Finite Group Databasebeta

← C47×#23972 #26063670

Subgroups — C47×#23972 #26063670

Order 12032.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#547C211yesmaximal, characteristic, complemented
2C2×C47×#449C211yesmaximal, characteristic, complemented
3C2×C47×#417C211yesmaximal, characteristic, complemented
4C47×#2407C211yesmaximal, characteristic, complemented
5C47×#2024C211yesmaximal, characteristic, complemented
6C47×#2023C211yesmaximal, characteristic, complemented
7C47×#2000C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1879C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1872C211yesmaximal, characteristic, complemented
14C47×#1870C211yesmaximal, characteristic, complemented
15C47×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C47—21no—
17C22×#41×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C47×#547—24no—
22C47×#547—24no—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×#123×C47—21no—
25C2×#123×C47—21no—
26C2×C22⋊Q8×C47—21no—
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C47×#449—24no—
36C47×#417—24no—
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#394—21no—
49C47×#392—21no—
50C47×#391C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#386—21no—
53C47×#385—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—28no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—41no—
69C2×#41×C47—41no—
70C2×#41×C47—44no—
71C2×#41×C47—44no—
72C22×Q8×C47—21no—
73C22×Q8×C47C2311yescharacteristic
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47D411yescharacteristic
79C22×D4×C47C2311yescharacteristic
80C22×D4×C47C2311yescharacteristic
81C23×C4×C47—21no—
82C23×C4×C47—21no—
83C23×C4×C47—21no—
84C23×C4×C47—21no—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C2×SD16×C47—22no—
88C2×SD16×C47—22no—
89C2×SD16×C47—41no—
90C2×D8×C47—22no—
91C2×D8×C47—22no—
92C2×D8×C47—41no—
93C2×M16×C47—22no—
94C2×M16×C47—41no—
95C2×M16×C47—41no—
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100C4⋊Q8×C47—22no—
101C4⋊Q8×C47—22no—
102#123×C47—28no—
103#123×C47—28no—
104C22⋊Q8×C47—28no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—41no—
107#121×C47—22no—
108#121×C47—22no—
109#121×C47—22no—
110#121×C47—22no—
111#121×C47—41no—
112#121×C47D414yescomplemented
113C4×D4×C47—22no—
114C4×D4×C47—22no—
115C4×D4×C47—22no—
116C4×D4×C47—22no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—22no—
120C2×C4⋊C4×C47—21no—
121C2×C4⋊C4×C47—22no—
122C2×C4⋊C4×C47—22no—
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47D411yescharacteristic
125C2×C4⋊C4×C47D414yescomplemented
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47D411yescharacteristic
140C2×C22⋊C4×C47D411yescharacteristic
141C2×C42×C47C2311yescharacteristic
142#103×C47—22no—
143#103×C47—22no—
144#103×C47—22no—
145#102×C47—22no—
146#102×C47—22no—
147#102×C47—22no—
148#102×C47—41no—
149#102×C47—41no—
150C22⋊C8×C47—22no—
151C22⋊C8×C47—41no—
152C22⋊C8×C47—41no—
153#95×C47—21no—
154#95×C47—21no—
155#95×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47C2×D411yescharacteristic
159C24×C47C2×D411yescharacteristic
160#41×C47—28no—
161#41×C47—44no—
162#41×C47—44no—
163#41×C47—44no—
164#41×C47—432no—
165C2×Q8×C47—24no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—42no—
172C2×Q8×C47—42no—
173C2×Q8×C47#4112yescomplemented
174C2×D4×C47—22no—
175C2×D4×C47—22no—
176C2×D4×C47—24no—
177C2×D4×C47—24no—
178C2×D4×C47—22no—
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—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
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—81no—
199C2×D4×C47C2×D412yes—
200C2×D4×C47#4112yescomplemented
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—24no—
206C22×C4×C47—24no—
207C22×C4×C47—24no—
208C22×C4×C47—21no—
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—21no—
219C22×C4×C47—21no—
220C22×C4×C47—42no—
221C22×C4×C47—42no—
222C22×C4×C47—42no—
223C22×C4×C47—42no—
224C22×C4×C47—42no—
225C22×C4×C47—42no—
226C22×C4×C47—42no—
227C22×C4×C47—42no—
228C22×C4×C47—42no—
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D412yes—
233C22×C4×C47C2×D412yes—
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2411yescharacteristic
236SD16×C47—44no—
237D8×C47—44no—
238M16×C47—44no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—22no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—42no—
263C4⋊C4×C47C2×D412yes—
264C4⋊C4×C47C2×D412yes—
265C4⋊C4×C47C2×D412yes—
266C22⋊C4×C47—24no—
267C22⋊C4×C47—24no—
268C22⋊C4×C47—22no—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—22no—
271C22⋊C4×C47—42no—
272C22⋊C4×C47—42no—
273C22⋊C4×C47—42no—
274C22⋊C4×C47—81no—
275C22⋊C4×C47—81no—
276C42×C47—21no—
277C42×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47#12012yes—
305C23×C47AGL(1,ℤ/8)12yes—
306C23×C47C22×D411yescharacteristic
307Q8×C47—22no—
308Q8×C47—22no—
309Q8×C47—48no—
310Q8×C47—41no—
311Q8×C47—41no—
312D4×C47—28no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—48no—
318D4×C47—48no—
319D4×C47—48no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—84no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—21no—
339C2×C4×C47—22no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—48no—
344C2×C4×C47—48no—
345C2×C4×C47—48no—
346C2×C4×C47—48no—
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—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47#12012yes—
366C2×C4×C47AGL(1,ℤ/8)12yes—
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C2×#4111yescharacteristic
370C2×C4×C47C2×#4111yescharacteristic
371C2×C4×C47H(5,𝔽2)11yescharacteristic
372C2×C4×C47H(5,𝔽2)11yescharacteristic
373C8×C47—41no—
374C8×C47—41no—
375C8×C47—41no—
376C8×C47—41no—
377#23972C4711yesmaximal, characteristic, direct product factor, Sylow
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—81no—
399C22×C47—81no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47C2×#12011yescharacteristic
407C22×C47#54611yescharacteristic
408C22×C47#54611yescharacteristic
409C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C47#57711yescharacteristic
412C22×C47#57811yescharacteristic
413C4×C47—22no—
414C4×C47—22no—
415C4×C47—41no—
416C4×C47—42no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47—41no—
421C4×C47—81no—
422C4×C47—81no—
423C4×C47#52511yescharacteristic
424C4×C47#53511yescharacteristic
425C4×C47#54611yescharacteristic
426C4×C47#54611yescharacteristic
427C2×#547C2×C4711yescharacteristic, complemented
428C2×#449C2×C4711yescharacteristic, complemented
429C2×#417C2×C4711yescharacteristic, complemented
430#2407C2×C4711yescharacteristic, complemented
431#2024C2×C4711yescharacteristic, complemented
432#2023C2×C4711yescharacteristic, complemented
433#2000C2×C4711yescharacteristic, complemented
434#1999C2×C4711yescharacteristic, complemented
435#1895C2×C4711yescharacteristic, complemented
436#1879C2×C4711yescharacteristic, complemented
437#1877C2×C4711yescharacteristic, complemented
438#1874C2×C4711yescharacteristic, complemented
439#1872C2×C4711yescharacteristic, complemented
440#1870C2×C4711yescharacteristic, complemented
441#1824C2×C4711yescharacteristic, complemented
442C2×C47—42no—
443C2×C47—42no—
444C2×C47—82no—
445C2×C47—82no—
446C2×C47#240411yescharacteristic
447C2×C47#300311yescharacteristic
448C2×C47#301311yescharacteristic
449C2×C47#330611yescharacteristic
450C2×C47#330811yescharacteristic
451C2×C47#333011yescharacteristic
452C2×C47#333211yescharacteristic
453C22×#41—21no—
454C22×#41C22×C4711yescharacteristic
455C22×SD16C22×C4711yescharacteristic
456C22×D8C22×C4711yescharacteristic
457C22×M16C22×C4711yescharacteristic
458#547—24no—
459#547—24no—
460C2×C4⋊Q8C22×C4711yescharacteristic
461C2×#123—21no—
462C2×#123—21no—
463C2×C22⋊Q8—21no—
464C2×C22⋊Q8C22×C4711yescharacteristic
465C2×#121C22×C4711yescharacteristic
466C2×#121C22×C4711yescharacteristic
467C2×#121C22×C4711yescharacteristic
468C2×C4×D4C22×C4711yescharacteristic
469C2×C4×D4C22×C4711yescharacteristic
470C22×C4⋊C4C22×C4711yescharacteristic
471C22×C4⋊C4C22×C4711yescharacteristic
472#449—24no—
473#417—24no—
474C2×#103C22×C4711yescharacteristic
475C2×#103C22×C4711yescharacteristic
476C2×#103C22×C4711yescharacteristic
477C2×#102C22×C4711yescharacteristic
478C2×#102C22×C4711yescharacteristic
479C2×#102C22×C4711yescharacteristic
480C2×#102C22×C4711yescharacteristic
481C2×#102C22×C4711yescharacteristic
482C2×C22⋊C8C22×C4711yescharacteristic
483C2×C22⋊C8C22×C4711yescharacteristic
484C2×C22⋊C8C22×C4711yescharacteristic
485#394—21no—
486#392—21no—
487#391C22×C4711yescharacteristic
488#390C22×C4711yescharacteristic
489#386—21no—
490#385—21no—
491#380C22×C4711yescharacteristic
492#340C22×C4711yescharacteristic
493#340C22×C4711yescharacteristic
494#340C22×C4711yescharacteristic
495#340C22×C4711yescharacteristic
496#340C22×C4711yescharacteristic
497#340C22×C4711yescharacteristic
498#336C22×C4711yescharacteristic
499#336C22×C4711yescharacteristic
500C47#2397211yescharacteristic, direct product factor, Sylow
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C4711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C4711yescharacteristic
517C22×D4C23×C4711yescharacteristic
518C22×D4C23×C4711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C4711yescharacteristic
524C23×C4C23×C4711yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C4711yescharacteristic
535C22×C8C23×C4711yescharacteristic
536C22×C8C23×C4711yescharacteristic
537C22×C8C23×C4711yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C4714yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C4711yescharacteristic
563C2×C4⋊C4D4×C4714yescomplemented
564C2×C4⋊C4C23×C4711yescharacteristic
565C2×C4⋊C4C23×C4711yescharacteristic
566C2×C4⋊C4C23×C4711yescharacteristic
567C2×C4⋊C4C23×C4711yescharacteristic
568C2×C4⋊C4C23×C4711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C4711yescharacteristic
578C2×C22⋊C4D4×C4711yescharacteristic
579C2×C42C23×C4711yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C4711yescharacteristic
597C24C2×D4×C4711yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C4712yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
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—81no—
637C2×D4C2×D4×C4712yes—
638C2×D4#41×C4712yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
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—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C4711yescharacteristic
668C22×C4C2×D4×C4711yescharacteristic
669C22×C4C2×D4×C4711yescharacteristic
670C22×C4C2×D4×C4712yes—
671C22×C4C2×D4×C4712yes—
672C22×C4C2×D4×C4711yescharacteristic
673C22×C4C24×C4711yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C4712yes—
702C4⋊C4C2×D4×C4712yes—
703C4⋊C4C2×D4×C4712yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C4712yes—
743C23AGL(1,ℤ/8)×C4712yes—
744C23C22×D4×C4711yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
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—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C4712yes—
804C2×C4AGL(1,ℤ/8)×C4712yes—
805C2×C4C22×D4×C4711yescharacteristic
806C2×C4C22×D4×C4711yescharacteristic
807C2×C4C2×#41×C4711yescharacteristic
808C2×C4C2×#41×C4711yescharacteristic
809C2×C4H(5,𝔽2)×C4711yescharacteristic
810C2×C4H(5,𝔽2)×C4711yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C4711yescharacteristic
844C22C47×#54611yescharacteristic
845C22C47×#54611yescharacteristic
846C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
847C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
848C22C47×#57711yescharacteristic
849C22C47×#57811yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4C47×#52511yescharacteristic
861C4C47×#53511yescharacteristic
862C4C47×#54611yescharacteristic
863C4C47×#54611yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C47×#240411yescharacteristic
869C2C47×#300311yescharacteristic
870C2C47×#301311yescharacteristic
871C2C47×#330611yescharacteristic
872C2C47×#330811yescharacteristic
873C2C47×#333011yescharacteristic
874C2C47×#333211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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×#547C2semidirect
2. C2×C47×#449C2semidirect
3. C2×C47×#417C2semidirect
4. C47×#2407C2semidirect
5. C47×#2024C2semidirect
6. C47×#2023C2semidirect
7. C47×#2000C2semidirect
8. C47×#1999C2semidirect
9. C47×#1895C2semidirect
10. C47×#1879C2semidirect
11. C47×#1877C2semidirect
12. C47×#1874C2semidirect
13. C47×#1872C2semidirect
14. C47×#1870C2semidirect
15. C47×#1824C2semidirect
112. #121×C47D4semidirect
125. C2×C4⋊C4×C47D4semidirect
173. C2×Q8×C47#41semidirect
200. C2×D4×C47#41semidirect
377. #23972C47direct (N × H)
427. C2×#547C2×C47semidirect
428. C2×#449C2×C47semidirect
429. C2×#417C2×C47semidirect
430. #2407C2×C47semidirect
431. #2024C2×C47semidirect
432. #2023C2×C47semidirect
433. #2000C2×C47semidirect
434. #1999C2×C47semidirect
435. #1895C2×C47semidirect
436. #1879C2×C47semidirect
437. #1877C2×C47semidirect
438. #1874C2×C47semidirect
439. #1872C2×C47semidirect
440. #1870C2×C47semidirect
441. #1824C2×C47semidirect
500. C47#23972direct (N × H)
550. #121D4×C47semidirect
563. C2×C4⋊C4D4×C47semidirect
611. C2×Q8#41×C47semidirect
638. C2×D4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5472
C2×C47×#4492
C2×C47×#4172
C47×#24072
C47×#20242
C47×#20232
C47×#20002
C47×#19992
C47×#18952
C47×#18792
C47×#18772
C47×#18742
C47×#18722
C47×#18702
C47×#18242
#2397247