Finite Group Databasebeta

← C47×#24767 #26064465

Subgroups — C47×#24767 #26064465

Order 12032.

1002 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#469C211yesmaximal, characteristic
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#463C211yesmaximal, characteristic, complemented
4C2×C47×#424C211yesmaximal, characteristic, complemented
5C47×#2620C211yesmaximal, characteristic, complemented
6C47×#2324C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2055C211yesmaximal, characteristic, complemented
10C47×#2054C211yesmaximal, characteristic, complemented
11C47×#1983C211yesmaximal, characteristic, complemented
12C47×#1948C211yesmaximal, characteristic, complemented
13C47×#1894C211yesmaximal, characteristic, complemented
14C47×#1893C211yesmaximal, characteristic, complemented
15C47×#1802C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C47×#469—24no—
27C47×#465—24no—
28C47×#463—24no—
29C2×#106×C47C2211yescharacteristic
30C2×#106×C47C2211yescharacteristic
31C47×#424—24no—
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×C4⋊C8×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C47×#396—21no—
45C47×#396—21no—
46C47×#394—21no—
47C47×#394—21no—
48C47×#391C2211yescharacteristic
49C47×#390—21no—
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#386—21no—
55C47×#385—21no—
56C47×#384C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C23×C4×C47—21no—
69C23×C4×C47C2311yescharacteristic
70C2×SD16×C47—22no—
71C2×SD16×C47—22no—
72C2×SD16×C47—41no—
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—41no—
76C2×M16×C47—22no—
77C2×M16×C47—22no—
78C2×M16×C47—41no—
79C22×C8×C47—22no—
80C22×C8×C47—22no—
81C22×C8×C47—41no—
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86#124×C47—22no—
87#124×C47—22no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47D414yes—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96#117×C47—22no—
97#117×C47—22no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47D411yescharacteristic
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47D411yescharacteristic
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C42×C47—21no—
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125#106×C47—22no—
126#106×C47—22no—
127C4⋊C8×C47—22no—
128C4⋊C8×C47—22no—
129C4⋊C8×C47—22no—
130C4⋊C8×C47D414yescomplemented
131#103×C47—22no—
132#103×C47—22no—
133#103×C47—41no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—41no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47C2×D411yescharacteristic
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×D4×C47—24no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—42no—
166C2×D4×C47—81no—
167C2×D4×C47—81no—
168C2×D4×C47—81no—
169C2×D4×C47—81no—
170C2×D4×C47C2×D412yes—
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—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—42no—
182C22×C4×C47—81no—
183C22×C4×C47—81no—
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D412yes—
190C22×C4×C47#4112yes—
191C22×C4×C47C2411yescharacteristic
192SD16×C47—44no—
193D8×C47—44no—
194M16×C47—44no—
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—
204C2×C8×C47—21no—
205C2×C8×C47—44no—
206C2×C8×C47C2×D412yes—
207C2×C8×C47C2×D412yes—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—22no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—42no—
220C4⋊C4×C47—81no—
221C4⋊C4×C47—81no—
222C4⋊C4×C47—81no—
223C4⋊C4×C47C2×D412yes—
224C22⋊C4×C47—24no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—81no—
233C22⋊C4×C47—81no—
234C22⋊C4×C47—81no—
235C22⋊C4×C47—81no—
236C22⋊C4×C47—81no—
237C42×C47—21no—
238C42×C47—21no—
239C42×C47—81no—
240C42×C47C2×D412yes—
241C42×C47#4112yes—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—22no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47#12112yes—
263C23×C47C22×D411yescharacteristic
264Q8×C47—41no—
265Q8×C47—41no—
266Q8×C47—41no—
267Q8×C47—41no—
268D4×C47—22no—
269D4×C47—22no—
270D4×C47—41no—
271D4×C47—41no—
272D4×C47—41no—
273D4×C47—41no—
274D4×C47—41no—
275D4×C47—41no—
276D4×C47—84no—
277D4×C47—84no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—22no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
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—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—84no—
313C2×C4×C47#12112yes—
314C2×C4×C47#12112yes—
315C2×C4×C47#12112yes—
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47H(5,𝔽2)11yescharacteristic
321C2×C4×C472−1+411yescharacteristic
322C8×C47—22no—
323C8×C47—22no—
324C8×C47—41no—
325C8×C47—41no—
326#24767C4711yesmaximal, characteristic, direct product factor, Sylow
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—81no—
338C22×C47—81no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47—81no—
344C22×C47—81no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47C2×#12111yescharacteristic
349C22×C47C2×#12111yescharacteristic
350C22×C47#53711yescharacteristic
351C22×C47#57611yescharacteristic
352C22×C47#57711yescharacteristic
353C22×C47#57711yescharacteristic
354C22×C47#57711yescharacteristic
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—81no—
362C4×C47—81no—
363C4×C47—81no—
364C4×C47—81no—
365C4×C47—81no—
366C4×C47D4211yescharacteristic
367C4×C47#54711yescharacteristic
368C4×C47#54811yescharacteristic
369C4×C47#55311yescharacteristic
370C2×#469C2×C4711yescharacteristic
371C2×#465C2×C4711yescharacteristic, complemented
372C2×#463C2×C4711yescharacteristic, complemented
373C2×#424C2×C4711yescharacteristic, complemented
374#2620C2×C4711yescharacteristic, complemented
375#2324C2×C4711yescharacteristic, complemented
376#2066C2×C4711yescharacteristic, complemented
377#2065C2×C4711yescharacteristic, complemented
378#2055C2×C4711yescharacteristic, complemented
379#2054C2×C4711yescharacteristic, complemented
380#1983C2×C4711yescharacteristic, complemented
381#1948C2×C4711yescharacteristic, complemented
382#1894C2×C4711yescharacteristic, complemented
383#1893C2×C4711yescharacteristic, complemented
384#1802C2×C4711yescharacteristic, complemented
385C2×C47—42no—
386C2×C47—82no—
387C2×C47—161no—
388C2×C47#241611yescharacteristic
389C2×C47#304211yescharacteristic
390C2×C47#304511yescharacteristic
391C2×C47#306011yescharacteristic
392C2×C47#306211yescharacteristic
393C2×C47#325711yescharacteristic
394C2×C47#326311yescharacteristic
395C22×SD16C22×C4711yescharacteristic
396C22×D8C22×C4711yescharacteristic
397C22×M16C22×C4711yescharacteristic
398C23×C8C22×C4711yescharacteristic
399C2×#124C22×C4711yescharacteristic
400C2×C22⋊Q8C22×C4711yescharacteristic
401C2×#121C22×C4711yescharacteristic
402C2×#121C22×C4711yescharacteristic
403C2×C4×D4C22×C4711yescharacteristic
404C2×#117C22×C4711yescharacteristic
405#469—24no—
406#465—24no—
407#463—24no—
408C2×#106C22×C4711yescharacteristic
409C2×#106C22×C4711yescharacteristic
410#424—24no—
411C2×C4⋊C8C22×C4711yescharacteristic
412C2×C4⋊C8C22×C4711yescharacteristic
413C2×C4⋊C8C22×C4711yescharacteristic
414C2×C4⋊C8C22×C4711yescharacteristic
415C2×#103C22×C4711yescharacteristic
416C2×#103C22×C4711yescharacteristic
417C2×#103C22×C4711yescharacteristic
418C2×#102C22×C4711yescharacteristic
419C2×#102C22×C4711yescharacteristic
420C2×#102C22×C4711yescharacteristic
421C2×#102C22×C4711yescharacteristic
422C2×#102C22×C4711yescharacteristic
423#396—21no—
424#396—21no—
425#394—21no—
426#394—21no—
427#391C22×C4711yescharacteristic
428#390—21no—
429#390C22×C4711yescharacteristic
430#390C22×C4711yescharacteristic
431#389C22×C4711yescharacteristic
432#388—21no—
433#386—21no—
434#385—21no—
435#384C22×C4711yescharacteristic
436#380C22×C4711yescharacteristic
437C4×C4⋊C4C22×C4711yescharacteristic
438#340C22×C4711yescharacteristic
439#340C22×C4711yescharacteristic
440#340C22×C4711yescharacteristic
441#340C22×C4711yescharacteristic
442C47#2476711yescharacteristic, direct product factor, Sylow
443C22×Q8C23×C4711yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C23×C4711yescharacteristic
447C22×D4C23×C4711yescharacteristic
448C23×C4—21no—
449C23×C4C23×C4711yescharacteristic
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—41no—
453C2×D8—22no—
454C2×D8—22no—
455C2×D8—41no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—41no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—41no—
462C22×C8C23×C4711yescharacteristic
463C22×C8C23×C4711yescharacteristic
464C22×C8C23×C4711yescharacteristic
465C22×C8C23×C4711yescharacteristic
466#124—22no—
467#124—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121D4×C4714yes—
474C4×D4—22no—
475C4×D4—22no—
476#117—22no—
477#117—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4D4×C4711yescharacteristic
483C2×C4⋊C4D4×C4711yescharacteristic
484C2×C4⋊C4C23×C4711yescharacteristic
485C2×C4⋊C4C23×C4711yescharacteristic
486C2×C4⋊C4C23×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
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×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4D4×C4711yescharacteristic
501C2×C22⋊C4D4×C4711yescharacteristic
502C2×C42—21no—
503C2×C42C23×C4711yescharacteristic
504C2×C42C23×C4711yescharacteristic
505#106—22no—
506#106—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8D4×C4714yescomplemented
511#103—22no—
512#103—22no—
513#103—41no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—22no—
518#102—41no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—21no—
525C24—21no—
526C24C2×D4×C4711yescharacteristic
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4C2×D4×C4712yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4C2×D4×C4711yescharacteristic
565C22×C4C2×D4×C4711yescharacteristic
566C22×C4C2×D4×C4711yescharacteristic
567C22×C4C2×D4×C4711yescharacteristic
568C22×C4C2×D4×C4711yescharacteristic
569C22×C4C2×D4×C4712yes—
570C22×C4#41×C4712yes—
571C22×C4C24×C4711yescharacteristic
572SD16—44no—
573D8—44no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
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—44no—
586C2×C8C2×D4×C4712yes—
587C2×C8C2×D4×C4712yes—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C4⋊C4—81no—
603C4⋊C4C2×D4×C4712yes—
604C22⋊C4—24no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—21no—
618C42—21no—
619C42—81no—
620C42C2×D4×C4712yes—
621C42#41×C4712yes—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23#121×C4712yes—
643C23C22×D4×C4711yescharacteristic
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648D4—22no—
649D4—22no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
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—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4#121×C4712yes—
694C2×C4#121×C4712yes—
695C2×C4#121×C4712yes—
696C2×C4C22×D4×C4711yescharacteristic
697C2×C4C22×D4×C4711yescharacteristic
698C2×C4C2×#41×C4711yescharacteristic
699C2×C4C2×#41×C4711yescharacteristic
700C2×C4H(5,𝔽2)×C4711yescharacteristic
701C2×C42−1+4×C4711yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C2×#121×C4711yescharacteristic
728C22C2×#121×C4711yescharacteristic
729C22C47×#53711yescharacteristic
730C22C47×#57611yescharacteristic
731C22C47×#57711yescharacteristic
732C22C47×#57711yescharacteristic
733C22C47×#57711yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4D42×C4711yescharacteristic
746C4C47×#54711yescharacteristic
747C4C47×#54811yescharacteristic
748C4C47×#55311yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2C47×#241611yescharacteristic
753C2C47×#304211yescharacteristic
754C2C47×#304511yescharacteristic
755C2C47×#306011yescharacteristic
756C2C47×#306211yescharacteristic
757C2C47×#325711yescharacteristic
758C2C47×#326311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#469C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#465C2semidirect
3. C2×C47×#463C2semidirect
4. C2×C47×#424C2semidirect
5. C47×#2620C2semidirect
6. C47×#2324C2semidirect
7. C47×#2066C2semidirect
8. C47×#2065C2semidirect
9. C47×#2055C2semidirect
10. C47×#2054C2semidirect
11. C47×#1983C2semidirect
12. C47×#1948C2semidirect
13. C47×#1894C2semidirect
14. C47×#1893C2semidirect
15. C47×#1802C2semidirect
130. C4⋊C8×C47D4semidirect
326. #24767C47direct (N × H)
371. C2×#465C2×C47semidirect
372. C2×#463C2×C47semidirect
373. C2×#424C2×C47semidirect
374. #2620C2×C47semidirect
375. #2324C2×C47semidirect
376. #2066C2×C47semidirect
377. #2065C2×C47semidirect
378. #2055C2×C47semidirect
379. #2054C2×C47semidirect
380. #1983C2×C47semidirect
381. #1948C2×C47semidirect
382. #1894C2×C47semidirect
383. #1893C2×C47semidirect
384. #1802C2×C47semidirect
442. C47#24767direct (N × H)
510. C4⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4692
C2×C47×#4652
C2×C47×#4632
C2×C47×#4242
C47×#26202
C47×#23242
C47×#20662
C47×#20652
C47×#20552
C47×#20542
C47×#19832
C47×#19482
C47×#18942
C47×#18932
C47×#18022
#2476747