Finite Group Databasebeta

← C47×#24657 #26064355

Subgroups — C47×#24657 #26064355

Order 12032.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#464C211yesmaximal, characteristic, complemented
2C2×C47×#432C211yesmaximal, characteristic, complemented
3C47×#2850C211yesmaximal, characteristic
4C4×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
5C47×#2036C211yesmaximal, characteristic, complemented
6C47×#2034C211yesmaximal, characteristic
7C47×#2001C211yesmaximal, characteristic, complemented
8C47×#2000C211yesmaximal, characteristic
9C47×#1983C211yesmaximal, characteristic, complemented
10C47×#1973C211yesmaximal, characteristic, complemented
11C47×#1971C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1936C211yesmaximal, characteristic, complemented
14C47×#1935C211yesmaximal, characteristic, complemented
15C47×#1805C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C2×#124×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C22×C42×C47C2211yescharacteristic
24C47×#464—24no—
25C47×#432—24no—
26C2×#107×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×#97×C47C2211yescharacteristic
41C2×#97×C47C2211yescharacteristic
42C47×#391C2211yescharacteristic
43C47×#391C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#389C2211yescharacteristic
46C47×#388—21no—
47C47×#388—21no—
48C47×#387—21no—
49C47×#386—21no—
50C47×#386—21no—
51C47×#385—21no—
52C47×#382C2211yescharacteristic
53C47×#380C2211yescharacteristic
54C4×C4⋊C4×C47—21no—
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C22⋊C4×C47—21no—
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C22×Q8×C47C2311yescharacteristic
62C22×Q8×C47C2311yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47C2311yescharacteristic
65C23×C4×C47D411yescharacteristic
66C23×C4×C47D411yescharacteristic
67C23×C4×C47C2311yescharacteristic
68C2×Q16×C47—22no—
69C2×Q16×C47—22no—
70C2×Q16×C47—41no—
71C2×SD16×C47—22no—
72C2×SD16×C47—22no—
73C2×SD16×C47—41no—
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78#124×C47—22no—
79#124×C47—22no—
80C22⋊Q8×C47—22no—
81C22⋊Q8×C47—22no—
82C22⋊Q8×C47—41no—
83C22⋊Q8×C47—41no—
84#121×C47—41no—
85#121×C47—41no—
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
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×C42×C47—22no—
106C2×C42×C47—22no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47D411yescharacteristic
110C2×C42×C47D411yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113#107×C47—41no—
114#106×C47—41no—
115C4⋊C8×C47—22no—
116C4⋊C8×C47D414yescomplemented
117#103×C47—22no—
118#103×C47—22no—
119#103×C47—41no—
120#103×C47—41no—
121#103×C47—41no—
122#102×C47—22no—
123#102×C47—22no—
124#102×C47—41no—
125C22⋊C8×C47—22no—
126C22⋊C8×C47—22no—
127#97×C47—22no—
128#97×C47—22no—
129#95×C47—21no—
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×C47—21no—
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
140C2×Q8×C47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
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#4112yes—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—42no—
159C2×D4×C47—42no—
160C2×D4×C47—42no—
161C22×C4×C47—22no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
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—41no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2411yescharacteristic
186Q16×C47—44no—
187SD16×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×C47C2×D412yes—
199C2×C8×C47C2×D412yes—
200C4⋊C4×C47—24no—
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—42no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47—42no—
213C4⋊C4×C47#4112yes—
214C22⋊C4×C47—24no—
215C22⋊C4×C47—42no—
216C22⋊C4×C47—42no—
217C22⋊C4×C47—42no—
218C22⋊C4×C47—42no—
219C22⋊C4×C47—42no—
220C22⋊C4×C47—42no—
221C22⋊C4×C47—42no—
222C42×C47—22no—
223C42×C47—22no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—42no—
227C42×C47—42no—
228C42×C47C2×D412yes—
229C42×C47#4112yes—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47#13712yes—
244C23×C47C22×D411yescharacteristic
245Q8×C47—22no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249Q8×C47—41no—
250Q8×C47—41no—
251Q8×C47—41no—
252Q8×C47—41no—
253D4×C47—41no—
254D4×C47—41no—
255D4×C47—41no—
256D4×C47—41no—
257D4×C47—84no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—44no—
274C2×C4×C47—44no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
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#12112yes—
299C2×C4×C47#12112yes—
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47C2×#4111yescharacteristic
303C2×C4×C47C2×#4111yescharacteristic
304C2×C4×C47H(5,𝔽2)11yescharacteristic
305C2×C4×C47H(5,𝔽2)11yescharacteristic
306C8×C47—22no—
307C8×C47—22no—
308C8×C47—41no—
309C8×C47—41no—
310#24657C4711yesmaximal, characteristic, direct product factor, Sylow
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—41no—
315C22×C47—41no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47—81no—
321C22×C47—81no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47C2×#12111yescharacteristic
326C22×C47#52511yescharacteristic
327C22×C47#53511yescharacteristic
328C22×C47C2×#13711yescharacteristic
329C22×C47#57511yescharacteristic
330C22×C47#57511yescharacteristic
331C22×C47#57511yescharacteristic
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—42no—
335C4×C47—41no—
336C4×C47—42no—
337C4×C47—41no—
338C4×C47—41no—
339C4×C47—81no—
340C4×C47—81no—
341C4×C47—81no—
342C4×C47—81no—
343C4×C47—81no—
344C4×C47#54611yescharacteristic
345C4×C47#55011yescharacteristic
346C4×C47#55311yescharacteristic
347C4×C47#55511yescharacteristic
348C2×#464C2×C4711yescharacteristic, complemented
349C2×#432C2×C4711yescharacteristic, complemented
350#2850C2×C4711yescharacteristic
351C4×C22⋊Q8C2×C4711yescharacteristic, complemented
352#2036C2×C4711yescharacteristic, complemented
353#2034C2×C4711yescharacteristic
354#2001C2×C4711yescharacteristic, complemented
355#2000C2×C4711yescharacteristic
356#1983C2×C4711yescharacteristic, complemented
357#1973C2×C4711yescharacteristic, complemented
358#1971C2×C4711yescharacteristic, complemented
359#1949C2×C4711yescharacteristic, complemented
360#1936C2×C4711yescharacteristic, complemented
361#1935C2×C4711yescharacteristic, complemented
362#1805C2×C4711yescharacteristic, complemented
363C2×C47—42no—
364C2×C47—161no—
365C2×C47#241411yescharacteristic
366C2×C47#305411yescharacteristic
367C2×C47#305611yescharacteristic
368C2×C47#311111yescharacteristic
369C2×C47#311711yescharacteristic
370C2×C47#321511yescharacteristic
371C2×C47#321911yescharacteristic
372C22×Q16C22×C4711yescharacteristic
373C22×SD16C22×C4711yescharacteristic
374C2×#124C22×C4711yescharacteristic
375C2×C22⋊Q8C22×C4711yescharacteristic
376C2×C22⋊Q8C22×C4711yescharacteristic
377C2×#121C22×C4711yescharacteristic
378C2×C4×Q8C22×C4711yescharacteristic
379C22×C42C22×C4711yescharacteristic
380#464—24no—
381#432—24no—
382C2×#107C22×C4711yescharacteristic
383C2×#106C22×C4711yescharacteristic
384C2×C4⋊C8C22×C4711yescharacteristic
385C2×C4⋊C8C22×C4711yescharacteristic
386C2×#103C22×C4711yescharacteristic
387C2×#103C22×C4711yescharacteristic
388C2×#103C22×C4711yescharacteristic
389C2×#103C22×C4711yescharacteristic
390C2×#103C22×C4711yescharacteristic
391C2×#102C22×C4711yescharacteristic
392C2×#102C22×C4711yescharacteristic
393C2×#102C22×C4711yescharacteristic
394C2×C22⋊C8C22×C4711yescharacteristic
395C2×C22⋊C8C22×C4711yescharacteristic
396C2×#97C22×C4711yescharacteristic
397C2×#97C22×C4711yescharacteristic
398#391C22×C4711yescharacteristic
399#391C22×C4711yescharacteristic
400#390C22×C4711yescharacteristic
401#389C22×C4711yescharacteristic
402#388—21no—
403#388—21no—
404#387—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#382C22×C4711yescharacteristic
409#380C22×C4711yescharacteristic
410C4×C4⋊C4—21no—
411C4×C4⋊C4C22×C4711yescharacteristic
412C4×C22⋊C4—21no—
413#340C22×C4711yescharacteristic
414#340C22×C4711yescharacteristic
415#340C22×C4711yescharacteristic
416#340C22×C4711yescharacteristic
417C47#2465711yescharacteristic, direct product factor, Sylow
418C22×Q8C23×C4711yescharacteristic
419C22×Q8C23×C4711yescharacteristic
420C22×D4—21no—
421C22×D4C23×C4711yescharacteristic
422C23×C4D4×C4711yescharacteristic
423C23×C4D4×C4711yescharacteristic
424C23×C4C23×C4711yescharacteristic
425C2×Q16—22no—
426C2×Q16—22no—
427C2×Q16—41no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—41no—
431C22×C8C23×C4711yescharacteristic
432C22×C8C23×C4711yescharacteristic
433C22×C8C23×C4711yescharacteristic
434C22×C8C23×C4711yescharacteristic
435#124—22no—
436#124—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—41no—
440C22⋊Q8—41no—
441#121—41no—
442#121—41no—
443C4×Q8—22no—
444C4×Q8—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C23×C4711yescharacteristic
450C2×C4⋊C4C23×C4711yescharacteristic
451C2×C4⋊C4C23×C4711yescharacteristic
452C2×C4⋊C4C23×C4711yescharacteristic
453C2×C4⋊C4C23×C4711yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42D4×C4711yescharacteristic
467C2×C42D4×C4711yescharacteristic
468C2×C42C23×C4711yescharacteristic
469C2×C42C23×C4711yescharacteristic
470#107—41no—
471#106—41no—
472C4⋊C8—22no—
473C4⋊C8D4×C4714yescomplemented
474#103—22no—
475#103—22no—
476#103—41no—
477#103—41no—
478#103—41no—
479#102—22no—
480#102—22no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484#97—22no—
485#97—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—21no—
496C24C2×D4×C4711yescharacteristic
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8#41×C4712yes—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4C2×D4×C4711yescharacteristic
538C22×C4C2×D4×C4711yescharacteristic
539C22×C4C2×D4×C4711yescharacteristic
540C22×C4C2×D4×C4711yescharacteristic
541C22×C4C2×D4×C4711yescharacteristic
542C22×C4C24×C4711yescharacteristic
543Q16—44no—
544SD16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8C2×D4×C4712yes—
556C2×C8C2×D4×C4712yes—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4#41×C4712yes—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C42—22no—
580C42—22no—
581C42—21no—
582C42—21no—
583C42—42no—
584C42—42no—
585C42C2×D4×C4712yes—
586C42#41×C4712yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23#137×C4712yes—
601C23C22×D4×C4711yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
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#121×C4712yes—
656C2×C4#121×C4712yes—
657C2×C4C22×D4×C4711yescharacteristic
658C2×C4C2×#41×C4711yescharacteristic
659C2×C4C2×#41×C4711yescharacteristic
660C2×C4C2×#41×C4711yescharacteristic
661C2×C4H(5,𝔽2)×C4711yescharacteristic
662C2×C4H(5,𝔽2)×C4711yescharacteristic
663C8—22no—
664C8—22no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#121×C4711yescharacteristic
682C22C47×#52511yescharacteristic
683C22C47×#53511yescharacteristic
684C22C2×#137×C4711yescharacteristic
685C22C47×#57511yescharacteristic
686C22C47×#57511yescharacteristic
687C22C47×#57511yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—41no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C47×#54611yescharacteristic
701C4C47×#55011yescharacteristic
702C4C47×#55311yescharacteristic
703C4C47×#55511yescharacteristic
704C2—42no—
705C2—161no—
706C2C47×#241411yescharacteristic
707C2C47×#305411yescharacteristic
708C2C47×#305611yescharacteristic
709C2C47×#311111yescharacteristic
710C2C47×#311711yescharacteristic
711C2C47×#321511yescharacteristic
712C2C47×#321911yescharacteristic
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
1. C2×C47×#464C2semidirect
2. C2×C47×#432C2semidirect
4. C4×C22⋊Q8×C47C2semidirect
5. C47×#2036C2semidirect
7. C47×#2001C2semidirect
9. C47×#1983C2semidirect
10. C47×#1973C2semidirect
11. C47×#1971C2semidirect
12. C47×#1949C2semidirect
13. C47×#1936C2semidirect
14. C47×#1935C2semidirect
15. C47×#1805C2semidirect
116. C4⋊C8×C47D4semidirect
310. #24657C47direct (N × H)
348. C2×#464C2×C47semidirect
349. C2×#432C2×C47semidirect
351. C4×C22⋊Q8C2×C47semidirect
352. #2036C2×C47semidirect
354. #2001C2×C47semidirect
356. #1983C2×C47semidirect
357. #1973C2×C47semidirect
358. #1971C2×C47semidirect
359. #1949C2×C47semidirect
360. #1936C2×C47semidirect
361. #1935C2×C47semidirect
362. #1805C2×C47semidirect
417. C47#24657direct (N × H)
473. 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×#4642
C2×C47×#4322
C47×#28502
C4×C22⋊Q8×C472
C47×#20362
C47×#20342
C47×#20012
C47×#20002
C47×#19832
C47×#19732
C47×#19712
C47×#19492
C47×#19362
C47×#19352
C47×#18052
#2465747