Finite Group Databasebeta

← C47×#24489 #26064187

Subgroups — C47×#24489 #26064187

Order 12032.

992 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#484C211yesmaximal, characteristic, complemented
2C2×C47×#417C211yesmaximal, characteristic
3C47×#2432C211yesmaximal, characteristic
4C47×#2344C211yesmaximal, characteristic, complemented
5C47×#2068C211yesmaximal, characteristic, complemented
6C47×#2067C211yesmaximal, characteristic, complemented
7C47×#2043C211yesmaximal, characteristic, complemented
8C47×#2042C211yesmaximal, characteristic, complemented
9C47×#1983C211yesmaximal, characteristic, complemented
10C47×#1981C211yesmaximal, characteristic, complemented
11C47×#1928C211yesmaximal, characteristic, complemented
12C47×#1925C211yesmaximal, characteristic, complemented
13C47×#1894C211yesmaximal, characteristic, complemented
14C47×#1851C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic
16C22×#41×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C2×C4⋊Q8×C47C2211yescharacteristic
19C2×#124×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#117×C47—21no—
22C22×C4⋊C4×C47C2211yescharacteristic
23C47×#484—24no—
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C47×#417—24no—
29C2×#103×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×C22⋊C8×C47C2211yescharacteristic
42C47×#394—21no—
43C47×#394—21no—
44C47×#391C2211yescharacteristic
45C47×#390C2211yescharacteristic
46C47×#389C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#387—21no—
49C47×#387—21no—
50C47×#385—21no—
51C47×#385—21no—
52C47×#381—21no—
53C47×#380C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C2×#41×C47—22no—
62C2×#41×C47—22no—
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C22×Q8×C47C2311yescharacteristic
68C22×Q8×C47C2311yescharacteristic
69C22×D4×C47—21no—
70C22×D4×C47C2311yescharacteristic
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74C2×M16×C47—22no—
75C2×M16×C47—41no—
76C2×M16×C47—41no—
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C4⋊Q8×C47—22no—
82C4⋊Q8×C47—41no—
83#124×C47—22no—
84#124×C47—41no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87#117×C47—44no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47D414yes—
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47D411yescharacteristic
108C2×C22⋊C4×C47D411yescharacteristic
109C2×C42×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113#107×C47—22no—
114#107×C47—22no—
115C4⋊C8×C47—41no—
116C4⋊C8×C47—41no—
117#103×C47—22no—
118#103×C47—22no—
119#103×C47—22no—
120#103×C47—22no—
121#103×C47—22no—
122#103×C47—41no—
123#103×C47—41no—
124#103×C47—41no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—41no—
129C22⋊C8×C47—22no—
130#95×C47—21no—
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47D411yescharacteristic
138#95×C47D411yescharacteristic
139C24×C47—21no—
140C24×C47C2×D411yescharacteristic
141#41×C47—28no—
142#41×C47—44no—
143#41×C47—44no—
144#41×C47—44no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47#4112yes—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47#4112yes—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—24no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—42no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D412yes—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47#4112yes—
190C22×C4×C47C2411yescharacteristic
191M16×C47—44no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C4⋊C4×C47—24no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—42no—
214C4⋊C4×C47—42no—
215C4⋊C4×C47—42no—
216C4⋊C4×C47—42no—
217C4⋊C4×C47—42no—
218C4⋊C4×C47C2×D412yes—
219C4⋊C4×C47C2×D412yes—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—42no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—42no—
233C42×C47—42no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—22no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47#12112yes—
248C23×C47C22×D411yescharacteristic
249Q8×C47—22no—
250Q8×C47—22no—
251Q8×C47—41no—
252Q8×C47—41no—
253Q8×C47—41no—
254Q8×C47—41no—
255Q8×C47—41no—
256Q8×C47—41no—
257D4×C47—22no—
258D4×C47—22no—
259D4×C47—48no—
260D4×C47—41no—
261D4×C47—41no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—48no—
283C2×C4×C47—48no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47#12112yes—
303C2×C4×C47AGL(1,ℤ/8)12yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×C4×C47H(5,𝔽2)11yescharacteristic
309C2×C4×C47H(5,𝔽2)11yescharacteristic
310C8×C47—41no—
311C8×C47—41no—
312C8×C47—41no—
313C8×C47—41no—
314#24489C4711yesmaximal, characteristic, direct product factor, Sylow
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47—81no—
326C22×C47—81no—
327C22×C47—81no—
328C22×C47—81no—
329C22×C47C2×#12111yescharacteristic
330C22×C47#54611yescharacteristic
331C22×C47#54611yescharacteristic
332C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C47#57511yescharacteristic
334C22×C47#57811yescharacteristic
335C22×C47#57811yescharacteristic
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—41no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—41no—
343C4×C47—41no—
344C4×C47—81no—
345C4×C47—81no—
346C4×C47—81no—
347C4×C47—81no—
348C4×C47#52511yescharacteristic
349C4×C47#53511yescharacteristic
350C4×C47#55111yescharacteristic
351C4×C47#55111yescharacteristic
352C2×#484C2×C4711yescharacteristic, complemented
353C2×#417C2×C4711yescharacteristic
354#2432C2×C4711yescharacteristic
355#2344C2×C4711yescharacteristic, complemented
356#2068C2×C4711yescharacteristic, complemented
357#2067C2×C4711yescharacteristic, complemented
358#2043C2×C4711yescharacteristic, complemented
359#2042C2×C4711yescharacteristic, complemented
360#1983C2×C4711yescharacteristic, complemented
361#1981C2×C4711yescharacteristic, complemented
362#1928C2×C4711yescharacteristic, complemented
363#1925C2×C4711yescharacteristic, complemented
364#1894C2×C4711yescharacteristic, complemented
365#1851C2×C4711yescharacteristic, complemented
366#1788C2×C4711yescharacteristic
367C2×C47—42no—
368C2×C47—82no—
369C2×C47#241111yescharacteristic
370C2×C47#303611yescharacteristic
371C2×C47#304411yescharacteristic
372C2×C47#330811yescharacteristic
373C2×C47#331511yescharacteristic
374C2×C47#332711yescharacteristic
375C2×C47#333011yescharacteristic
376C22×#41C22×C4711yescharacteristic
377C22×M16C22×C4711yescharacteristic
378C2×C4⋊Q8C22×C4711yescharacteristic
379C2×#124C22×C4711yescharacteristic
380C2×C22⋊Q8C22×C4711yescharacteristic
381C2×#117—21no—
382C22×C4⋊C4C22×C4711yescharacteristic
383#484—24no—
384C2×#107C22×C4711yescharacteristic
385C2×#107C22×C4711yescharacteristic
386C2×C4⋊C8C22×C4711yescharacteristic
387C2×C4⋊C8C22×C4711yescharacteristic
388#417—24no—
389C2×#103C22×C4711yescharacteristic
390C2×#103C22×C4711yescharacteristic
391C2×#103C22×C4711yescharacteristic
392C2×#103C22×C4711yescharacteristic
393C2×#103C22×C4711yescharacteristic
394C2×#103C22×C4711yescharacteristic
395C2×#103C22×C4711yescharacteristic
396C2×#103C22×C4711yescharacteristic
397C2×#102C22×C4711yescharacteristic
398C2×#102C22×C4711yescharacteristic
399C2×#102C22×C4711yescharacteristic
400C2×#102C22×C4711yescharacteristic
401C2×C22⋊C8C22×C4711yescharacteristic
402#394—21no—
403#394—21no—
404#391C22×C4711yescharacteristic
405#390C22×C4711yescharacteristic
406#389C22×C4711yescharacteristic
407#389C22×C4711yescharacteristic
408#387—21no—
409#387—21no—
410#385—21no—
411#385—21no—
412#381—21no—
413#380C22×C4711yescharacteristic
414C4×C4⋊C4C22×C4711yescharacteristic
415C4×C4⋊C4C22×C4711yescharacteristic
416C4×C22⋊C4C22×C4711yescharacteristic
417#340C22×C4711yescharacteristic
418#340C22×C4711yescharacteristic
419#336C22×C4711yescharacteristic
420#336C22×C4711yescharacteristic
421C47#2448911yescharacteristic, direct product factor, Sylow
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—41no—
427C2×#41—41no—
428C22×Q8C23×C4711yescharacteristic
429C22×Q8C23×C4711yescharacteristic
430C22×D4—21no—
431C22×D4C23×C4711yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C4711yescharacteristic
435C2×M16—22no—
436C2×M16—41no—
437C2×M16—41no—
438C22×C8C23×C4711yescharacteristic
439C22×C8C23×C4711yescharacteristic
440C22×C8C23×C4711yescharacteristic
441C22×C8C23×C4711yescharacteristic
442C4⋊Q8—22no—
443C4⋊Q8—41no—
444#124—22no—
445#124—41no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448#117—44no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4D4×C4714yes—
457C2×C4⋊C4C23×C4711yescharacteristic
458C2×C4⋊C4C23×C4711yescharacteristic
459C2×C4⋊C4C23×C4711yescharacteristic
460C2×C4⋊C4C23×C4711yescharacteristic
461C2×C4⋊C4C23×C4711yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4D4×C4711yescharacteristic
469C2×C22⋊C4D4×C4711yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C23×C4711yescharacteristic
473C2×C42C23×C4711yescharacteristic
474#107—22no—
475#107—22no—
476C4⋊C8—41no—
477C4⋊C8—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#103—41no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—41no—
490C22⋊C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C4711yescharacteristic
499#95D4×C4711yescharacteristic
500C24—21no—
501C24C2×D4×C4711yescharacteristic
502#41—28no—
503#41—44no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8#41×C4712yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4#41×C4712yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4C2×D4×C4711yescharacteristic
545C22×C4C2×D4×C4711yescharacteristic
546C22×C4C2×D4×C4711yescharacteristic
547C22×C4C2×D4×C4711yescharacteristic
548C22×C4C2×D4×C4712yes—
549C22×C4C2×D4×C4711yescharacteristic
550C22×C4#41×C4712yes—
551C22×C4C24×C4711yescharacteristic
552M16—44no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4C2×D4×C4712yes—
580C4⋊C4C2×D4×C4712yes—
581C22⋊C4—22no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—42no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23#121×C4712yes—
609C23C22×D4×C4711yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—48no—
621D4—41no—
622D4—41no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
644C2×C4—48no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4#121×C4712yes—
664C2×C4AGL(1,ℤ/8)×C4712yes—
665C2×C4C22×D4×C4711yescharacteristic
666C2×C4C2×#41×C4711yescharacteristic
667C2×C4C2×#41×C4711yescharacteristic
668C2×C4C2×#41×C4711yescharacteristic
669C2×C4H(5,𝔽2)×C4711yescharacteristic
670C2×C4H(5,𝔽2)×C4711yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#121×C4711yescharacteristic
690C22C47×#54611yescharacteristic
691C22C47×#54611yescharacteristic
692C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
693C22C47×#57511yescharacteristic
694C22C47×#57811yescharacteristic
695C22C47×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—42no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—42no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C47×#52511yescharacteristic
709C4C47×#53511yescharacteristic
710C4C47×#55111yescharacteristic
711C4C47×#55111yescharacteristic
712C2—42no—
713C2—82no—
714C2C47×#241111yescharacteristic
715C2C47×#303611yescharacteristic
716C2C47×#304411yescharacteristic
717C2C47×#330811yescharacteristic
718C2C47×#331511yescharacteristic
719C2C47×#332711yescharacteristic
720C2C47×#333011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×#41×C47C22
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×#484C2semidirect
4. C47×#2344C2semidirect
5. C47×#2068C2semidirect
6. C47×#2067C2semidirect
7. C47×#2043C2semidirect
8. C47×#2042C2semidirect
9. C47×#1983C2semidirect
10. C47×#1981C2semidirect
11. C47×#1928C2semidirect
12. C47×#1925C2semidirect
13. C47×#1894C2semidirect
14. C47×#1851C2semidirect
314. #24489C47direct (N × H)
352. C2×#484C2×C47semidirect
355. #2344C2×C47semidirect
356. #2068C2×C47semidirect
357. #2067C2×C47semidirect
358. #2043C2×C47semidirect
359. #2042C2×C47semidirect
360. #1983C2×C47semidirect
361. #1981C2×C47semidirect
362. #1928C2×C47semidirect
363. #1925C2×C47semidirect
364. #1894C2×C47semidirect
365. #1851C2×C47semidirect
421. C47#24489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4842
C2×C47×#4172
C47×#24322
C47×#23442
C47×#20682
C47×#20672
C47×#20432
C47×#20422
C47×#19832
C47×#19812
C47×#19282
C47×#19252
C47×#18942
C47×#18512
C47×#17882
#2448947