Finite Group Databasebeta

← C47×#24787 #26064485

Subgroups — C47×#24787 #26064485

Order 12032.

1054 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
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C22×#107×C47C211yesmaximal, characteristic, complemented
5C47×#2417C211yesmaximal, characteristic, complemented
6C47×#2416C211yesmaximal, characteristic
7C47×#2068C211yesmaximal, characteristic, complemented
8C47×#2067C211yesmaximal, characteristic, complemented
9C47×#2036C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#1973C211yesmaximal, characteristic, complemented
12C47×#1943C211yesmaximal, characteristic, complemented
13C47×#1874C211yesmaximal, characteristic, complemented
14C47×#1872C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47—21no—
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C47×#468—24no—
28C47×#465—24no—
29C47×#435—24no—
30C2×#107×C47—24no—
31C2×#107×C47C2211yescharacteristic
32C2×#107×C47C2211yescharacteristic
33C2×#107×C47C2211yescharacteristic
34C2×#107×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×#97×C47C2211yescharacteristic
46C47×#398—21no—
47C47×#396—21no—
48C47×#396—21no—
49C47×#394—21no—
50C47×#391C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#386—21no—
55C47×#386—21no—
56C47×#380—21no—
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47D411yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C2×SD16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×M16×C47—22no—
76C2×M16×C47—22no—
77C2×M16×C47—22no—
78C22×C8×C47—22no—
79C22×C8×C47—22no—
80C22×C8×C47D414yescomplemented
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—41no—
89#121×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—41no—
93#121×C47—44no—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×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×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—41no—
105C2×C4⋊C4×C47—41no—
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C22⋊C4×C47D411yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#107×C47—22no—
125#107×C47—22no—
126#107×C47—22no—
127#107×C47D414yescomplemented
128#106×C47—22no—
129C4⋊C8×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—41no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47—41no—
136C22⋊C8×C47—22no—
137C22⋊C8×C47—22no—
138#97×C47—22no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145C24×C47—21no—
146C24×C47C2×D411yescharacteristic
147C24×C47C2×D411yescharacteristic
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×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
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—42no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
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×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—81no—
191C22×C4×C47—81no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D412yes—
197C22×C4×C47#4112yes—
198C22×C4×C47C2411yescharacteristic
199SD16×C47—44no—
200M16×C47—44no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—28no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47C2×D412yes—
211C2×C8×C47C2×D412yes—
212C2×C8×C47C2×D412yes—
213C2×C8×C47#4112yes—
214C4⋊C4×C47—22no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—42no—
226C4⋊C4×C47—42no—
227C4⋊C4×C47—42no—
228C4⋊C4×C47—42no—
229C4⋊C4×C47—42no—
230C4⋊C4×C47—81no—
231C4⋊C4×C47C2×D412yes—
232C4⋊C4×C47C2×D412yes—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—81no—
242C22⋊C4×C47—81no—
243C42×C47—21no—
244C42×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47#12112yes—
264C23×C47AGL(1,ℤ/8)12yes—
265C23×C47#13712yes—
266C23×C47C22×D411yescharacteristic
267Q8×C47—41no—
268Q8×C47—41no—
269Q8×C47—41no—
270Q8×C47—41no—
271D4×C47—44no—
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—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—21no—
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—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—84no—
319C2×C4×C47—84no—
320C2×C4×C47#12112yes—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4111yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C472−1+411yescharacteristic
327C8×C47—22no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47#12114yescomplemented
331#24787C4711yesmaximal, characteristic, direct product factor, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47#46814yescomplemented
353C22×C47C2×#12111yescharacteristic
354C22×C47D4211yescharacteristic
355C22×C47#54711yescharacteristic
356C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C47C2×#13711yescharacteristic
358C22×C47#57611yescharacteristic
359C22×C47#57811yescharacteristic
360C4×C47—22no—
361C4×C47—41no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—81no—
367C4×C47—81no—
368C4×C47—81no—
369C4×C47—81no—
370C4×C47—81no—
371C4×C47C2×#12111yescharacteristic
372C4×C47#53711yescharacteristic
373C4×C47#54811yescharacteristic
374C4×C47#55311yescharacteristic
375C2×#468C2×C4711yescharacteristic, complemented
376C2×#465C2×C4711yescharacteristic, complemented
377C2×#435C2×C4711yescharacteristic, complemented
378C22×#107C2×C4711yescharacteristic, complemented
379#2417C2×C4711yescharacteristic, complemented
380#2416C2×C4711yescharacteristic
381#2068C2×C4711yescharacteristic, complemented
382#2067C2×C4711yescharacteristic, complemented
383#2036C2×C4711yescharacteristic, complemented
384#2033C2×C4711yescharacteristic, complemented
385#1973C2×C4711yescharacteristic, complemented
386#1943C2×C4711yescharacteristic, complemented
387#1874C2×C4711yescharacteristic, complemented
388#1872C2×C4711yescharacteristic, complemented
389#1809C2×C4711yescharacteristic, complemented
390C2×C47—24no—
391C2×C47—81no—
392C2×C47—161no—
393C2×C47#241611yescharacteristic
394C2×C47C2×#46811yescharacteristic
395C2×C47#306111yescharacteristic
396C2×C47#326411yescharacteristic
397C2×C47#327011yescharacteristic
398C2×C47#334311yescharacteristic
399C2×C47#334611yescharacteristic
400C22×SD16C22×C4711yescharacteristic
401C22×M16C22×C4711yescharacteristic
402C23×C8C22×C4711yescharacteristic
403C2×C22⋊Q8C22×C4711yescharacteristic
404C2×C22⋊Q8C22×C4711yescharacteristic
405C2×#121—21no—
406C2×#121C22×C4711yescharacteristic
407C2×#121C22×C4711yescharacteristic
408C2×C4×D4C22×C4711yescharacteristic
409C22×C4⋊C4C22×C4711yescharacteristic
410C22×C4⋊C4C22×C4711yescharacteristic
411#468—24no—
412#465—24no—
413#435—24no—
414C2×#107—24no—
415C2×#107C22×C4711yescharacteristic
416C2×#107C22×C4711yescharacteristic
417C2×#107C22×C4711yescharacteristic
418C2×#107C22×C4711yescharacteristic
419C2×#106C22×C4711yescharacteristic
420C2×C4⋊C8C22×C4711yescharacteristic
421C2×#103C22×C4711yescharacteristic
422C2×#103C22×C4711yescharacteristic
423C2×#103C22×C4711yescharacteristic
424C2×#102C22×C4711yescharacteristic
425C2×#102C22×C4711yescharacteristic
426C2×#102C22×C4711yescharacteristic
427C2×C22⋊C8C22×C4711yescharacteristic
428C2×C22⋊C8C22×C4711yescharacteristic
429C2×#97C22×C4711yescharacteristic
430#398—21no—
431#396—21no—
432#396—21no—
433#394—21no—
434#391C22×C4711yescharacteristic
435#390C22×C4711yescharacteristic
436#389C22×C4711yescharacteristic
437#389C22×C4711yescharacteristic
438#386—21no—
439#386—21no—
440#380—21no—
441#380C22×C4711yescharacteristic
442#380C22×C4711yescharacteristic
443#340C22×C4711yescharacteristic
444#340C22×C4711yescharacteristic
445#340C22×C4711yescharacteristic
446#340C22×C4711yescharacteristic
447C47#2478711yescharacteristic, direct product factor, Sylow
448C22×Q8C23×C4711yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4D4×C4711yescharacteristic
452C22×D4C23×C4711yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C23×C4711yescharacteristic
456C23×C4C23×C4711yescharacteristic
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—22no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8D4×C4714yescomplemented
466C22×C8C23×C4711yescharacteristic
467C22×C8C23×C4711yescharacteristic
468C22×C8C23×C4711yescharacteristic
469C22×C8C23×C4711yescharacteristic
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—41no—
474#121—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—44no—
479C4×D4—22no—
480C4×D4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C4711yescharacteristic
492C2×C4⋊C4C23×C4711yescharacteristic
493C2×C4⋊C4C23×C4711yescharacteristic
494C2×C4⋊C4C23×C4711yescharacteristic
495C2×C4⋊C4C23×C4711yescharacteristic
496C2×C4⋊C4C23×C4711yescharacteristic
497C2×C4⋊C4C23×C4711yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4D4×C4711yescharacteristic
507C2×C22⋊C4D4×C4711yescharacteristic
508C2×C42C23×C4711yescharacteristic
509#107—22no—
510#107—22no—
511#107—22no—
512#107D4×C4714yescomplemented
513#106—22no—
514C4⋊C8—22no—
515#103—22no—
516#103—22no—
517#103—41no—
518#102—22no—
519#102—22no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24C2×D4×C4711yescharacteristic
532C24C2×D4×C4711yescharacteristic
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—81no—
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×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4C2×D4×C4711yescharacteristic
578C22×C4C2×D4×C4711yescharacteristic
579C22×C4C2×D4×C4711yescharacteristic
580C22×C4C2×D4×C4711yescharacteristic
581C22×C4C2×D4×C4712yes—
582C22×C4#41×C4712yes—
583C22×C4C24×C4711yescharacteristic
584SD16—44no—
585M16—44no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—28no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8C2×D4×C4712yes—
596C2×C8C2×D4×C4712yes—
597C2×C8C2×D4×C4712yes—
598C2×C8#41×C4712yes—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—81no—
616C4⋊C4C2×D4×C4712yes—
617C4⋊C4C2×D4×C4712yes—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C42—21no—
629C42—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23#121×C4712yes—
649C23AGL(1,ℤ/8)×C4712yes—
650C23#137×C4712yes—
651C23C22×D4×C4711yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656D4—44no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—84no—
662D4—84no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
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×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—84no—
704C2×C4—84no—
705C2×C4#121×C4712yes—
706C2×C4C22×D4×C4711yescharacteristic
707C2×C4C22×D4×C4711yescharacteristic
708C2×C4C2×#41×C4711yescharacteristic
709C2×C4C2×#41×C4711yescharacteristic
710C2×C4H(5,𝔽2)×C4711yescharacteristic
711C2×C42−1+4×C4711yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8#121×C4714yescomplemented
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C47×#46814yescomplemented
737C22C2×#121×C4711yescharacteristic
738C22D42×C4711yescharacteristic
739C22C47×#54711yescharacteristic
740C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
741C22C2×#137×C4711yescharacteristic
742C22C47×#57611yescharacteristic
743C22C47×#57811yescharacteristic
744C4—22no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—42no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4C2×#121×C4711yescharacteristic
756C4C47×#53711yescharacteristic
757C4C47×#54811yescharacteristic
758C4C47×#55311yescharacteristic
759C2—24no—
760C2—81no—
761C2—161no—
762C2C47×#241611yescharacteristic
763C2C2×C47×#46811yescharacteristic
764C2C47×#306111yescharacteristic
765C2C47×#326411yescharacteristic
766C2C47×#327011yescharacteristic
767C2C47×#334311yescharacteristic
768C2C47×#334611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#468C2semidirect
2. C2×C47×#465C2semidirect
3. C2×C47×#435C2semidirect
4. C22×#107×C47C2semidirect
5. C47×#2417C2semidirect
7. C47×#2068C2semidirect
8. C47×#2067C2semidirect
9. C47×#2036C2semidirect
10. C47×#2033C2semidirect
11. C47×#1973C2semidirect
12. C47×#1943C2semidirect
13. C47×#1874C2semidirect
14. C47×#1872C2semidirect
15. C47×#1809C2semidirect
80. C22×C8×C47D4semidirect
127. #107×C47D4semidirect
330. C8×C47#121semidirect
331. #24787C47direct (N × H)
352. C22×C47#468semidirect
375. C2×#468C2×C47semidirect
376. C2×#465C2×C47semidirect
377. C2×#435C2×C47semidirect
378. C22×#107C2×C47semidirect
379. #2417C2×C47semidirect
381. #2068C2×C47semidirect
382. #2067C2×C47semidirect
383. #2036C2×C47semidirect
384. #2033C2×C47semidirect
385. #1973C2×C47semidirect
386. #1943C2×C47semidirect
387. #1874C2×C47semidirect
388. #1872C2×C47semidirect
389. #1809C2×C47semidirect
447. C47#24787direct (N × H)
465. C22×C8D4×C47semidirect
512. #107D4×C47semidirect
715. C8#121×C47semidirect
736. C22C47×#468semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4652
C2×C47×#4352
C22×#107×C472
C47×#24172
C47×#24162
C47×#20682
C47×#20672
C47×#20362
C47×#20332
C47×#19732
C47×#19432
C47×#18742
C47×#18722
C47×#18092
#2478747