Finite Group Databasebeta

← C47×#25164 #26064862

Subgroups — C47×#25164 #26064862

Order 12032.

1296 conjugacy classes of subgroups.

The subgroup lattice has 856 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×#440C211yesmaximal, characteristic, complemented
5C47×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1972C211yesmaximal, characteristic, complemented
12C47×#1924C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic, complemented
14C47×#1879C211yesmaximal, characteristic, complemented
15C47×#1864C211yesmaximal, 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×Q8×C47C2211yescharacteristic, complemented
25C2×C4×D4×C47C2211yescharacteristic
26C2×C4×D4×C47C2211yescharacteristic
27C22×C22⋊C4×C47—21no—
28C47×#463—24no—
29C47×#450—24no—
30C47×#447—24no—
31C47×#440—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×#396—21no—
47C47×#394—21no—
48C47×#390—21no—
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic, complemented
52C47×#389C2211yescharacteristic, complemented
53C47×#388—21no—
54C47×#386—21no—
55C47×#386—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×C47C2311yescharacteristic
79C2×SD16×C47—22no—
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—41no—
84C2×SD16×C47D414yescomplemented
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—22no—
88C2×D8×C47—22no—
89C2×D8×C47—22no—
90C2×D8×C47—41no—
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95#124×C47—22no—
96#124×C47—41no—
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—41no—
99#121×C47—22no—
100#121×C47—41no—
101C4×Q8×C47—22no—
102C4×Q8×C47—41no—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105C4×D4×C47—41no—
106C4×D4×C47—41no—
107C2×C4⋊C4×C47—21no—
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—21no—
127C2×C22⋊C4×C47—44no—
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133#107×C47—22no—
134#106×C47—41no—
135C4⋊C8×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—41no—
143#102×C47D414yes—
144C22⋊C8×C47—22no—
145C22⋊C8×C47—22no—
146#97×C47—22no—
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×C47C2×D412yes—
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—21no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—44no—
187C2×D4×C47—44no—
188C2×D4×C47—44no—
189C2×D4×C47—44no—
190C2×D4×C47—42no—
191C2×D4×C47—81no—
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—81no—
212C22×C4×C47—81no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2411yescharacteristic
219SD16×C47—28no—
220SD16×C47—44no—
221D8×C47—44no—
222D8×C47—44no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
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×C47C2×D412yes—
234C2×C8×C47C2×D412yes—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—42no—
243C4⋊C4×C47—42no—
244C4⋊C4×C47—81no—
245C4⋊C4×C47C2×D412yes—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—41no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
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—81no—
259C22⋊C4×C47—81no—
260C22⋊C4×C47—81no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—42no—
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—48no—
277C23×C47—48no—
278C23×C47—41no—
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—22no—
303Q8×C47—22no—
304Q8×C47—41no—
305Q8×C47—41no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—48no—
312D4×C47—41no—
313D4×C47—41no—
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—22no—
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—21no—
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×C47C22×D411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C2×#4111yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47H(5,𝔽2)11yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C8×C47—22no—
363C8×C47—22no—
364C8×C47—41no—
365C8×C47—41no—
366#25164C4711yesmaximal, characteristic, direct product factor, Sylow
367C22×C47—22no—
368C22×C47—24no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—42no—
372C22×C47—41no—
373C22×C47—42no—
374C22×C47—41no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—41no—
378C22×C47—42no—
379C22×C47—41no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—816no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47#52511yescharacteristic
397C22×C47D4211yescharacteristic
398C22×C47D4211yescharacteristic
399C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C47#57511yescharacteristic
401C22×C47#57611yescharacteristic
402C22×C47#57711yescharacteristic
403C4×C47—41no—
404C4×C47—42no—
405C4×C47—41no—
406C4×C47—42no—
407C4×C47—41no—
408C4×C47—41no—
409C4×C47—41no—
410C4×C47—81no—
411C4×C47—81no—
412C4×C47—81no—
413C4×C47C2×#12111yescharacteristic
414C4×C47#53811yescharacteristic
415C4×C47#54611yescharacteristic
416C4×C47#54611yescharacteristic
417C2×#463C2×C4711yescharacteristic, complemented
418C2×#450C2×C4711yescharacteristic, complemented
419C2×#447C2×C4711yescharacteristic
420C2×#440C2×C4711yescharacteristic, complemented
421#2426C2×C4711yescharacteristic, complemented
422D4×C22⋊C4C2×C4711yescharacteristic, complemented
423#2067C2×C4711yescharacteristic, complemented
424#2035C2×C4711yescharacteristic, complemented
425#2033C2×C4711yescharacteristic, complemented
426#2012C2×C4711yescharacteristic, complemented
427#1972C2×C4711yescharacteristic, complemented
428#1924C2×C4711yescharacteristic, complemented
429#1880C2×C4711yescharacteristic, complemented
430#1879C2×C4711yescharacteristic, complemented
431#1864C2×C4711yescharacteristic, complemented
432C2×C47—42no—
433C2×C47—44no—
434C2×C47—82no—
435C2×C47—161no—
436C2×C47#242411yescharacteristic
437C2×C47#311411yescharacteristic
438C2×C47#311811yescharacteristic
439C2×C47#326411yescharacteristic
440C2×C47#326511yescharacteristic
441C2×C47#326811yescharacteristic
442C2×C47#327511yescharacteristic
443C23×D4C22×C4711yescharacteristic
444C22×SD16C22×C4711yescharacteristic
445C22×SD16C22×C4711yescharacteristic
446C22×D8C22×C4711yescharacteristic
447C22×D8C22×C4711yescharacteristic
448C2×#124C22×C4711yescharacteristic, complemented
449C2×C22⋊Q8C22×C4711yescharacteristic
450C2×#121C22×C4711yescharacteristic
451C2×C4×Q8C22×C4711yescharacteristic, complemented
452C2×C4×D4C22×C4711yescharacteristic
453C2×C4×D4C22×C4711yescharacteristic
454C22×C22⋊C4—21no—
455#463—24no—
456#450—24no—
457#447—24no—
458#440—24no—
459C2×#107C22×C4711yescharacteristic, complemented
460C2×#106C22×C4711yescharacteristic, complemented
461C2×C4⋊C8C22×C4711yescharacteristic, complemented
462C2×#103C22×C4711yescharacteristic, complemented
463C2×#103C22×C4711yescharacteristic, complemented
464C2×#102C22×C4711yescharacteristic
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic
467C2×#102C22×C4711yescharacteristic
468C2×#102C22×C4711yescharacteristic, complemented
469C2×#102C22×C4711yescharacteristic, complemented
470C2×C22⋊C8C22×C4711yescharacteristic
471C2×C22⋊C8C22×C4711yescharacteristic
472C2×#97C22×C4711yescharacteristic, complemented
473#396—21no—
474#394—21no—
475#390—21no—
476#390C22×C4711yescharacteristic
477#390C22×C4711yescharacteristic
478#390C22×C4711yescharacteristic, complemented
479#389C22×C4711yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#386—21no—
483#380C22×C4711yescharacteristic
484#379—21no—
485C4×C22⋊C4C22×C4711yescharacteristic
486#340C22×C4711yescharacteristic, complemented
487#340C22×C4711yescharacteristic, complemented
488#336C22×C4711yescharacteristic, complemented
489#336C22×C4711yescharacteristic, complemented
490C47#2516411yescharacteristic, direct product factor, Sylow
491C25—21no—
492C22×Q8C23×C4711yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C4711yescharacteristic
502C22×D4C23×C4711yescharacteristic
503C22×D4C23×C4711yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C4711yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C4714yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C4711yescharacteristic
520C22×C8C23×C4711yescharacteristic
521C22×C8C23×C4711yescharacteristic
522C22×C8C23×C4711yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C4711yescharacteristic
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C4⋊C4C23×C4711yescharacteristic
542C2×C22⋊C4—21no—
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×C42—21no—
559C2×C42C23×C4711yescharacteristic
560C2×C42C23×C4711yescharacteristic
561#107—22no—
562#106—41no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C4714yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95D4×C4711yescharacteristic
578#95D4×C4711yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C4711yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C4712yes—
596C2×D4—24no—
597C2×D4—21no—
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—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C4712yes—
621C2×D4C2×D4×C4712yes—
622C2×D4#41×C4712yes—
623C2×D4#41×C4712yes—
624C22×C4—21no—
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—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C4711yescharacteristic
642C22×C4C2×D4×C4711yescharacteristic
643C22×C4C2×D4×C4711yescharacteristic
644C22×C4C2×D4×C4711yescharacteristic
645C22×C4C2×D4×C4711yescharacteristic
646C22×C4C24×C4711yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C4712yes—
662C2×C8C2×D4×C4712yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C4712yes—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
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—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23AGL(1,ℤ/8)×C4712yes—
729C23C22×D4×C4711yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C4714yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
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—84no—
783C2×C4—84no—
784C2×C4C22×D4×C4711yescharacteristic
785C2×C4C22×D4×C4711yescharacteristic
786C2×C4C2×#41×C4711yescharacteristic
787C2×C4C2×#41×C4711yescharacteristic
788C2×C4H(5,𝔽2)×C4711yescharacteristic
789C2×C4H(5,𝔽2)×C4711yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22C47×#52511yescharacteristic
824C22D42×C4711yescharacteristic
825C22D42×C4711yescharacteristic
826C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
827C22C47×#57511yescharacteristic
828C22C47×#57611yescharacteristic
829C22C47×#57711yescharacteristic
830C4—41no—
831C4—42no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C4711yescharacteristic
841C4C47×#53811yescharacteristic
842C4C47×#54611yescharacteristic
843C4C47×#54611yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C47×#242411yescharacteristic
849C2C47×#311411yescharacteristic
850C2C47×#311811yescharacteristic
851C2C47×#326411yescharacteristic
852C2C47×#326511yescharacteristic
853C2C47×#326811yescharacteristic
854C2C47×#327511yescharacteristic
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×#440C2semidirect
5. C47×#2426C2semidirect
6. D4×C22⋊C4×C47C2semidirect
7. C47×#2067C2semidirect
8. C47×#2035C2semidirect
9. C47×#2033C2semidirect
10. C47×#2012C2semidirect
11. C47×#1972C2semidirect
12. C47×#1924C2semidirect
13. C47×#1880C2semidirect
14. C47×#1879C2semidirect
15. C47×#1864C2semidirect
21. C2×#124×C47C22semidirect
24. C2×C4×Q8×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
51. C47×#390C22semidirect
52. C47×#389C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
84. C2×SD16×C47D4semidirect
366. #25164C47direct (N × H)
417. C2×#463C2×C47semidirect
418. C2×#450C2×C47semidirect
420. C2×#440C2×C47semidirect
421. #2426C2×C47semidirect
422. D4×C22⋊C4C2×C47semidirect
423. #2067C2×C47semidirect
424. #2035C2×C47semidirect
425. #2033C2×C47semidirect
426. #2012C2×C47semidirect
427. #1972C2×C47semidirect
428. #1924C2×C47semidirect
429. #1880C2×C47semidirect
430. #1879C2×C47semidirect
431. #1864C2×C47semidirect
448. C2×#124C22×C47semidirect
451. C2×C4×Q8C22×C47semidirect
459. C2×#107C22×C47semidirect
460. C2×#106C22×C47semidirect
461. C2×C4⋊C8C22×C47semidirect
462. C2×#103C22×C47semidirect
463. C2×#103C22×C47semidirect
468. C2×#102C22×C47semidirect
469. C2×#102C22×C47semidirect
472. C2×#97C22×C47semidirect
478. #390C22×C47semidirect
479. #389C22×C47semidirect
486. #340C22×C47semidirect
487. #340C22×C47semidirect
488. #336C22×C47semidirect
489. #336C22×C47semidirect
490. C47#25164direct (N × H)
512. C2×SD16D4×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×#4402
C47×#24262
D4×C22⋊C4×C472
C47×#20672
C47×#20352
C47×#20332
C47×#20122
C47×#19722
C47×#19242
C47×#18802
C47×#18792
C47×#18642
#2516447