Finite Group Databasebeta

← C47×#32730 #26072428

Subgroups — C47×#32730 #26072428

Order 12032.

824 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2624C211yesmaximal, characteristic, complemented
2C47×#2619C211yesmaximal, characteristic, complemented
3C47×#2101C211yesmaximal, characteristic, complemented
4C47×#2092C211yesmaximal, characteristic, complemented
5C47×#2067C211yesmaximal, characteristic, complemented
6C47×#2065C211yesmaximal, characteristic, complemented
7C47×#2054C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2041C211yesmaximal, characteristic, complemented
10C47×#2034C211yesmaximal, characteristic, complemented
11C47×#2033C211yesmaximal, characteristic, complemented
12C47×#2011C211yesmaximal, characteristic, complemented
13C47×#1999C211yesmaximal, characteristic, complemented
14C47×#1999C211yesmaximal, characteristic, complemented
15C47×#1798C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×#127×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#117×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#102×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C47×#399—21no—
38C47×#397—21no—
39C47×#394—21no—
40C47×#394—21no—
41C47×#394—21no—
42C47×#394—21no—
43C47×#392—21no—
44C47×#392—21no—
45C47×#390C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#390C2211yescharacteristic
48C47×#390C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#382C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×D4×C47—21no—
60C22×D4×C47—21no—
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47C2311yescharacteristic
65C22×D4×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47C2311yescharacteristic
68C2×D8×C47—41no—
69C2×D8×C47—41no—
70C2×D8×C47—41no—
71C2×D8×C47—41no—
72C2×D8×C47—41no—
73C2×D8×C47—41no—
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78#127×C47—41no—
79#127×C47—41no—
80#121×C47—41no—
81#121×C47—41no—
82#121×C47—41no—
83#121×C47—41no—
84#121×C47—41no—
85#121×C47—41no—
86#117×C47—41no—
87#117×C47—41no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47D411yescharacteristic
91C2×C4⋊C4×C47D411yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
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×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47D411yescharacteristic
110C2×C22⋊C4×C47D411yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113#107×C47—41no—
114#106×C47—41no—
115C4⋊C8×C47—41no—
116C4⋊C8×C47—41no—
117#102×C47—41no—
118#102×C47—41no—
119#102×C47—41no—
120#102×C47—41no—
121#102×C47—41no—
122#102×C47—41no—
123#102×C47—41no—
124#102×C47—41no—
125C22⋊C8×C47—41no—
126C22⋊C8×C47—41no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—21no—
135C24×C47C2×D411yescharacteristic
136C2×D4×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47—21no—
140C2×D4×C47—21no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—42no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47—42no—
158C2×D4×C47—42no—
159C2×D4×C47—81no—
160C2×D4×C47—81no—
161C2×D4×C47—81no—
162C2×D4×C47—81no—
163C2×D4×C47—81no—
164C2×D4×C47—81no—
165C2×D4×C47—81no—
166C2×D4×C47—81no—
167C2×D4×C47—81no—
168C2×D4×C47—81no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
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×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2411yescharacteristic
186D8×C47—44no—
187D8×C47—44no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
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—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47—41no—
212C4⋊C4×C47—81no—
213C4⋊C4×C47—81no—
214C22⋊C4×C47—41no—
215C22⋊C4×C47—41no—
216C22⋊C4×C47—42no—
217C22⋊C4×C47—42no—
218C22⋊C4×C47—42no—
219C22⋊C4×C47—81no—
220C22⋊C4×C47—81no—
221C22⋊C4×C47—81no—
222C22⋊C4×C47—81no—
223C22⋊C4×C47—81no—
224C22⋊C4×C47—81no—
225C22⋊C4×C47—81no—
226C22⋊C4×C47—81no—
227C22⋊C4×C47—81no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
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×C47C22×D411yescharacteristic
261D4×C47—41no—
262D4×C47—41no—
263D4×C47—41no—
264D4×C47—41no—
265D4×C47—41no—
266D4×C47—41no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—41no—
270D4×C47—41no—
271D4×C47—41no—
272D4×C47—41no—
273D4×C47—84no—
274D4×C47—84no—
275D4×C47—84no—
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—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
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—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×C47H(5,𝔽2)11yescharacteristic
313C2×C4×C47H(5,𝔽2)11yescharacteristic
314C2×C4×C47H(5,𝔽2)11yescharacteristic
315C2×C4×C47H(5,𝔽2)11yescharacteristic
316C2×C4×C47H(5,𝔽2)11yescharacteristic
317C2×C4×C472−1+411yescharacteristic
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321C8×C47—41no—
322#32730C4711yesmaximal, characteristic, direct product factor, Sylow
323C22×C47—41no—
324C22×C47—41no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—81no—
331C22×C47—81no—
332C22×C47—81no—
333C22×C47—81no—
334C22×C47—81no—
335C22×C47—81no—
336C22×C47—81no—
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×C47—81no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47#53411yescharacteristic
352C22×C47#53511yescharacteristic
353C22×C47#53711yescharacteristic
354C22×C47#57611yescharacteristic
355C22×C47#57611yescharacteristic
356C22×C47#57611yescharacteristic
357C22×C47#57711yescharacteristic
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—41no—
362C4×C47—41no—
363C4×C47—81no—
364C4×C47—81no—
365C4×C47—81no—
366C4×C47—81no—
367C4×C47—81no—
368C4×C47#56011yescharacteristic
369C4×C47#56011yescharacteristic
370C4×C47#56211yescharacteristic
371C4×C47#56211yescharacteristic
372#2624C2×C4711yescharacteristic, complemented
373#2619C2×C4711yescharacteristic, complemented
374#2101C2×C4711yescharacteristic, complemented
375#2092C2×C4711yescharacteristic, complemented
376#2067C2×C4711yescharacteristic, complemented
377#2065C2×C4711yescharacteristic, complemented
378#2054C2×C4711yescharacteristic, complemented
379#2054C2×C4711yescharacteristic, complemented
380#2041C2×C4711yescharacteristic, complemented
381#2034C2×C4711yescharacteristic, complemented
382#2033C2×C4711yescharacteristic, complemented
383#2011C2×C4711yescharacteristic, complemented
384#1999C2×C4711yescharacteristic, complemented
385#1999C2×C4711yescharacteristic, complemented
386#1798C2×C4711yescharacteristic, complemented
387C2×C47—81no—
388C2×C47—161no—
389C2×C47—161no—
390C2×C47—161no—
391C2×C47#281311yescharacteristic
392C2×C47#319811yescharacteristic
393C2×C47#319911yescharacteristic
394C2×C47#322011yescharacteristic
395C2×C47#322411yescharacteristic
396C2×C47#325711yescharacteristic
397C2×C47#325911yescharacteristic
398C22×D8C22×C4711yescharacteristic
399C22×D8C22×C4711yescharacteristic
400C2×#127C22×C4711yescharacteristic
401C2×#121C22×C4711yescharacteristic
402C2×#121C22×C4711yescharacteristic
403C2×#121C22×C4711yescharacteristic
404C2×#117C22×C4711yescharacteristic
405C2×#107C22×C4711yescharacteristic
406C2×#106C22×C4711yescharacteristic
407C2×C4⋊C8C22×C4711yescharacteristic
408C2×C4⋊C8C22×C4711yescharacteristic
409C2×#102C22×C4711yescharacteristic
410C2×#102C22×C4711yescharacteristic
411C2×#102C22×C4711yescharacteristic
412C2×#102C22×C4711yescharacteristic
413C2×#102C22×C4711yescharacteristic
414C2×#102C22×C4711yescharacteristic
415C2×#102C22×C4711yescharacteristic
416C2×#102C22×C4711yescharacteristic
417C2×C22⋊C8C22×C4711yescharacteristic
418C2×C22⋊C8C22×C4711yescharacteristic
419#399—21no—
420#397—21no—
421#394—21no—
422#394—21no—
423#394—21no—
424#394—21no—
425#392—21no—
426#392—21no—
427#390C22×C4711yescharacteristic
428#390C22×C4711yescharacteristic
429#390C22×C4711yescharacteristic
430#390C22×C4711yescharacteristic
431#389C22×C4711yescharacteristic
432#389C22×C4711yescharacteristic
433#382C22×C4711yescharacteristic
434#380C22×C4711yescharacteristic
435#340C22×C4711yescharacteristic
436#340C22×C4711yescharacteristic
437#340C22×C4711yescharacteristic
438#340C22×C4711yescharacteristic
439#336C22×C4711yescharacteristic
440#336C22×C4711yescharacteristic
441C47#3273011yescharacteristic, direct product factor, Sylow
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C23×C4711yescharacteristic
448C22×D4C23×C4711yescharacteristic
449C22×D4C23×C4711yescharacteristic
450C23×C4C23×C4711yescharacteristic
451C2×D8—41no—
452C2×D8—41no—
453C2×D8—41no—
454C2×D8—41no—
455C2×D8—41no—
456C2×D8—41no—
457C22×C8C23×C4711yescharacteristic
458C22×C8C23×C4711yescharacteristic
459C22×C8C23×C4711yescharacteristic
460C22×C8C23×C4711yescharacteristic
461#127—41no—
462#127—41no—
463#121—41no—
464#121—41no—
465#121—41no—
466#121—41no—
467#121—41no—
468#121—41no—
469#117—41no—
470#117—41no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4D4×C4711yescharacteristic
474C2×C4⋊C4D4×C4711yescharacteristic
475C2×C4⋊C4C23×C4711yescharacteristic
476C2×C4⋊C4C23×C4711yescharacteristic
477C2×C4⋊C4C23×C4711yescharacteristic
478C2×C4⋊C4C23×C4711yescharacteristic
479C2×C4⋊C4C23×C4711yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C4711yescharacteristic
493C2×C22⋊C4D4×C4711yescharacteristic
494C2×C42C23×C4711yescharacteristic
495C2×C42C23×C4711yescharacteristic
496#107—41no—
497#106—41no—
498C4⋊C8—41no—
499C4⋊C8—41no—
500#102—41no—
501#102—41no—
502#102—41no—
503#102—41no—
504#102—41no—
505#102—41no—
506#102—41no—
507#102—41no—
508C22⋊C8—41no—
509C22⋊C8—41no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C2×D4×C4711yescharacteristic
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
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—21no—
562C22×C4—21no—
563C22×C4C2×D4×C4711yescharacteristic
564C22×C4C2×D4×C4711yescharacteristic
565C22×C4C2×D4×C4711yescharacteristic
566C22×C4C2×D4×C4711yescharacteristic
567C22×C4C2×D4×C4711yescharacteristic
568C22×C4C24×C4711yescharacteristic
569D8—44no—
570D8—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
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—41no—
643C23C22×D4×C4711yescharacteristic
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658D4—84no—
659D4—84no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
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—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4H(5,𝔽2)×C4711yescharacteristic
696C2×C4H(5,𝔽2)×C4711yescharacteristic
697C2×C4H(5,𝔽2)×C4711yescharacteristic
698C2×C4H(5,𝔽2)×C4711yescharacteristic
699C2×C4H(5,𝔽2)×C4711yescharacteristic
700C2×C42−1+4×C4711yescharacteristic
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C47×#53411yescharacteristic
734C22C47×#53511yescharacteristic
735C22C47×#53711yescharacteristic
736C22C47×#57611yescharacteristic
737C22C47×#57611yescharacteristic
738C22C47×#57611yescharacteristic
739C22C47×#57711yescharacteristic
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4C47×#56011yescharacteristic
751C4C47×#56011yescharacteristic
752C4C47×#56211yescharacteristic
753C4C47×#56211yescharacteristic
754C2—81no—
755C2—161no—
756C2—161no—
757C2—161no—
758C2C47×#281311yescharacteristic
759C2C47×#319811yescharacteristic
760C2C47×#319911yescharacteristic
761C2C47×#322011yescharacteristic
762C2C47×#322411yescharacteristic
763C2C47×#325711yescharacteristic
764C2C47×#325911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C47×#2624C2semidirect
2. C47×#2619C2semidirect
3. C47×#2101C2semidirect
4. C47×#2092C2semidirect
5. C47×#2067C2semidirect
6. C47×#2065C2semidirect
7. C47×#2054C2semidirect
8. C47×#2054C2semidirect
9. C47×#2041C2semidirect
10. C47×#2034C2semidirect
11. C47×#2033C2semidirect
12. C47×#2011C2semidirect
13. C47×#1999C2semidirect
14. C47×#1999C2semidirect
15. C47×#1798C2semidirect
322. #32730C47direct (N × H)
372. #2624C2×C47semidirect
373. #2619C2×C47semidirect
374. #2101C2×C47semidirect
375. #2092C2×C47semidirect
376. #2067C2×C47semidirect
377. #2065C2×C47semidirect
378. #2054C2×C47semidirect
379. #2054C2×C47semidirect
380. #2041C2×C47semidirect
381. #2034C2×C47semidirect
382. #2033C2×C47semidirect
383. #2011C2×C47semidirect
384. #1999C2×C47semidirect
385. #1999C2×C47semidirect
386. #1798C2×C47semidirect
441. C47#32730direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26242
C47×#26192
C47×#21012
C47×#20922
C47×#20672
C47×#20652
C47×#20542
C47×#20412
C47×#20342
C47×#20332
C47×#20112
C47×#19992
C47×#17982
#3273047