Finite Group Databasebeta

← C47×#24769 #26064467

Subgroups — C47×#24769 #26064467

Order 12032.

946 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#470C211yesmaximal, characteristic, complemented
2C2×C47×#465C211yesmaximal, characteristic
3C2×C47×#464C211yesmaximal, characteristic, complemented
4C2×C47×#424C211yesmaximal, characteristic, complemented
5C47×#2620C211yesmaximal, characteristic
6C47×#2323C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2056C211yesmaximal, characteristic, complemented
10C47×#2055C211yesmaximal, characteristic, complemented
11C47×#1983C211yesmaximal, characteristic, complemented
12C47×#1948C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic
14C47×#1892C211yesmaximal, characteristic, complemented
15C47×#1803C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×Q8×C47C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C47×#470—24no—
27C47×#465—24no—
28C47×#464—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×#103×C47C2211yescharacteristic
40C2×#103×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×#391C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389—21no—
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#387—21no—
56C47×#384C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
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—
74C2×M16×C47—22no—
75C2×M16×C47—22no—
76C2×M16×C47—41no—
77C22×C8×C47—22no—
78C22×C8×C47—22no—
79C22×C8×C47—41no—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84#124×C47—22no—
85#124×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47D414yes—
90#121×C47—22no—
91#121×C47—22no—
92C4×Q8×C47—22no—
93C4×Q8×C47—22no—
94#117×C47—22no—
95#117×C47—22no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
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×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#106×C47—22no—
124#106×C47—22no—
125C4⋊C8×C47—22no—
126C4⋊C8×C47—22no—
127C4⋊C8×C47—22no—
128C4⋊C8×C47D414yescomplemented
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—22no—
133#103×C47—41no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—41no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144C24×C47—21no—
145C24×C47C2×D411yescharacteristic
146C2×Q8×C47—21no—
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×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47C2×D412yes—
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—42no—
165C2×D4×C47—81no—
166C2×D4×C47—81no—
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—21no—
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D412yes—
184C22×C4×C47#4112yes—
185C22×C4×C47C2411yescharacteristic
186Q16×C47—44no—
187SD16×C47—44no—
188M16×C47—44no—
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—44no—
200C2×C8×C47C2×D412yes—
201C2×C8×C47C2×D412yes—
202C4⋊C4×C47—24no—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—22no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—42no—
215C4⋊C4×C47—42no—
216C4⋊C4×C47—81no—
217C4⋊C4×C47—81no—
218C4⋊C4×C47—81no—
219C4⋊C4×C47C2×D412yes—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—42no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—81no—
228C22⋊C4×C47—81no—
229C22⋊C4×C47—81no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—42no—
233C42×C47—81no—
234C42×C47C2×D412yes—
235C42×C47#4112yes—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47#12112yes—
250C23×C47C22×D411yescharacteristic
251Q8×C47—22no—
252Q8×C47—22no—
253Q8×C47—41no—
254Q8×C47—41no—
255Q8×C47—41no—
256Q8×C47—41no—
257Q8×C47—41no—
258Q8×C47—41no—
259D4×C47—41no—
260D4×C47—41no—
261D4×C47—41no—
262D4×C47—41no—
263D4×C47—84no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
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—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47#12112yes—
302C2×C4×C47#12112yes—
303C2×C4×C47#12112yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×C4×C47H(5,𝔽2)11yescharacteristic
309C2×C4×C472−1+411yescharacteristic
310C8×C47—22no—
311C8×C47—22no—
312C8×C47—41no—
313C8×C47—41no—
314#24769C4711yesmaximal, characteristic, direct product factor, Sylow
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47—81no—
327C22×C47—81no—
328C22×C47—81no—
329C22×C47C2×#12111yescharacteristic
330C22×C47C2×#12111yescharacteristic
331C22×C47#53711yescharacteristic
332C22×C47#57711yescharacteristic
333C22×C47#57711yescharacteristic
334C22×C47#57711yescharacteristic
335C22×C47#57811yescharacteristic
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—41no—
342C4×C47—41no—
343C4×C47—81no—
344C4×C47—81no—
345C4×C47—81no—
346C4×C47—81no—
347C4×C47—81no—
348C4×C47D4211yescharacteristic
349C4×C47#54711yescharacteristic
350C4×C47#54811yescharacteristic
351C4×C47#55311yescharacteristic
352C2×#470C2×C4711yescharacteristic, complemented
353C2×#465C2×C4711yescharacteristic
354C2×#464C2×C4711yescharacteristic, complemented
355C2×#424C2×C4711yescharacteristic, complemented
356#2620C2×C4711yescharacteristic
357#2323C2×C4711yescharacteristic, complemented
358#2066C2×C4711yescharacteristic, complemented
359#2065C2×C4711yescharacteristic, complemented
360#2056C2×C4711yescharacteristic, complemented
361#2055C2×C4711yescharacteristic, complemented
362#1983C2×C4711yescharacteristic, complemented
363#1948C2×C4711yescharacteristic, complemented
364#1895C2×C4711yescharacteristic
365#1892C2×C4711yescharacteristic, complemented
366#1803C2×C4711yescharacteristic, complemented
367C2×C47—42no—
368C2×C47—161no—
369C2×C47#241611yescharacteristic
370C2×C47#304311yescharacteristic
371C2×C47#304611yescharacteristic
372C2×C47#306011yescharacteristic
373C2×C47#306311yescharacteristic
374C2×C47#325811yescharacteristic
375C2×C47#326311yescharacteristic
376C22×Q16C22×C4711yescharacteristic
377C22×SD16C22×C4711yescharacteristic
378C22×M16C22×C4711yescharacteristic
379C23×C8C22×C4711yescharacteristic
380C2×#124C22×C4711yescharacteristic
381C2×C22⋊Q8C22×C4711yescharacteristic
382C2×C22⋊Q8C22×C4711yescharacteristic
383C2×#121C22×C4711yescharacteristic
384C2×C4×Q8C22×C4711yescharacteristic
385C2×#117C22×C4711yescharacteristic
386#470—24no—
387#465—24no—
388#464—24no—
389C2×#106C22×C4711yescharacteristic
390C2×#106C22×C4711yescharacteristic
391#424—24no—
392C2×C4⋊C8C22×C4711yescharacteristic
393C2×C4⋊C8C22×C4711yescharacteristic
394C2×C4⋊C8C22×C4711yescharacteristic
395C2×C4⋊C8C22×C4711yescharacteristic
396C2×#103C22×C4711yescharacteristic
397C2×#103C22×C4711yescharacteristic
398C2×#103C22×C4711yescharacteristic
399C2×#103C22×C4711yescharacteristic
400C2×#103C22×C4711yescharacteristic
401C2×#102C22×C4711yescharacteristic
402C2×#102C22×C4711yescharacteristic
403C2×#102C22×C4711yescharacteristic
404#396—21no—
405#396—21no—
406#394—21no—
407#394—21no—
408#391C22×C4711yescharacteristic
409#391C22×C4711yescharacteristic
410#390C22×C4711yescharacteristic
411#389—21no—
412#389C22×C4711yescharacteristic
413#388—21no—
414#388—21no—
415#387—21no—
416#384C22×C4711yescharacteristic
417#380C22×C4711yescharacteristic
418C4×C4⋊C4C22×C4711yescharacteristic
419#340C22×C4711yescharacteristic
420#340C22×C4711yescharacteristic
421#340C22×C4711yescharacteristic
422#340C22×C4711yescharacteristic
423C47#2476911yescharacteristic, direct product factor, Sylow
424C22×Q8C23×C4711yescharacteristic
425C22×Q8C23×C4711yescharacteristic
426C22×D4—21no—
427C22×D4C23×C4711yescharacteristic
428C23×C4C23×C4711yescharacteristic
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—41no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—41no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—41no—
438C22×C8—22no—
439C22×C8—22no—
440C22×C8—41no—
441C22×C8C23×C4711yescharacteristic
442C22×C8C23×C4711yescharacteristic
443C22×C8C23×C4711yescharacteristic
444C22×C8C23×C4711yescharacteristic
445#124—22no—
446#124—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8D4×C4714yes—
451#121—22no—
452#121—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C4711yescharacteristic
464C2×C4⋊C4D4×C4711yescharacteristic
465C2×C4⋊C4C23×C4711yescharacteristic
466C2×C4⋊C4C23×C4711yescharacteristic
467C2×C4⋊C4C23×C4711yescharacteristic
468C2×C4⋊C4C23×C4711yescharacteristic
469C2×C4⋊C4C23×C4711yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4D4×C4711yescharacteristic
479C2×C22⋊C4D4×C4711yescharacteristic
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C4711yescharacteristic
483C2×C42C23×C4711yescharacteristic
484#106—22no—
485#106—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8D4×C4714yescomplemented
490#103—22no—
491#103—22no—
492#103—22no—
493#103—22no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—41no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505C24—21no—
506C24C2×D4×C4711yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C2×D4×C4712yes—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—81no—
527C2×D4—81no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C2×D4×C4711yescharacteristic
540C22×C4C2×D4×C4711yescharacteristic
541C22×C4C2×D4×C4711yescharacteristic
542C22×C4C2×D4×C4711yescharacteristic
543C22×C4C2×D4×C4711yescharacteristic
544C22×C4C2×D4×C4712yes—
545C22×C4#41×C4712yes—
546C22×C4C24×C4711yescharacteristic
547Q16—44no—
548SD16—44no—
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—44no—
561C2×C8C2×D4×C4712yes—
562C2×C8C2×D4×C4712yes—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C4712yes—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—81no—
595C42C2×D4×C4712yes—
596C42#41×C4712yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23#121×C4712yes—
611C23C22×D4×C4711yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
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—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4#121×C4712yes—
663C2×C4#121×C4712yes—
664C2×C4#121×C4712yes—
665C2×C4C22×D4×C4711yescharacteristic
666C2×C4C22×D4×C4711yescharacteristic
667C2×C4C2×#41×C4711yescharacteristic
668C2×C4C2×#41×C4711yescharacteristic
669C2×C4H(5,𝔽2)×C4711yescharacteristic
670C2×C42−1+4×C4711yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#121×C4711yescharacteristic
690C22C2×#121×C4711yescharacteristic
691C22C47×#53711yescharacteristic
692C22C47×#57711yescharacteristic
693C22C47×#57711yescharacteristic
694C22C47×#57711yescharacteristic
695C22C47×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—42no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4D42×C4711yescharacteristic
709C4C47×#54711yescharacteristic
710C4C47×#54811yescharacteristic
711C4C47×#55311yescharacteristic
712C2—42no—
713C2—161no—
714C2C47×#241611yescharacteristic
715C2C47×#304311yescharacteristic
716C2C47×#304611yescharacteristic
717C2C47×#306011yescharacteristic
718C2C47×#306311yescharacteristic
719C2C47×#325811yescharacteristic
720C2C47×#326311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
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. C2×C47×#470C2semidirect
3. C2×C47×#464C2semidirect
4. C2×C47×#424C2semidirect
6. C47×#2323C2semidirect
7. C47×#2066C2semidirect
8. C47×#2065C2semidirect
9. C47×#2056C2semidirect
10. C47×#2055C2semidirect
11. C47×#1983C2semidirect
12. C47×#1948C2semidirect
14. C47×#1892C2semidirect
15. C47×#1803C2semidirect
128. C4⋊C8×C47D4semidirect
314. #24769C47direct (N × H)
352. C2×#470C2×C47semidirect
354. C2×#464C2×C47semidirect
355. C2×#424C2×C47semidirect
357. #2323C2×C47semidirect
358. #2066C2×C47semidirect
359. #2065C2×C47semidirect
360. #2056C2×C47semidirect
361. #2055C2×C47semidirect
362. #1983C2×C47semidirect
363. #1948C2×C47semidirect
365. #1892C2×C47semidirect
366. #1803C2×C47semidirect
423. C47#24769direct (N × H)
489. 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×#4702
C2×C47×#4652
C2×C47×#4642
C2×C47×#4242
C47×#26202
C47×#23232
C47×#20662
C47×#20652
C47×#20562
C47×#20552
C47×#19832
C47×#19482
C47×#18952
C47×#18922
C47×#18032
#2476947