Finite Group Databasebeta

← C47×#25104 #26064802

Subgroups — C47×#25104 #26064802

Order 12032.

1172 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic
4C2×C47×#417C211yesmaximal, characteristic, complemented
5C47×#2432C211yesmaximal, characteristic, complemented
6C47×#2361C211yesmaximal, characteristic, complemented
7C47×#2068C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2013C211yesmaximal, characteristic, complemented
11C47×#1981C211yesmaximal, characteristic, complemented
12C47×#1925C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic, complemented
14C47×#1872C211yesmaximal, characteristic, complemented
15C47×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C2×C4⋊Q8×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47—21no—
26C2×C4×D4×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#468—24no—
29C47×#463—24no—
30C47×#449—24no—
31C2×#107×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C47×#417—24no—
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C47×#394—21no—
47C47×#394—21no—
48C47×#391C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#386—21no—
54C47×#385—21no—
55C47×#385—21no—
56C47×#385—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C22×Q8×C47C2311yescharacteristic
70C22×Q8×C47C2311yescharacteristic
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47C2311yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47C2311yescharacteristic
79C2×SD16×C47—22no—
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—41no—
84C2×SD16×C47—41no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—41no—
88C2×M16×C47—22no—
89C2×M16×C47—22no—
90C2×M16×C47—41no—
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C4⋊Q8×C47—22no—
96C4⋊Q8×C47—41no—
97#124×C47—22no—
98#124×C47—41no—
99C22⋊Q8×C47—22no—
100C22⋊Q8×C47—22no—
101#121×C47—22no—
102#121×C47D414yes—
103C4×D4×C47—22no—
104C4×D4×C47—41no—
105C4×D4×C47—44no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—41no—
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C42×C47—21no—
129C2×C42×C47C2311yescharacteristic
130C2×C42×C47C2311yescharacteristic
131#107×C47—22no—
132C4⋊C8×C47—22no—
133C4⋊C8×C47—41no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#103×C47—22no—
139#103×C47—41no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47D414yescomplemented
144C22⋊C8×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47D411yescharacteristic
150#95×C47D411yescharacteristic
151C24×C47—21no—
152C24×C47—21no—
153C24×C47C2×D411yescharacteristic
154#41×C47—28no—
155#41×C47—44no—
156#41×C47—44no—
157#41×C47—44no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47#4112yes—
170C2×D4×C47—24no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47C2×D412yes—
187C2×D4×C47C2×D412yes—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—42no—
199C22×C4×C47—42no—
200C22×C4×C47—42no—
201C22×C4×C47—42no—
202C22×C4×C47—42no—
203C22×C4×C47—42no—
204C22×C4×C47—42no—
205C22×C4×C47—81no—
206C22×C4×C47—81no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D412yes—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47#4112yes—
214C22×C4×C47C2411yescharacteristic
215SD16×C47—44no—
216SD16×C47—44no—
217D8×C47—44no—
218M16×C47—44no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47C2×D412yes—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—42no—
238C4⋊C4×C47—42no—
239C4⋊C4×C47—42no—
240C4⋊C4×C47—42no—
241C4⋊C4×C47—42no—
242C4⋊C4×C47C2×D412yes—
243C4⋊C4×C47C2×D412yes—
244C22⋊C4×C47—24no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—41no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—81no—
255C42×C47—21no—
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—42no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47#12112yes—
281C23×C47C22×D411yescharacteristic
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—41no—
285Q8×C47—41no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—41no—
289Q8×C47—41no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—22no—
294D4×C47—48no—
295D4×C47—48no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—22no—
312C2×C4×C47—21no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—48no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—84no—
337C2×C4×C47—84no—
338C2×C4×C47#12112yes—
339C2×C4×C47AGL(1,ℤ/8)12yes—
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C2×#4111yescharacteristic
343C2×C4×C47C2×#4111yescharacteristic
344C2×C4×C47H(5,𝔽2)11yescharacteristic
345C2×C4×C47H(5,𝔽2)11yescharacteristic
346C8×C47—22no—
347C8×C47—41no—
348C8×C47—41no—
349C8×C47—41no—
350#25104C4711yesmaximal, characteristic, direct product factor, Sylow
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47C2×#12111yescharacteristic
373C22×C47D4211yescharacteristic
374C22×C47#54611yescharacteristic
375C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C47#57511yescharacteristic
377C22×C47#57711yescharacteristic
378C22×C47#57811yescharacteristic
379C4×C47—22no—
380C4×C47—22no—
381C4×C47—42no—
382C4×C47—41no—
383C4×C47—41no—
384C4×C47—42no—
385C4×C47—42no—
386C4×C47—41no—
387C4×C47—81no—
388C4×C47—81no—
389C4×C47—81no—
390C4×C47#52511yescharacteristic
391C4×C47#53811yescharacteristic
392C4×C47D4211yescharacteristic
393C4×C47#54611yescharacteristic
394C2×#468C2×C4711yescharacteristic, complemented
395C2×#463C2×C4711yescharacteristic, complemented
396C2×#449C2×C4711yescharacteristic
397C2×#417C2×C4711yescharacteristic, complemented
398#2432C2×C4711yescharacteristic, complemented
399#2361C2×C4711yescharacteristic, complemented
400#2068C2×C4711yescharacteristic, complemented
401#2054C2×C4711yescharacteristic, complemented
402#2042C2×C4711yescharacteristic, complemented
403#2013C2×C4711yescharacteristic, complemented
404#1981C2×C4711yescharacteristic, complemented
405#1925C2×C4711yescharacteristic, complemented
406#1877C2×C4711yescharacteristic, complemented
407#1872C2×C4711yescharacteristic, complemented
408#1851C2×C4711yescharacteristic, complemented
409C2×C47—42no—
410C2×C47—82no—
411C2×C47—82no—
412C2×C47#242411yescharacteristic
413C2×C47#303611yescharacteristic
414C2×C47#304611yescharacteristic
415C2×C47#326911yescharacteristic
416C2×C47#327211yescharacteristic
417C2×C47#330811yescharacteristic
418C2×C47#332611yescharacteristic
419C22×#41C22×C4711yescharacteristic
420C22×SD16C22×C4711yescharacteristic
421C22×SD16C22×C4711yescharacteristic
422C22×D8C22×C4711yescharacteristic
423C22×M16C22×C4711yescharacteristic
424C2×C4⋊Q8C22×C4711yescharacteristic
425C2×#124C22×C4711yescharacteristic
426C2×C22⋊Q8C22×C4711yescharacteristic
427C2×#121C22×C4711yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4C22×C4711yescharacteristic
430C22×C4⋊C4C22×C4711yescharacteristic
431#468—24no—
432#463—24no—
433#449—24no—
434C2×#107C22×C4711yescharacteristic
435C2×C4⋊C8C22×C4711yescharacteristic
436C2×C4⋊C8C22×C4711yescharacteristic
437#417—24no—
438C2×#103C22×C4711yescharacteristic
439C2×#103C22×C4711yescharacteristic
440C2×#103C22×C4711yescharacteristic
441C2×#103C22×C4711yescharacteristic
442C2×#103C22×C4711yescharacteristic
443C2×#103C22×C4711yescharacteristic
444C2×#102C22×C4711yescharacteristic
445C2×#102C22×C4711yescharacteristic
446C2×#102C22×C4711yescharacteristic
447C2×#102C22×C4711yescharacteristic
448C2×C22⋊C8C22×C4711yescharacteristic
449#394—21no—
450#394—21no—
451#391C22×C4711yescharacteristic
452#390C22×C4711yescharacteristic
453#390C22×C4711yescharacteristic
454#389C22×C4711yescharacteristic
455#388—21no—
456#386—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460C4×C4⋊C4C22×C4711yescharacteristic
461C4×C22⋊C4C22×C4711yescharacteristic
462#340C22×C4711yescharacteristic
463#340C22×C4711yescharacteristic
464#336C22×C4711yescharacteristic
465#336C22×C4711yescharacteristic
466C47#2510411yescharacteristic, direct product factor, Sylow
467C2×#41—22no—
468C2×#41—22no—
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—41no—
472C2×#41—41no—
473C22×Q8C23×C4711yescharacteristic
474C22×Q8C23×C4711yescharacteristic
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C4711yescharacteristic
478C22×D4C23×C4711yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C4711yescharacteristic
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16—41no—
489C2×D8—22no—
490C2×D8—22no—
491C2×D8—41no—
492C2×M16—22no—
493C2×M16—22no—
494C2×M16—41no—
495C22×C8C23×C4711yescharacteristic
496C22×C8C23×C4711yescharacteristic
497C22×C8C23×C4711yescharacteristic
498C22×C8C23×C4711yescharacteristic
499C4⋊Q8—22no—
500C4⋊Q8—41no—
501#124—22no—
502#124—41no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505#121—22no—
506#121D4×C4714yes—
507C4×D4—22no—
508C4×D4—41no—
509C4×D4—44no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4C23×C4711yescharacteristic
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4711yescharacteristic
520C2×C4⋊C4C23×C4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4D4×C4711yescharacteristic
531C2×C22⋊C4D4×C4711yescharacteristic
532C2×C42—21no—
533C2×C42C23×C4711yescharacteristic
534C2×C42C23×C4711yescharacteristic
535#107—22no—
536C4⋊C8—22no—
537C4⋊C8—41no—
538#103—22no—
539#103—22no—
540#103—22no—
541#103—22no—
542#103—22no—
543#103—41no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102D4×C4714yescomplemented
548C22⋊C8—22no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95D4×C4711yescharacteristic
554#95D4×C4711yescharacteristic
555C24—21no—
556C24—21no—
557C24C2×D4×C4711yescharacteristic
558#41—28no—
559#41—44no—
560#41—44no—
561#41—44no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8#41×C4712yes—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4C2×D4×C4712yes—
591C2×D4C2×D4×C4712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4C2×D4×C4711yescharacteristic
612C22×C4C2×D4×C4711yescharacteristic
613C22×C4C2×D4×C4711yescharacteristic
614C22×C4C2×D4×C4711yescharacteristic
615C22×C4C2×D4×C4712yes—
616C22×C4C2×D4×C4711yescharacteristic
617C22×C4#41×C4712yes—
618C22×C4C24×C4711yescharacteristic
619SD16—44no—
620SD16—44no—
621D8—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8C2×D4×C4712yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4C2×D4×C4712yes—
647C4⋊C4C2×D4×C4712yes—
648C22⋊C4—24no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23#121×C4712yes—
685C23C22×D4×C4711yescharacteristic
686Q8—22no—
687Q8—22no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—48no—
699D4—48no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—48no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4#121×C4712yes—
743C2×C4AGL(1,ℤ/8)×C4712yes—
744C2×C4C22×D4×C4711yescharacteristic
745C2×C4C22×D4×C4711yescharacteristic
746C2×C4C2×#41×C4711yescharacteristic
747C2×C4C2×#41×C4711yescharacteristic
748C2×C4H(5,𝔽2)×C4711yescharacteristic
749C2×C4H(5,𝔽2)×C4711yescharacteristic
750C8—22no—
751C8—41no—
752C8—41no—
753C8—41no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22C2×#121×C4711yescharacteristic
776C22D42×C4711yescharacteristic
777C22C47×#54611yescharacteristic
778C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
779C22C47×#57511yescharacteristic
780C22C47×#57711yescharacteristic
781C22C47×#57811yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4C47×#52511yescharacteristic
794C4C47×#53811yescharacteristic
795C4D42×C4711yescharacteristic
796C4C47×#54611yescharacteristic
797C2—42no—
798C2—82no—
799C2—82no—
800C2C47×#242411yescharacteristic
801C2C47×#303611yescharacteristic
802C2C47×#304611yescharacteristic
803C2C47×#326911yescharacteristic
804C2C47×#327211yescharacteristic
805C2C47×#330811yescharacteristic
806C2C47×#332611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#449C2
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. C2×C47×#468C2semidirect
2. C2×C47×#463C2semidirect
4. C2×C47×#417C2semidirect
5. C47×#2432C2semidirect
6. C47×#2361C2semidirect
7. C47×#2068C2semidirect
8. C47×#2054C2semidirect
9. C47×#2042C2semidirect
10. C47×#2013C2semidirect
11. C47×#1981C2semidirect
12. C47×#1925C2semidirect
13. C47×#1877C2semidirect
14. C47×#1872C2semidirect
15. C47×#1851C2semidirect
143. #102×C47D4semidirect
350. #25104C47direct (N × H)
394. C2×#468C2×C47semidirect
395. C2×#463C2×C47semidirect
397. C2×#417C2×C47semidirect
398. #2432C2×C47semidirect
399. #2361C2×C47semidirect
400. #2068C2×C47semidirect
401. #2054C2×C47semidirect
402. #2042C2×C47semidirect
403. #2013C2×C47semidirect
404. #1981C2×C47semidirect
405. #1925C2×C47semidirect
406. #1877C2×C47semidirect
407. #1872C2×C47semidirect
408. #1851C2×C47semidirect
466. C47#25104direct (N × H)
547. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4632
C2×C47×#4492
C2×C47×#4172
C47×#24322
C47×#23612
C47×#20682
C47×#20542
C47×#20422
C47×#20132
C47×#19812
C47×#19252
C47×#18772
C47×#18722
C47×#18512
#2510447