C2×#135—22no—
551C2×#135—22no—
552C22×M16C22×C4711yescharacteristic
553C22×M16C22×C4711yescharacteristic
554#537—22no—
555#536—21no—
556#536C22×C4712yescomplemented
557#535—21no—
558#535C22×C4712yescomplemented
559#534—22no—
560#532—22no—
561#525—22no—
562#525—22no—
563C2×#117C22×C4711yescharacteristic
564C2×#117C22×C4711yescharacteristic
565#421—22no—
566#421C22×C4714yescomplemented
567C2×#104—22no—
568#419C22×C4712yescomplemented
569#418C22×C4712yescomplemented
570#417—22no—
571#416—22no—
572#410—22no—
573#410C22×C4714yescomplemented
574C2×#99—22no—
575#344C22×C4714yescomplemented
576C47#2341211yescharacteristic, direct product factor, Sylow
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C4712yes—
608C2×#41D4×C4712yes—
609C2×#41D4×C4712yes—
610C2×#41D4×C4712yescomplemented
611C2×#41C23×C4712yes—
612C2×#41C23×C4712yes—
613C22×Q8D4×C4711yescharacteristic
614C22×Q8D4×C4711yescharacteristic, complemented
615C22×Q8C23×C4711yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C4711yescharacteristic
620C22×D4D4×C4711yescharacteristic, complemented
621C22×D4C23×C4711yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C4711yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C4712yescomplemented
662C2×M16D4×C4712yescomplemented
663C2×M16D4×C4712yescomplemented
664C2×M16C23×C4712yes—
665C2×M16C23×C4712yes—
666C22×C8—21no—
667C22×C8D4×C4712yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C4712yes—
688#117C23×C4712yes—
689#117C23×C4712yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C4712yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C4711yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C4712yes—
768C2×Q8C2×D4×C4712yes—
769C2×Q8C2×D4×C4712yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C4712yes—
805C2×D4C2×D4×C4712yes—
806C2×D4C2×D4×C4712yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C4711yescharacteristic
831C22×C4C2×D4×C4711yescharacteristic
832C22×C4C2×D4×C4711yescharacteristic
833C22×C4C2×D4×C4711yescharacteristic
834C22×C4C2×D4×C4711yescharacteristic
835C22×C4C2×D4×C4711yescharacteristic
836C22×C4C2×D4×C4711yescharacteristic
837C22×C4C2×D4×C4711yescharacteristic
838C22×C4C2×D4×C4711yescharacteristic
839C22×C4C2×D4×C4711yescharacteristic
840C22×C4C2×D4×C4711yescharacteristic
841C22×C4#41×C4711yescharacteristic
842C22×C4#41×C4711yescharacteristic
843C22×C4C24×C4711yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C4714yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C4714yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C4714yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C4711yescharacteristic
895C23#120×C4711yescharacteristic
896C23#121×C4711yescharacteristic
897C23#121×C4711yescharacteristic
898C23#127×C4711yescharacteristic
899C23#127×C4711yescharacteristic
900C23C22×D4×C4711yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C4711yescharacteristic
964C2×C4#120×C4711yescharacteristic
965C2×C4#120×C4711yescharacteristic
966C2×C4#120×C4711yescharacteristic
967C2×C4#120×C4711yescharacteristic
968C2×C4#120×C4711yescharacteristic
969C2×C4#120×C4711yescharacteristic
970C2×C4#120×C4711yescharacteristic
971C2×C4#120×C4711yescharacteristic
972C2×C4#120×C4711yescharacteristic
973C2×C4#121×C4711yescharacteristic
974C2×C4#121×C4711yescharacteristic
975C2×C4#121×C4711yescharacteristic
976C2×C4#121×C4711yescharacteristic
977C2×C4#121×C4711yescharacteristic
978C2×C4#121×C4711yescharacteristic
979C2×C4#121×C4711yescharacteristic
980C2×C4#121×C4711yescharacteristic
981C2×C4#121×C4711yescharacteristic
982C2×C4#121×C4711yescharacteristic
983C2×C4#127×C4711yescharacteristic
984C2×C4#127×C4711yescharacteristic
985C2×C4C22×D4×C4711yescharacteristic
986C2×C4C22×D4×C4711yescharacteristic
987C2×C4C22×D4×C4711yescharacteristic
988C2×C4C22×D4×C4711yescharacteristic
989C2×C4C22×D4×C4711yescharacteristic
990C2×C4C2×#41×C4711yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22C47×#39211yescharacteristic
1013C22C47×#39211yescharacteristic
1014C22C47×#39211yescharacteristic
1015C22C47×#39211yescharacteristic
1016C22C2×#120×C4711yescharacteristic
1017C22C2×#121×C4711yescharacteristic
1018C22C2×#127×C4711yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4C47×#39211yescharacteristic
1025C4C47×#39211yescharacteristic
1026C4C47×#39211yescharacteristic
1027C4C47×#39211yescharacteristic
1028C4C2×#120×C4711yescharacteristic
1029C4C2×#120×C4711yescharacteristic
1030C4C2×#121×C4711yescharacteristic
1031C4C2×#121×C4711yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×C47×#39211yescharacteristic
subgroupG/H
centerC4×C47#392
commutator, Frattini, cosocleC22×C4C24×C47
socleC2×C47C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#575C2semidirect
2. C2×C47×#575C2semidirect
3. C47×#3449C2semidirect
4. C2×C47×#421C2semidirect
5. C47×#2896C2semidirect
6. C2×C47×#410C2semidirect
7. C47×#2009C2semidirect
8. C47×#2008C2semidirect
9. C2×C47×#344C2semidirect
24. C2×#137×C47C22semidirect
28. C2×AGL(1,ℤ/8)×C47C22semidirect
35. C47×#536C22semidirect
37. C47×#535C22semidirect
45. C47×#421C22semidirect
47. C47×#419C22semidirect
48. C47×#418C22semidirect
52. C47×#410C22semidirect
54. C47×#344C22semidirect
88. C2×#41×C47D4semidirect
92. C22×Q8×C47D4semidirect
98. C22×D4×C47D4semidirect
139. C2×M16×C47D4semidirect
140. C2×M16×C47D4semidirect
141. C2×M16×C47D4semidirect
145. C22×C8×C47D4semidirect
471. #23412C47direct (N × H)
511. C2×#575C2×C47semidirect
512. C2×#575C2×C47semidirect
513. #3449C2×C47semidirect
514. C2×#421C2×C47semidirect
515. #2896C2×C47semidirect
516. C2×#410C2×C47semidirect
517. #2009C2×C47semidirect
518. #2008C2×C47semidirect
519. C2×#344C2×C47semidirect
545. C2×#137C22×C47semidirect
549. C2×AGL(1,ℤ/8)C22×C47semidirect
556. #536C22×C47semidirect
558. #535C22×C47semidirect
566. #421C22×C47semidirect
568. #419C22×C47semidirect
569. #418C22×C47semidirect
573. #410C22×C47semidirect
575. #344C22×C47semidirect
576. C47#23412direct (N × H)
610. C2×#41D4×C47semidirect
614. C22×Q8D4×C47semidirect
620. C22×D4D4×C47semidirect
661. C2×M16D4×C47semidirect
662. C2×M16D4×C47semidirect
663. C2×M16D4×C47semidirect
667. C22×C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5752
C47×#34492
C2×C47×#4212
C47×#28962
C2×C47×#4102
C47×#20092
C47×#20082
C2×C47×#3442
#2341247