Finite Group Databasebeta

← C47×#25172 #26064870

Subgroups — C47×#25172 #26064870

Order 12032.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#463C211yesmaximal, characteristic, complemented
2C2×C47×#450C211yesmaximal, characteristic, complemented
3C2×C47×#447C211yesmaximal, characteristic
4C2×C47×#442C211yesmaximal, characteristic, complemented
5C47×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2065C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1973C211yesmaximal, characteristic, complemented
12C47×#1924C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1877C211yesmaximal, characteristic, complemented
15C47×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic, complemented
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C2×C4×D4×C47C2211yescharacteristic, complemented
27C22×C22⋊C4×C47—21no—
28C47×#463—24no—
29C47×#450—24no—
30C47×#447—24no—
31C47×#442—24no—
32C2×#107×C47C2211yescharacteristic, complemented
33C2×#106×C47C2211yescharacteristic, complemented
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic, complemented
42C2×#102×C47C2211yescharacteristic, complemented
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×#97×C47C2211yescharacteristic, complemented
46C47×#397—21no—
47C47×#394—21no—
48C47×#391C2211yescharacteristic, complemented
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389C2211yescharacteristic, complemented
52C47×#386—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#380—21no—
56C47×#380C2211yescharacteristic
57C47×#379—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—22no—
68C22×D4×C47—22no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—41no—
72C22×D4×C47—41no—
73C22×D4×C47C2311yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47—21no—
79C23×C4×C47C2311yescharacteristic
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—22no—
85C2×SD16×C47—41no—
86C2×D8×C47—22no—
87C2×D8×C47—22no—
88C2×D8×C47—22no—
89C2×D8×C47—22no—
90C2×D8×C47—41no—
91C2×D8×C47D414yes—
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96#124×C47—22no—
97#124×C47—41no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47—41no—
100#121×C47—22no—
101#121×C47—41no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105C4×D4×C47—41no—
106C4×D4×C47—41no—
107C4×D4×C47—41no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—44no—
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47C2311yescharacteristic
130C2×C42×C47C2311yescharacteristic
131#107×C47—41no—
132#106×C47—22no—
133C4⋊C8×C47—22no—
134#103×C47—22no—
135#103×C47—41no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47D414yescomplemented
142C22⋊C8×C47—22no—
143C22⋊C8×C47—22no—
144#97×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47D411yescharacteristic
150#95×C47D411yescharacteristic
151C24×C47—21no—
152C24×C47—24no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—81no—
160C24×C47—81no—
161C24×C47C2×D411yescharacteristic
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×D4×C47—24no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—44no—
185C2×D4×C47—44no—
186C2×D4×C47—44no—
187C2×D4×C47—44no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—81no—
191C2×D4×C47C2×D412yes—
192C2×D4×C47C2×D412yes—
193C2×D4×C47C2×D412yes—
194C2×D4×C47#4112yes—
195C2×D4×C47#4112yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—81no—
214C22×C4×C47—81no—
215C22×C4×C47—81no—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2411yescharacteristic
222SD16×C47—44no—
223SD16×C47—44no—
224D8×C47—28no—
225D8×C47—44no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47C2×D412yes—
237C2×C8×C47C2×D412yes—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—42no—
246C4⋊C4×C47—81no—
247C4⋊C4×C47C2×D412yes—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—41no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—81no—
261C22⋊C4×C47—81no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—21no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—21no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—48no—
278C23×C47—48no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—84no—
296C23×C47—84no—
297C23×C47—84no—
298C23×C47—84no—
299C23×C47—84no—
300C23×C47AGL(1,ℤ/8)12yes—
301C23×C47C22×D411yescharacteristic
302Q8×C47—41no—
303Q8×C47—41no—
304Q8×C47—41no—
305Q8×C47—41no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—48no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—84no—
319D4×C47#12114yes—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—84no—
355C2×C4×C47—84no—
356C2×C4×C47—84no—
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C8×C47—22no—
364C8×C47—22no—
365C8×C47—41no—
366C8×C47—41no—
367#25172C4711yesmaximal, characteristic, direct product factor, Sylow
368C22×C47—22no—
369C22×C47—24no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—42no—
373C22×C47—41no—
374C22×C47—42no—
375C22×C47—41no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47—41no—
379C22×C47—42no—
380C22×C47—41no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—816no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47—81no—
397C22×C47#52511yescharacteristic
398C22×C47D4211yescharacteristic
399C22×C47D4211yescharacteristic
400C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C47#57511yescharacteristic
402C22×C47#57611yescharacteristic
403C22×C47#57711yescharacteristic
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—41no—
407C4×C47—41no—
408C4×C47—41no—
409C4×C47—42no—
410C4×C47—81no—
411C4×C47—81no—
412C4×C47—81no—
413C4×C47—81no—
414C4×C47C2×#12111yescharacteristic
415C4×C47#53811yescharacteristic
416C4×C47#54611yescharacteristic
417C4×C47#54611yescharacteristic
418C2×#463C2×C4711yescharacteristic, complemented
419C2×#450C2×C4711yescharacteristic, complemented
420C2×#447C2×C4711yescharacteristic
421C2×#442C2×C4711yescharacteristic, complemented
422#2427C2×C4711yescharacteristic, complemented
423D4×C22⋊C4C2×C4711yescharacteristic, complemented
424#2065C2×C4711yescharacteristic, complemented
425#2035C2×C4711yescharacteristic, complemented
426#2033C2×C4711yescharacteristic, complemented
427#2012C2×C4711yescharacteristic, complemented
428#1973C2×C4711yescharacteristic, complemented
429#1924C2×C4711yescharacteristic, complemented
430#1879C2×C4711yescharacteristic, complemented
431#1877C2×C4711yescharacteristic, complemented
432#1862C2×C4711yescharacteristic, complemented
433C2×C47—42no—
434C2×C47—44no—
435C2×C47—82no—
436C2×C47—82no—
437C2×C47#242411yescharacteristic
438C2×C47#311411yescharacteristic
439C2×C47#311811yescharacteristic
440C2×C47#326411yescharacteristic
441C2×C47#326511yescharacteristic
442C2×C47#326711yescharacteristic
443C2×C47#327311yescharacteristic
444C23×D4C22×C4711yescharacteristic
445C22×SD16C22×C4711yescharacteristic
446C22×SD16C22×C4711yescharacteristic
447C22×D8C22×C4711yescharacteristic
448C22×D8C22×C4711yescharacteristic
449C2×#124C22×C4711yescharacteristic, complemented
450C2×C22⋊Q8C22×C4711yescharacteristic
451C2×#121C22×C4711yescharacteristic
452C2×C4×D4C22×C4711yescharacteristic
453C2×C4×D4C22×C4711yescharacteristic
454C2×C4×D4C22×C4711yescharacteristic, complemented
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459#442—24no—
460C2×#107C22×C4711yescharacteristic, complemented
461C2×#106C22×C4711yescharacteristic, complemented
462C2×C4⋊C8C22×C4711yescharacteristic, complemented
463C2×#103C22×C4711yescharacteristic, complemented
464C2×#103C22×C4711yescharacteristic, complemented
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic
467C2×#102C22×C4711yescharacteristic
468C2×#102C22×C4711yescharacteristic
469C2×#102C22×C4711yescharacteristic, complemented
470C2×#102C22×C4711yescharacteristic, complemented
471C2×C22⋊C8C22×C4711yescharacteristic
472C2×C22⋊C8C22×C4711yescharacteristic
473C2×#97C22×C4711yescharacteristic, complemented
474#397—21no—
475#394—21no—
476#391C22×C4711yescharacteristic, complemented
477#390C22×C4711yescharacteristic
478#390C22×C4711yescharacteristic
479#389C22×C4711yescharacteristic, complemented
480#386—21no—
481#386—21no—
482#386—21no—
483#380—21no—
484#380C22×C4711yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C4711yescharacteristic
487#340C22×C4711yescharacteristic, complemented
488#340C22×C4711yescharacteristic, complemented
489#336C22×C4711yescharacteristic, complemented
490#336C22×C4711yescharacteristic, complemented
491C47#2517211yescharacteristic, direct product factor, Sylow
492C25—21no—
493C22×Q8C23×C4711yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C4711yescharacteristic
503C22×D4C23×C4711yescharacteristic
504C22×D4C23×C4711yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C4711yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C4714yes—
521C22×C8C23×C4711yescharacteristic
522C22×C8C23×C4711yescharacteristic
523C22×C8C23×C4711yescharacteristic
524C22×C8C23×C4711yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C4⋊C4C23×C4711yescharacteristic
542C2×C4⋊C4C23×C4711yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C4711yescharacteristic
557C2×C22⋊C4D4×C4711yescharacteristic
558C2×C42C23×C4711yescharacteristic
559C2×C42C23×C4711yescharacteristic
560#107—41no—
561#106—22no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C4714yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573#97—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C4711yescharacteristic
579#95D4×C4711yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C4711yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C4712yes—
621C2×D4C2×D4×C4712yes—
622C2×D4C2×D4×C4712yes—
623C2×D4#41×C4712yes—
624C2×D4#41×C4712yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C4711yescharacteristic
646C22×C4C2×D4×C4711yescharacteristic
647C22×C4C2×D4×C4711yescharacteristic
648C22×C4C2×D4×C4711yescharacteristic
649C22×C4C2×D4×C4711yescharacteristic
650C22×C4C24×C4711yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C4712yes—
666C2×C8C2×D4×C4712yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C4712yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23AGL(1,ℤ/8)×C4712yes—
730C23C22×D4×C4711yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C4714yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C22×D4×C4711yescharacteristic
787C2×C4C22×D4×C4711yescharacteristic
788C2×C4C2×#41×C4711yescharacteristic
789C2×C4C2×#41×C4711yescharacteristic
790C2×C4H(5,𝔽2)×C4711yescharacteristic
791C2×C4H(5,𝔽2)×C4711yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—24no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C47×#52511yescharacteristic
826C22D42×C4711yescharacteristic
827C22D42×C4711yescharacteristic
828C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
829C22C47×#57511yescharacteristic
830C22C47×#57611yescharacteristic
831C22C47×#57711yescharacteristic
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—42no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C4711yescharacteristic
843C4C47×#53811yescharacteristic
844C4C47×#54611yescharacteristic
845C4C47×#54611yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C47×#242411yescharacteristic
851C2C47×#311411yescharacteristic
852C2C47×#311811yescharacteristic
853C2C47×#326411yescharacteristic
854C2C47×#326511yescharacteristic
855C2C47×#326711yescharacteristic
856C2C47×#327311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#463C2semidirect
2. C2×C47×#450C2semidirect
4. C2×C47×#442C2semidirect
5. C47×#2427C2semidirect
6. D4×C22⋊C4×C47C2semidirect
7. C47×#2065C2semidirect
8. C47×#2035C2semidirect
9. C47×#2033C2semidirect
10. C47×#2012C2semidirect
11. C47×#1973C2semidirect
12. C47×#1924C2semidirect
13. C47×#1879C2semidirect
14. C47×#1877C2semidirect
15. C47×#1862C2semidirect
21. C2×#124×C47C22semidirect
26. C2×C4×D4×C47C22semidirect
32. C2×#107×C47C22semidirect
33. C2×#106×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
41. C2×#102×C47C22semidirect
42. C2×#102×C47C22semidirect
45. C2×#97×C47C22semidirect
48. C47×#391C22semidirect
51. C47×#389C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
141. #102×C47D4semidirect
367. #25172C47direct (N × H)
418. C2×#463C2×C47semidirect
419. C2×#450C2×C47semidirect
421. C2×#442C2×C47semidirect
422. #2427C2×C47semidirect
423. D4×C22⋊C4C2×C47semidirect
424. #2065C2×C47semidirect
425. #2035C2×C47semidirect
426. #2033C2×C47semidirect
427. #2012C2×C47semidirect
428. #1973C2×C47semidirect
429. #1924C2×C47semidirect
430. #1879C2×C47semidirect
431. #1877C2×C47semidirect
432. #1862C2×C47semidirect
449. C2×#124C22×C47semidirect
454. C2×C4×D4C22×C47semidirect
460. C2×#107C22×C47semidirect
461. C2×#106C22×C47semidirect
462. C2×C4⋊C8C22×C47semidirect
463. C2×#103C22×C47semidirect
464. C2×#103C22×C47semidirect
469. C2×#102C22×C47semidirect
470. C2×#102C22×C47semidirect
473. C2×#97C22×C47semidirect
476. #391C22×C47semidirect
479. #389C22×C47semidirect
487. #340C22×C47semidirect
488. #340C22×C47semidirect
489. #336C22×C47semidirect
490. #336C22×C47semidirect
491. C47#25172direct (N × H)
570. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4632
C2×C47×#4502
C2×C47×#4472
C2×C47×#4422
C47×#24272
D4×C22⋊C4×C472
C47×#20652
C47×#20352
C47×#20332
C47×#20122
C47×#19732
C47×#19242
C47×#18792
C47×#18772
C47×#18622
#2517247