Finite Group Databasebeta

← C47×#13912 #26053610

Subgroups — C47×#13912 #26053610

Order 12032.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C47C211yesmaximal, characteristic
2C2×C47×#388C212yesmaximal, complemented
3C2×C47×#381C211yesmaximal, characteristic, complemented
4C2×C47×#380C211yesmaximal, characteristic, complemented
5C47×#1441C212yesmaximal, complemented
6C47×#1438C212yesmaximal
7C47×#1437C212yesmaximal, complemented
8C47×#1434C211yesmaximal, characteristic, complemented
9C47×C22⋊#95C211yesmaximal, characteristic, complemented
10C47×C22⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C47C211yesmaximal, characteristic, complemented
12C23×D4×C47C2211yescharacteristic
13C24×C4×C47C2211yescharacteristic
14C24×C4×C47C2211yescharacteristic
15C2×C4×D4×C47—28no—
16C2×C4×D4×C47C418yescomplemented
17C22×C4⋊C4×C47C2212yes—
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C22⋊C4×C47C2212yes—
20C22×C22⋊C4×C47C2212yes—
21C22×C22⋊C4×C47C2212yes—
22C22×C22⋊C4×C47C2212yes—
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C42×C47C2212yes—
26C22×C42×C47C2211yescharacteristic
27C47×#388—28no—
28C47×#381—24no—
29C47×#380—24no—
30C2×#95×C47C2211yescharacteristic
31C2×#95×C47C2211yescharacteristic
32C2×#95×C47C2212yes—
33C2×#95×C47C2212yes—
34C2×#95×C47C2212yes—
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C2×#95×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C25×C47C2311yescharacteristic
41C25×C47C2311yescharacteristic
42C22×D4×C47—24no—
43C22×D4×C47—22no—
44C22×D4×C47—22no—
45C22×D4×C47—24no—
46C22×D4×C47C2×C414yes—
47C23×C4×C47—24no—
48C23×C4×C47—24no—
49C23×C4×C47—22no—
50C23×C4×C47—22no—
51C23×C4×C47—22no—
52C23×C4×C47—22no—
53C23×C4×C47—42no—
54C23×C4×C47—42no—
55C23×C4×C47C2×C414yes—
56C23×C4×C47C2×C414yes—
57C23×C4×C47C2312yes—
58C23×C4×C47C2312yes—
59C23×C4×C47C2311yescharacteristic
60C23×C4×C47C2312yes—
61C23×C4×C47C2312yes—
62C23×C4×C47C2311yescharacteristic
63C23×C4×C47C2311yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C4×D4×C47—232no—
67C2×C4⋊C4×C47—24no—
68C2×C4⋊C4×C47—24no—
69C2×C4⋊C4×C47—24no—
70C2×C4⋊C4×C47—42no—
71C2×C4⋊C4×C47C2×C414yes—
72C2×C22⋊C4×C47—24no—
73C2×C22⋊C4×C47—24no—
74C2×C22⋊C4×C47—24no—
75C2×C22⋊C4×C47—24no—
76C2×C22⋊C4×C47—24no—
77C2×C22⋊C4×C47—24no—
78C2×C22⋊C4×C47—24no—
79C2×C22⋊C4×C47—24no—
80C2×C22⋊C4×C47—24no—
81C2×C22⋊C4×C47—42no—
82C2×C22⋊C4×C47—42no—
83C2×C22⋊C4×C47—42no—
84C2×C22⋊C4×C47—42no—
85C2×C22⋊C4×C47C2×C414yes—
86C2×C22⋊C4×C47C2×C414yes—
87C2×C22⋊C4×C47D418yes—
88C2×C42×C47—24no—
89C2×C42×C47—24no—
90C2×C42×C47—24no—
91C2×C42×C47—42no—
92C2×C42×C47C2×C414yes—
93#95×C47—22no—
94#95×C47—24no—
95#95×C47—22no—
96#95×C47—24no—
97#95×C47—24no—
98#95×C47—24no—
99#95×C47—22no—
100#95×C47—24no—
101#95×C47—42no—
102#95×C47D414yescomplemented
103C24×C47—21no—
104C24×C47—21no—
105C24×C47—22no—
106C24×C47—22no—
107C24×C47—22no—
108C24×C47—21no—
109C24×C47—21no—
110C24×C47—22no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—22no—
114C24×C47—21no—
115C24×C47—21no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47C22×C412yes—
121C24×C47C22×C412yes—
122C24×C47C2×D414yes—
123C24×C47#4112yes—
124C24×C47#4112yes—
125C24×C47C2411yescharacteristic
126C2×D4×C47—216no—
127C2×D4×C47—216no—
128C2×D4×C47—28no—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—21no—
142C22×C4×C47—28no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—28no—
160C22×C4×C47—28no—
161C22×C4×C47—28no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—44no—
177C22×C4×C47—44no—
178C22×C4×C47—48no—
179C22×C4×C47—48no—
180C22×C4×C47—48no—
181C22×C4×C47—48no—
182C22×C4×C47C22×C412yes—
183C22×C4×C47C22×C412yes—
184C22×C4×C47C22×C412yes—
185C22×C4×C47C22×C412yes—
186C22×C4×C47C22×C412yes—
187C22×C4×C47C2×D414yes—
188C22×C4×C47C2×D414yes—
189C22×C4×C47C2×D414yes—
190C22×C4×C47C2×D412yes—
191C22×C4×C47#4114yes—
192C22×C4×C47#4114yes—
193C22×C4×C47#4112yes—
194C4⋊C4×C47—28no—
195C4⋊C4×C47—48no—
196C22⋊C4×C47—28no—
197C22⋊C4×C47—48no—
198C22⋊C4×C47—48no—
199C22⋊C4×C47—48no—
200C22⋊C4×C47—48no—
201C22⋊C4×C47C22⋊C4116yescomplemented
202C42×C47—28no—
203C42×C47—48no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—22no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—24no—
225C23×C47—22no—
226C23×C47—24no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—24no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47—42no—
241C23×C47—41no—
242C23×C47—42no—
243C23×C47—41no—
244C23×C47—42no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—42no—
248C23×C47C2×C22⋊C414yes—
249C23×C47#11714yes—
250C23×C47C23×C411yescharacteristic
251C23×C47C22×D412yes—
252C23×C47C22×D411yescharacteristic
253C23×C47C2×#4112yes—
254C23×C47C2×#4111yescharacteristic
255C23×C47C2×#4111yescharacteristic
256C23×C47C2×#4111yescharacteristic
257C23×C47C2×#4112yes—
258C23×C47H(5,𝔽2)12yes—
259C23×C47H(5,𝔽2)11yescharacteristic
260C23×C472−1+411yescharacteristic
261D4×C47—232no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—24no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—24no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—24no—
287C2×C4×C47—416no—
288C2×C4×C47—416no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47C2×C22⋊C414yes—
314C2×C4×C47C2×C22⋊C414yes—
315C2×C4×C47#11714yes—
316C2×C4×C47C4×D414yes—
317#13912C4711yesmaximal, characteristic, direct product factor, Sylow
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—24no—
321C22×C47—24no—
322C22×C47—24no—
323C22×C47—24no—
324C22×C47—42no—
325C22×C47—42no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—44no—
331C22×C47—44no—
332C22×C47—44no—
333C22×C47—44no—
334C22×C47—44no—
335C22×C47—44no—
336C22×C47—44no—
337C22×C47—44no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47C22×C22⋊C411yescharacteristic
341C22×C47C2×#11711yescharacteristic
342C22×C47C2×#11711yescharacteristic
343C22×C47C2×C4×D411yescharacteristic
344C22×C47C4×#4111yescharacteristic
345C22×C47#51811yescharacteristic
346C22×C47#52011yescharacteristic
347C22×C47#52512yes—
348C22×C47#52512yes—
349C22×C47#52912yes—
350C22×C47#53212yes—
351C22×C47#54012yes—
352C22×C47#54212yes—
353C22×C47D4212yes—
354C22×C47#54612yes—
355C22×C47#54612yes—
356C22×C47#54611yescharacteristic
357C22×C47#54712yes—
358C22×C47#54811yescharacteristic
359C22×C47#55112yes—
360C22×C47#55211yescharacteristic
361C22×C47#55311yescharacteristic
362C22×C47#55312yes—
363C4×C47—24no—
364C4×C47—24no—
365C4×C47—24no—
366C4×C47—24no—
367C4×C47—42no—
368C4×C47—44no—
369C4×C47—44no—
370C4×C47—82no—
371C4×C47—82no—
372C22×C4×D4C2×C4711yescharacteristic
373C2×#388C2×C4712yescomplemented
374C2×#381C2×C4711yescharacteristic, complemented
375C2×#380C2×C4711yescharacteristic, complemented
376#1441C2×C4712yescomplemented
377#1438C2×C4712yes—
378#1437C2×C4712yescomplemented
379#1434C2×C4711yescharacteristic, complemented
380C22⋊#95C2×C4711yescharacteristic, complemented
381C22⋊#95C2×C4711yescharacteristic, complemented
382C4×#95C2×C4711yescharacteristic, complemented
383C2×C47—44no—
384C2×C47—44no—
385C2×C47#228011yescharacteristic
386C2×C47#229311yescharacteristic
387C2×C47#231911yescharacteristic
388C2×C47D4×C22⋊C411yescharacteristic
389C2×C47#233911yescharacteristic
390C2×C47#235211yescharacteristic
391C2×C47#235311yescharacteristic
392C2×C47#245712yes—
393C2×C47#246112yes—
394C2×C47#246412yes—
395C2×C47#246812yes—
396C23×D4C22×C4711yescharacteristic
397C24×C4C22×C4711yescharacteristic
398C24×C4C22×C4711yescharacteristic
399C2×C4×D4—28no—
400C2×C4×D4C4×C4718yescomplemented
401C22×C4⋊C4C22×C4712yes—
402C22×C4⋊C4C22×C4711yescharacteristic
403C22×C22⋊C4C22×C4712yes—
404C22×C22⋊C4C22×C4712yes—
405C22×C22⋊C4C22×C4712yes—
406C22×C22⋊C4C22×C4712yes—
407C22×C22⋊C4C22×C4711yescharacteristic
408C22×C22⋊C4C22×C4711yescharacteristic
409C22×C42C22×C4712yes—
410C22×C42C22×C4711yescharacteristic
411#388—28no—
412#381—24no—
413#380—24no—
414C2×#95C22×C4711yescharacteristic
415C2×#95C22×C4712yes—
416C2×#95C22×C4711yescharacteristic
417C2×#95C22×C4711yescharacteristic
418C2×#95C22×C4712yes—
419C2×#95C22×C4712yes—
420C2×#95C22×C4712yes—
421C2×#95C22×C4712yes—
422C2×#95C22×C4712yes—
423C2×#95C22×C4711yescharacteristic
424C47#1391211yescharacteristic, direct product factor, Sylow
425C25C23×C4711yescharacteristic
426C25C23×C4711yescharacteristic
427C22×D4—24no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—24no—
431C22×D4C2×C4×C4714yes—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4C2×C4×C4714yes—
441C23×C4C2×C4×C4714yes—
442C23×C4C23×C4712yes—
443C23×C4C23×C4712yes—
444C23×C4C23×C4711yescharacteristic
445C23×C4C23×C4712yes—
446C23×C4C23×C4712yes—
447C23×C4C23×C4711yescharacteristic
448C23×C4C23×C4711yescharacteristic
449C23×C4C23×C4711yescharacteristic
450C23×C4C23×C4711yescharacteristic
451C4×D4—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4C2×C4×C4714yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4C2×C4×C4714yes—
471C2×C22⋊C4C2×C4×C4714yes—
472C2×C22⋊C4D4×C4718yes—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—42no—
477C2×C42C2×C4×C4714yes—
478#95—22no—
479#95—24no—
480#95—22no—
481#95—24no—
482#95—24no—
483#95—24no—
484#95—22no—
485#95—24no—
486#95—42no—
487#95D4×C4714yescomplemented
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24C22×C4×C4712yes—
506C24C22×C4×C4712yes—
507C24C2×D4×C4714yes—
508C24#41×C4712yes—
509C24#41×C4712yes—
510C24C24×C4711yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4C22×C4×C4712yes—
568C22×C4C22×C4×C4712yes—
569C22×C4C22×C4×C4712yes—
570C22×C4C22×C4×C4712yes—
571C22×C4C22×C4×C4712yes—
572C22×C4C2×D4×C4714yes—
573C22×C4C2×D4×C4714yes—
574C22×C4C2×D4×C4714yes—
575C22×C4C2×D4×C4712yes—
576C22×C4#41×C4714yes—
577C22×C4#41×C4714yes—
578C22×C4#41×C4712yes—
579C4⋊C4—28no—
580C4⋊C4—48no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4C22⋊C4×C47116yescomplemented
587C42—28no—
588C42—48no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23C2×C22⋊C4×C4714yes—
634C23#117×C4714yes—
635C23C23×C4×C4711yescharacteristic
636C23C22×D4×C4712yes—
637C23C22×D4×C4711yescharacteristic
638C23C2×#41×C4712yes—
639C23C2×#41×C4711yescharacteristic
640C23C2×#41×C4711yescharacteristic
641C23C2×#41×C4711yescharacteristic
642C23C2×#41×C4712yes—
643C23H(5,𝔽2)×C4712yes—
644C23H(5,𝔽2)×C4711yescharacteristic
645C232−1+4×C4711yescharacteristic
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4C2×C22⋊C4×C4714yes—
699C2×C4C2×C22⋊C4×C4714yes—
700C2×C4#117×C4714yes—
701C2×C4C4×D4×C4714yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22C22×C22⋊C4×C4711yescharacteristic
725C22C2×#117×C4711yescharacteristic
726C22C2×#117×C4711yescharacteristic
727C22C2×C4×D4×C4711yescharacteristic
728C22C4×#41×C4711yescharacteristic
729C22C47×#51811yescharacteristic
730C22C47×#52011yescharacteristic
731C22C47×#52512yes—
732C22C47×#52512yes—
733C22C47×#52912yes—
734C22C47×#53212yes—
735C22C47×#54012yes—
736C22C47×#54212yes—
737C22D42×C4712yes—
738C22C47×#54612yes—
739C22C47×#54612yes—
740C22C47×#54611yescharacteristic
741C22C47×#54712yes—
742C22C47×#54811yescharacteristic
743C22C47×#55112yes—
744C22C47×#55211yescharacteristic
745C22C47×#55311yescharacteristic
746C22C47×#55312yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—44no—
753C4—44no—
754C4—82no—
755C4—82no—
756C2—44no—
757C2—44no—
758C2C47×#228011yescharacteristic
759C2C47×#229311yescharacteristic
760C2C47×#231911yescharacteristic
761C2D4×C22⋊C4×C4711yescharacteristic
762C2C47×#233911yescharacteristic
763C2C47×#235211yescharacteristic
764C2C47×#235311yescharacteristic
765C2C47×#245712yes—
766C2C47×#246112yes—
767C2C47×#246412yes—
768C2C47×#246812yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#388C2semidirect
3. C2×C47×#381C2semidirect
4. C2×C47×#380C2semidirect
5. C47×#1441C2semidirect
7. C47×#1437C2semidirect
8. C47×#1434C2semidirect
9. C47×C22⋊#95C2semidirect
10. C47×C22⋊#95C2semidirect
11. C4×#95×C47C2semidirect
16. C2×C4×D4×C47C4semidirect
102. #95×C47D4semidirect
201. C22⋊C4×C47C22⋊C4semidirect
317. #13912C47direct (N × H)
373. C2×#388C2×C47semidirect
374. C2×#381C2×C47semidirect
375. C2×#380C2×C47semidirect
376. #1441C2×C47semidirect
378. #1437C2×C47semidirect
379. #1434C2×C47semidirect
380. C22⋊#95C2×C47semidirect
381. C22⋊#95C2×C47semidirect
382. C4×#95C2×C47semidirect
400. C2×C4×D4C4×C47semidirect
424. C47#13912direct (N × H)
487. #95D4×C47semidirect
586. C22⋊C4C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C472
C2×C47×#3882
C2×C47×#3812
C2×C47×#3802
C47×#14412
C47×#14382
C47×#14372
C47×#14342
C47×C22⋊#952
C4×#95×C472
#1391247