Finite Group Databasebeta

← C47×#25080 #26064778

Subgroups — C47×#25080 #26064778

Order 12032.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#465C211yesmaximal, characteristic, complemented
2C2×C47×#460C211yesmaximal, characteristic, complemented
3C2×C47×#450C211yesmaximal, characteristic, complemented
4C22×#102×C47C211yesmaximal, characteristic, complemented
5C47×#2433C211yesmaximal, characteristic
6C47×#2360C211yesmaximal, characteristic, complemented
7C47×#2065C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2041C211yesmaximal, characteristic, complemented
10C47×#2014C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1926C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic, complemented
14C47×#1874C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic, complemented
20C23×C8×C47C2211yescharacteristic
21C2×#127×C47C2211yescharacteristic
22C2×#127×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#120×C47—21no—
26C2×#120×C47—21no—
27C2×C4×Q8×C47C2211yescharacteristic, complemented
28C22×C4⋊C4×C47C2211yescharacteristic
29C47×#465—24no—
30C47×#460—24no—
31C47×#450—24no—
32C2×#106×C47C2211yescharacteristic, complemented
33C2×C4⋊C8×C47C2211yescharacteristic, complemented
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#102×C47—24no—
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic, complemented
44C2×#102×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic, complemented
46C2×C22⋊C8×C47C2211yescharacteristic
47C47×#392—21no—
48C47×#392—21no—
49C47×#391C2211yescharacteristic, complemented
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389—21no—
53C47×#389C2211yescharacteristic, complemented
54C47×#387—21no—
55C47×#385—21no—
56C4×C4⋊C4×C47C2211yescharacteristic, complemented
57C4×C22⋊C4×C47—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—21no—
68C22×D4×C47—22no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—41no—
76C22×D4×C47—41no—
77C22×D4×C47C2311yescharacteristic
78C22×D4×C47C2311yescharacteristic
79C22×D4×C47C2311yescharacteristic
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—22no—
85C2×SD16×C47—22no—
86C2×SD16×C47—22no—
87C2×SD16×C47—22no—
88C2×SD16×C47—41no—
89C2×SD16×C47—41no—
90C2×SD16×C47—41no—
91C22×C8×C47—22no—
92C22×C8×C47—22no—
93C22×C8×C47—41no—
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98#127×C47—22no—
99#127×C47—22no—
100#127×C47—41no—
101#127×C47—41no—
102C22⋊Q8×C47—22no—
103C22⋊Q8×C47D414yescomplemented
104#121×C47—22no—
105#121×C47—22no—
106#120×C47—44no—
107#120×C47—44no—
108C4×Q8×C47—22no—
109C4×Q8×C47—41no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—22no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—41no—
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
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×C47D411yescharacteristic
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C42×C47—21no—
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132#106×C47—22no—
133C4⋊C8×C47—22no—
134C4⋊C8×C47—41no—
135#103×C47—22no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—41no—
144#102×C47D414yescomplemented
145C22⋊C8×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47D411yescharacteristic
151#95×C47D411yescharacteristic
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—42no—
160C24×C47—81no—
161C24×C47—81no—
162C24×C47C2×D411yescharacteristic
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47C2×D412yes—
169C2×D4×C47—28no—
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—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—44no—
187C2×D4×C47—44no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—44no—
191C2×D4×C47—42no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—42no—
202C2×D4×C47—42no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47C2×D412yes—
208C2×D4×C47#4112yes—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—42no—
219C22×C4×C47—42no—
220C22×C4×C47—81no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D412yes—
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47#4112yes—
228C22×C4×C47C2411yescharacteristic
229SD16×C47—44no—
230SD16×C47—44no—
231SD16×C47—44no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—44no—
244C2×C8×C47C2×D412yes—
245C4⋊C4×C47—24no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—42no—
253C4⋊C4×C47—42no—
254C4⋊C4×C47—81no—
255C4⋊C4×C47C2×D412yes—
256C4⋊C4×C47C2×D412yes—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C22⋊C4×C47—42no—
262C22⋊C4×C47—42no—
263C22⋊C4×C47—42no—
264C22⋊C4×C47SD1614yescomplemented
265C42×C47—21no—
266C42×C47—21no—
267C42×C47—21no—
268C42×C47—21no—
269C42×C47—42no—
270C42×C47—81no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—22no—
276C23×C47—22no—
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—41no—
296C23×C47—41no—
297C23×C47—84no—
298C23×C47—84no—
299C23×C47—84no—
300C23×C47—84no—
301C23×C47—84no—
302C23×C47—84no—
303C23×C47#12112yes—
304C23×C47C2×SD1612yes—
305C23×C47AGL(1,ℤ/8)12yes—
306C23×C47C22×D411yescharacteristic
307Q8×C47—22no—
308Q8×C47—22no—
309Q8×C47—41no—
310Q8×C47—41no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—48no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—41no—
319D4×C47—41no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—84no—
325D4×C47—84no—
326D4×C47—84no—
327D4×C47—84no—
328D4×C47—84no—
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—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—21no—
342C2×C4×C47—22no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
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—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—84no—
361C2×C4×C47#12112yes—
362C2×C4×C47C2×SD1612yes—
363C2×C4×C47C2×SD1612yes—
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C2×#4111yescharacteristic
367C2×C4×C47C2×#4111yescharacteristic
368C2×C4×C47H(5,𝔽2)11yescharacteristic
369C2×C4×C47H(5,𝔽2)11yescharacteristic
370C8×C47—22no—
371C8×C47—41no—
372C8×C47—41no—
373C8×C47—41no—
374#25080C4711yesmaximal, characteristic, direct product factor, Sylow
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—816no—
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—81no—
397C22×C47—81no—
398C22×C47—81no—
399C22×C47—81no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47#46014yescomplemented
404C22×C47C2×#12111yescharacteristic
405C22×C47D4211yescharacteristic
406C22×C47#54611yescharacteristic
407C22×C47C22×SD1611yescharacteristic
408C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C47#57611yescharacteristic
410C22×C47#57711yescharacteristic
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—41no—
416C4×C47—42no—
417C4×C47—42no—
418C4×C47—41no—
419C4×C47—81no—
420C4×C47—81no—
421C4×C47#52511yescharacteristic
422C4×C47#53811yescharacteristic
423C4×C47D4211yescharacteristic
424C4×C47#54611yescharacteristic
425C2×#465C2×C4711yescharacteristic, complemented
426C2×#460C2×C4711yescharacteristic, complemented
427C2×#450C2×C4711yescharacteristic, complemented
428C22×#102C2×C4711yescharacteristic, complemented
429#2433C2×C4711yescharacteristic
430#2360C2×C4711yescharacteristic, complemented
431#2065C2×C4711yescharacteristic, complemented
432#2055C2×C4711yescharacteristic, complemented
433#2041C2×C4711yescharacteristic, complemented
434#2014C2×C4711yescharacteristic, complemented
435#1982C2×C4711yescharacteristic, complemented
436#1926C2×C4711yescharacteristic, complemented
437#1880C2×C4711yescharacteristic, complemented
438#1874C2×C4711yescharacteristic, complemented
439#1850C2×C4711yescharacteristic, complemented
440C2×C47—24no—
441C2×C47—82no—
442C2×C47—82no—
443C2×C47—161no—
444C2×C47#242411yescharacteristic
445C2×C47C2×#46011yescharacteristic
446C2×C47#304511yescharacteristic
447C2×C47#326411yescharacteristic
448C2×C47D4×SD1611yescharacteristic
449C2×C47#329511yescharacteristic
450C2×C47#331011yescharacteristic
451C23×D4C22×C4711yescharacteristic
452C22×SD16C22×C4711yescharacteristic
453C22×SD16C22×C4711yescharacteristic
454C22×SD16C22×C4711yescharacteristic, complemented
455C23×C8C22×C4711yescharacteristic
456C2×#127C22×C4711yescharacteristic
457C2×#127C22×C4711yescharacteristic
458C2×C22⋊Q8C22×C4711yescharacteristic
459C2×#121C22×C4711yescharacteristic
460C2×#120—21no—
461C2×#120—21no—
462C2×C4×Q8C22×C4711yescharacteristic, complemented
463C22×C4⋊C4C22×C4711yescharacteristic
464#465—24no—
465#460—24no—
466#450—24no—
467C2×#106C22×C4711yescharacteristic, complemented
468C2×C4⋊C8C22×C4711yescharacteristic, complemented
469C2×C4⋊C8C22×C4711yescharacteristic, complemented
470C2×#103C22×C4711yescharacteristic, complemented
471C2×#102—24no—
472C2×#102C22×C4711yescharacteristic
473C2×#102C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic
476C2×#102C22×C4711yescharacteristic
477C2×#102C22×C4711yescharacteristic
478C2×#102C22×C4711yescharacteristic, complemented
479C2×#102C22×C4711yescharacteristic, complemented
480C2×#102C22×C4711yescharacteristic, complemented
481C2×C22⋊C8C22×C4711yescharacteristic
482#392—21no—
483#392—21no—
484#391C22×C4711yescharacteristic, complemented
485#390C22×C4711yescharacteristic
486#390C22×C4711yescharacteristic
487#389—21no—
488#389C22×C4711yescharacteristic, complemented
489#387—21no—
490#385—21no—
491C4×C4⋊C4C22×C4711yescharacteristic, complemented
492C4×C22⋊C4—21no—
493C4×C22⋊C4C22×C4711yescharacteristic
494#340C22×C4711yescharacteristic, complemented
495#340C22×C4711yescharacteristic, complemented
496#336C22×C4711yescharacteristic, complemented
497#336C22×C4711yescharacteristic, complemented
498C47#2508011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C22×Q8C23×C4711yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C23×C4711yescharacteristic
514C22×D4C23×C4711yescharacteristic
515C22×D4C23×C4711yescharacteristic
516C23×C4—21no—
517C23×C4C23×C4711yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C23×C4711yescharacteristic
531C22×C8C23×C4711yescharacteristic
532C22×C8C23×C4711yescharacteristic
533C22×C8C23×C4711yescharacteristic
534#127—22no—
535#127—22no—
536#127—41no—
537#127—41no—
538C22⋊Q8—22no—
539C22⋊Q8D4×C4714yescomplemented
540#121—22no—
541#121—22no—
542#120—44no—
543#120—44no—
544C4×Q8—22no—
545C4×Q8—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C23×C4711yescharacteristic
553C2×C4⋊C4C23×C4711yescharacteristic
554C2×C4⋊C4C23×C4711yescharacteristic
555C2×C4⋊C4C23×C4711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4D4×C4711yescharacteristic
563C2×C22⋊C4D4×C4711yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C4711yescharacteristic
567C2×C42C23×C4711yescharacteristic
568#106—22no—
569C4⋊C8—22no—
570C4⋊C8—41no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—41no—
580#102D4×C4714yescomplemented
581C22⋊C8—22no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95D4×C4711yescharacteristic
587#95D4×C4711yescharacteristic
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C4711yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C4712yes—
605C2×D4—28no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C4712yes—
644C2×D4#41×C4712yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C4711yescharacteristic
658C22×C4C2×D4×C4711yescharacteristic
659C22×C4C2×D4×C4711yescharacteristic
660C22×C4C2×D4×C4712yes—
661C22×C4C2×D4×C4711yescharacteristic
662C22×C4C2×D4×C4711yescharacteristic
663C22×C4#41×C4712yes—
664C22×C4C24×C4711yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C4712yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C4712yes—
692C4⋊C4C2×D4×C4712yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C4714yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#121×C4712yes—
740C23C2×SD16×C4712yes—
741C23AGL(1,ℤ/8)×C4712yes—
742C23C22×D4×C4711yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4#121×C4712yes—
798C2×C4C2×SD16×C4712yes—
799C2×C4C2×SD16×C4712yes—
800C2×C4C22×D4×C4711yescharacteristic
801C2×C4C22×D4×C4711yescharacteristic
802C2×C4C2×#41×C4711yescharacteristic
803C2×C4C2×#41×C4711yescharacteristic
804C2×C4H(5,𝔽2)×C4711yescharacteristic
805C2×C4H(5,𝔽2)×C4711yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22C47×#46014yescomplemented
839C22C2×#121×C4711yescharacteristic
840C22D42×C4711yescharacteristic
841C22C47×#54611yescharacteristic
842C22C22×SD16×C4711yescharacteristic
843C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
844C22C47×#57611yescharacteristic
845C22C47×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4C47×#52511yescharacteristic
857C4C47×#53811yescharacteristic
858C4D42×C4711yescharacteristic
859C4C47×#54611yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2C47×#242411yescharacteristic
865C2C2×C47×#46011yescharacteristic
866C2C47×#304511yescharacteristic
867C2C47×#326411yescharacteristic
868C2D4×SD16×C4711yescharacteristic
869C2C47×#329511yescharacteristic
870C2C47×#331011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2433C2
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×#465C2semidirect
2. C2×C47×#460C2semidirect
3. C2×C47×#450C2semidirect
4. C22×#102×C47C2semidirect
6. C47×#2360C2semidirect
7. C47×#2065C2semidirect
8. C47×#2055C2semidirect
9. C47×#2041C2semidirect
10. C47×#2014C2semidirect
11. C47×#1982C2semidirect
12. C47×#1926C2semidirect
13. C47×#1880C2semidirect
14. C47×#1874C2semidirect
15. C47×#1850C2semidirect
19. C22×SD16×C47C22semidirect
27. C2×C4×Q8×C47C22semidirect
32. C2×#106×C47C22semidirect
33. C2×C4⋊C8×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
35. C2×#103×C47C22semidirect
43. C2×#102×C47C22semidirect
44. C2×#102×C47C22semidirect
45. C2×#102×C47C22semidirect
49. C47×#391C22semidirect
53. C47×#389C22semidirect
56. C4×C4⋊C4×C47C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
103. C22⋊Q8×C47D4semidirect
144. #102×C47D4semidirect
264. C22⋊C4×C47SD16semidirect
374. #25080C47direct (N × H)
403. C22×C47#460semidirect
425. C2×#465C2×C47semidirect
426. C2×#460C2×C47semidirect
427. C2×#450C2×C47semidirect
428. C22×#102C2×C47semidirect
430. #2360C2×C47semidirect
431. #2065C2×C47semidirect
432. #2055C2×C47semidirect
433. #2041C2×C47semidirect
434. #2014C2×C47semidirect
435. #1982C2×C47semidirect
436. #1926C2×C47semidirect
437. #1880C2×C47semidirect
438. #1874C2×C47semidirect
439. #1850C2×C47semidirect
454. C22×SD16C22×C47semidirect
462. C2×C4×Q8C22×C47semidirect
467. C2×#106C22×C47semidirect
468. C2×C4⋊C8C22×C47semidirect
469. C2×C4⋊C8C22×C47semidirect
470. C2×#103C22×C47semidirect
478. C2×#102C22×C47semidirect
479. C2×#102C22×C47semidirect
480. C2×#102C22×C47semidirect
484. #391C22×C47semidirect
488. #389C22×C47semidirect
491. C4×C4⋊C4C22×C47semidirect
494. #340C22×C47semidirect
495. #340C22×C47semidirect
496. #336C22×C47semidirect
497. #336C22×C47semidirect
498. C47#25080direct (N × H)
539. C22⋊Q8D4×C47semidirect
580. #102D4×C47semidirect
700. C22⋊C4SD16×C47semidirect
838. C22C47×#460semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4652
C2×C47×#4602
C2×C47×#4502
C22×#102×C472
C47×#24332
C47×#23602
C47×#20652
C47×#20552
C47×#20412
C47×#20142
C47×#19822
C47×#19262
C47×#18802
C47×#18742
C47×#18502
#2508047