Finite Group Databasebeta

← C47×#25505 #26065203

Subgroups — C47×#25505 #26065203

Order 12032.

1140 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#529C211yesmaximal, characteristic
2C2×C47×#470C211yesmaximal, characteristic, complemented
3C2×C47×#468C211yesmaximal, characteristic
4C47×#2855C211yesmaximal, characteristic, complemented
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2042C211yesmaximal, characteristic, complemented
7C47×#2026C211yesmaximal, characteristic, complemented
8C47×#2015C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic
10C47×#1894C211yesmaximal, characteristic, complemented
11C47×#1878C211yesmaximal, characteristic, complemented
12C47×#1877C211yesmaximal, characteristic, complemented
13C47×#1864C211yesmaximal, characteristic, complemented
14C47×#1863C211yesmaximal, characteristic, complemented
15C47×#1728C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C47×#529—24no—
21C47×#529—24no—
22C2×#126×C47—21no—
23C2×#125×C47C2211yescharacteristic
24C2×#124×C47C2211yescharacteristic
25C2×#123×C47—21no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×C4×Q8×C47C2211yescharacteristic
30C2×C4×D4×C47—21no—
31C2×C4×D4×C47C2211yescharacteristic
32C2×#117×C47—21no—
33C22×C42×C47C2211yescharacteristic
34C47×#470—24no—
35C47×#468—24no—
36C2×#107×C47C2211yescharacteristic
37C2×#106×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C47×#391C2211yescharacteristic
47C47×#391C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#387—21no—
51C47×#387—21no—
52C47×#385—21no—
53C47×#381—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47—21no—
68C23×C4×C47D411yescharacteristic
69C23×C4×C47D411yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C2×Q16×C47—22no—
72C2×Q16×C47—22no—
73C2×Q16×C47—41no—
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×SD16×C47—41no—
77C2×M16×C47—22no—
78C2×M16×C47—22no—
79C2×M16×C47—22no—
80C2×M16×C47—22no—
81C2×M16×C47—41no—
82C2×M16×C47—41no—
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87#126×C47—28no—
88#125×C47—22no—
89#125×C47—22no—
90#124×C47—22no—
91#124×C47—22no—
92#123×C47—28no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—22no—
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47D414yes—
97#121×C47—22no—
98#121×C47D414yes—
99C4×Q8×C47—22no—
100C4×Q8×C47—22no—
101C4×D4×C47—28no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104#117×C47—28no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
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×C47C2311yescharacteristic
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×C42×C47—22no—
125C2×C42×C47—22no—
126C2×C42×C47—21no—
127C2×C42×C47D411yescharacteristic
128C2×C42×C47D411yescharacteristic
129C2×C42×C47C2311yescharacteristic
130C2×C42×C47C2311yescharacteristic
131#107×C47—22no—
132#106×C47—22no—
133#103×C47—22no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—41no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—41no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148C24×C47—21no—
149C24×C47C2×D411yescharacteristic
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—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47C2×D412yes—
162C2×D4×C47—24no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47C2×D412yes—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—24no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—22no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—41no—
187C22×C4×C47—41no—
188C22×C4×C47—41no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199Q16×C47—44no—
200SD16×C47—44no—
201M16×C47—44no—
202M16×C47—44no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47#4112yes—
214C2×C8×C47#4112yes—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—24no—
217C4⋊C4×C47—24no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—42no—
228C4⋊C4×C47—42no—
229C4⋊C4×C47—42no—
230C4⋊C4×C47C2×D412yes—
231C4⋊C4×C47C2×D412yes—
232C22⋊C4×C47—24no—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—24no—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C42×C47—24no—
240C42×C47—22no—
241C42×C47—22no—
242C42×C47—21no—
243C42×C47—21no—
244C42×C47—21no—
245C42×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—22no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47#12012yes—
260C23×C47C22×D411yescharacteristic
261Q8×C47—22no—
262Q8×C47—22no—
263Q8×C47—41no—
264Q8×C47—41no—
265Q8×C47—41no—
266Q8×C47—41no—
267Q8×C47—41no—
268Q8×C47—41no—
269D4×C47—22no—
270D4×C47—22no—
271D4×C47—48no—
272D4×C47—41no—
273D4×C47—41no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—44no—
295C2×C4×C47—48no—
296C2×C4×C47—44no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47#12012yes—
316C2×C4×C47#13712yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47H(5,𝔽2)11yescharacteristic
322C2×C4×C472−1+411yescharacteristic
323C8×C47—22no—
324C8×C47—22no—
325C8×C47—41no—
326C8×C47—41no—
327#25505C4711yesmaximal, characteristic, direct product factor, Sylow
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—81no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47C2×#12011yescharacteristic
343C22×C47#53211yescharacteristic
344C22×C47#53711yescharacteristic
345C22×C47C2×#13711yescharacteristic
346C22×C47#57511yescharacteristic
347C22×C47#57511yescharacteristic
348C22×C47#57511yescharacteristic
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—42no—
355C4×C47—41no—
356C4×C47—42no—
357C4×C47—81no—
358C4×C47—81no—
359C4×C47—81no—
360C4×C47—81no—
361C4×C47#54611yescharacteristic
362C4×C47#54611yescharacteristic
363C4×C47#54711yescharacteristic
364C4×C47#54711yescharacteristic
365C2×#529C2×C4711yescharacteristic
366C2×#470C2×C4711yescharacteristic, complemented
367C2×#468C2×C4711yescharacteristic
368#2855C2×C4711yescharacteristic, complemented
369#2059C2×C4711yescharacteristic, complemented
370#2042C2×C4711yescharacteristic, complemented
371#2026C2×C4711yescharacteristic, complemented
372#2015C2×C4711yescharacteristic, complemented
373#1895C2×C4711yescharacteristic
374#1894C2×C4711yescharacteristic, complemented
375#1878C2×C4711yescharacteristic, complemented
376#1877C2×C4711yescharacteristic, complemented
377#1864C2×C4711yescharacteristic, complemented
378#1863C2×C4711yescharacteristic, complemented
379#1728C2×C4711yescharacteristic, complemented
380C2×C47—42no—
381C2×C47—82no—
382C2×C47#243011yescharacteristic
383C2×C47#300511yescharacteristic
384C2×C47#300711yescharacteristic
385C2×C47#317211yescharacteristic
386C2×C47#318311yescharacteristic
387C2×C47#325211yescharacteristic
388C2×C47#325611yescharacteristic
389C22×Q16C22×C4711yescharacteristic
390C22×SD16C22×C4711yescharacteristic
391C22×M16C22×C4711yescharacteristic
392C22×M16C22×C4711yescharacteristic
393#529—24no—
394#529—24no—
395C2×#126—21no—
396C2×#125C22×C4711yescharacteristic
397C2×#124C22×C4711yescharacteristic
398C2×#123—21no—
399C2×C22⋊Q8C22×C4711yescharacteristic
400C2×C22⋊Q8C22×C4711yescharacteristic
401C2×#121C22×C4711yescharacteristic
402C2×C4×Q8C22×C4711yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4C22×C4711yescharacteristic
405C2×#117—21no—
406C22×C42C22×C4711yescharacteristic
407#470—24no—
408#468—24no—
409C2×#107C22×C4711yescharacteristic
410C2×#106C22×C4711yescharacteristic
411C2×#103C22×C4711yescharacteristic
412C2×#103C22×C4711yescharacteristic
413C2×#103C22×C4711yescharacteristic
414C2×#103C22×C4711yescharacteristic
415C2×#103C22×C4711yescharacteristic
416C2×#102C22×C4711yescharacteristic
417C2×#102C22×C4711yescharacteristic
418C2×#102C22×C4711yescharacteristic
419#391C22×C4711yescharacteristic
420#391C22×C4711yescharacteristic
421#389C22×C4711yescharacteristic
422#389C22×C4711yescharacteristic
423#387—21no—
424#387—21no—
425#385—21no—
426#381—21no—
427#380C22×C4711yescharacteristic
428#340C22×C4711yescharacteristic
429#340C22×C4711yescharacteristic
430#340C22×C4711yescharacteristic
431#340C22×C4711yescharacteristic
432#336C22×C4711yescharacteristic
433#336C22×C4711yescharacteristic
434#336C22×C4711yescharacteristic
435#336C22×C4711yescharacteristic
436C47#2550511yescharacteristic, direct product factor, Sylow
437C22×Q8C23×C4711yescharacteristic
438C22×Q8C23×C4711yescharacteristic
439C22×D4—21no—
440C22×D4C23×C4711yescharacteristic
441C23×C4—21no—
442C23×C4D4×C4711yescharacteristic
443C23×C4D4×C4711yescharacteristic
444C23×C4C23×C4711yescharacteristic
445C2×Q16—22no—
446C2×Q16—22no—
447C2×Q16—41no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—41no—
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—41no—
456C2×M16—41no—
457C22×C8C23×C4711yescharacteristic
458C22×C8C23×C4711yescharacteristic
459C22×C8C23×C4711yescharacteristic
460C22×C8C23×C4711yescharacteristic
461#126—28no—
462#125—22no—
463#125—22no—
464#124—22no—
465#124—22no—
466#123—28no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8D4×C4714yes—
471#121—22no—
472#121D4×C4714yes—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×D4—28no—
476C4×D4—22no—
477C4×D4—22no—
478#117—28no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4C23×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C42—21no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42D4×C4711yescharacteristic
502C2×C42D4×C4711yescharacteristic
503C2×C42C23×C4711yescharacteristic
504C2×C42C23×C4711yescharacteristic
505#107—22no—
506#106—22no—
507#103—22no—
508#103—22no—
509#103—22no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—41no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522C24—21no—
523C24C2×D4×C4711yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C2×D4×C4712yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4C2×D4×C4712yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4C2×D4×C4711yescharacteristic
566C22×C4C2×D4×C4711yescharacteristic
567C22×C4C2×D4×C4711yescharacteristic
568C22×C4C2×D4×C4711yescharacteristic
569C22×C4C2×D4×C4712yes—
570C22×C4C2×D4×C4712yes—
571C22×C4C2×D4×C4711yescharacteristic
572C22×C4C24×C4711yescharacteristic
573Q16—44no—
574SD16—44no—
575M16—44no—
576M16—44no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8#41×C4712yes—
588C2×C8#41×C4712yes—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4C2×D4×C4712yes—
605C4⋊C4C2×D4×C4712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C42—24no—
614C42—22no—
615C42—22no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23#120×C4712yes—
634C23C22×D4×C4711yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—44no—
669C2×C4—48no—
670C2×C4—44no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4#120×C4712yes—
690C2×C4#137×C4712yes—
691C2×C4C22×D4×C4711yescharacteristic
692C2×C4C22×D4×C4711yescharacteristic
693C2×C4C2×#41×C4711yescharacteristic
694C2×C4C2×#41×C4711yescharacteristic
695C2×C4H(5,𝔽2)×C4711yescharacteristic
696C2×C42−1+4×C4711yescharacteristic
697C8—22no—
698C8—22no—
699C8—41no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×#120×C4711yescharacteristic
716C22C47×#53211yescharacteristic
717C22C47×#53711yescharacteristic
718C22C2×#137×C4711yescharacteristic
719C22C47×#57511yescharacteristic
720C22C47×#57511yescharacteristic
721C22C47×#57511yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4C47×#54611yescharacteristic
735C4C47×#54611yescharacteristic
736C4C47×#54711yescharacteristic
737C4C47×#54711yescharacteristic
738C2—42no—
739C2—82no—
740C2C47×#243011yescharacteristic
741C2C47×#300511yescharacteristic
742C2C47×#300711yescharacteristic
743C2C47×#317211yescharacteristic
744C2C47×#318311yescharacteristic
745C2C47×#325211yescharacteristic
746C2C47×#325611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#470C2semidirect
4. C47×#2855C2semidirect
5. C47×#2059C2semidirect
6. C47×#2042C2semidirect
7. C47×#2026C2semidirect
8. C47×#2015C2semidirect
10. C47×#1894C2semidirect
11. C47×#1878C2semidirect
12. C47×#1877C2semidirect
13. C47×#1864C2semidirect
14. C47×#1863C2semidirect
15. C47×#1728C2semidirect
327. #25505C47direct (N × H)
366. C2×#470C2×C47semidirect
368. #2855C2×C47semidirect
369. #2059C2×C47semidirect
370. #2042C2×C47semidirect
371. #2026C2×C47semidirect
372. #2015C2×C47semidirect
374. #1894C2×C47semidirect
375. #1878C2×C47semidirect
376. #1877C2×C47semidirect
377. #1864C2×C47semidirect
378. #1863C2×C47semidirect
379. #1728C2×C47semidirect
436. C47#25505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5292
C2×C47×#4702
C2×C47×#4682
C47×#28552
C47×#20592
C47×#20422
C47×#20262
C47×#20152
C47×#18952
C47×#18942
C47×#18782
C47×#18772
C47×#18642
C47×#18632
C47×#17282
#2550547