Finite Group Databasebeta

← C47×#24432 #26064130

Subgroups — C47×#24432 #26064130

Order 12032.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C47C211yesmaximal, characteristic
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#450C211yesmaximal, characteristic, complemented
4C2×C47×#450C211yesmaximal, characteristic, complemented
5C22×#102×C47C211yesmaximal, characteristic, complemented
6C47×#2417C211yesmaximal, characteristic, complemented
7C47×#2041C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2014C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1869C211yesmaximal, characteristic, complemented
14C47×#1864C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C47—21no—
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic, complemented
21C22×SD16×C47C2211yescharacteristic, complemented
22C23×C8×C47C2211yescharacteristic, complemented
23D42×C47—24no—
24D42×C47—24no—
25C2×#127×C47C2211yescharacteristic
26C2×C22⋊Q8×C47C2211yescharacteristic, complemented
27C2×C22⋊Q8×C47C2211yescharacteristic, complemented
28C2×#121×C47—21no—
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×#120×C47—21no—
32C2×#120×C47—21no—
33C2×C4×D4×C47C2211yescharacteristic
34C2×C4×D4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic, complemented
36C47×#465—24no—
37C47×#450—24no—
38C47×#450—24no—
39C2×#106×C47C2211yescharacteristic, complemented
40C2×#103×C47C2211yescharacteristic, complemented
41C2×#102×C47—24no—
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic, complemented
47C2×#102×C47C2211yescharacteristic, complemented
48C2×#102×C47C2211yescharacteristic, complemented
49C2×#102×C47C2211yescharacteristic, complemented
50C2×#102×C47C2211yescharacteristic, complemented
51C2×C22⋊C8×C47C2211yescharacteristic, complemented
52C2×C22⋊C8×C47C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C47×#398—21no—
55C47×#396—21no—
56C47×#391C2211yescharacteristic, complemented
57C47×#389C2211yescharacteristic, complemented
58C47×#386—21no—
59C47×#380—21no—
60C47×#380C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47—21no—
66C25×C47—21no—
67C22×Q8×C47C2311yescharacteristic
68C22×D4×C47—22no—
69C22×D4×C47—22no—
70C22×D4×C47—28no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—22no—
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—22no—
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—22no—
81C22×D4×C47—21no—
82C22×D4×C47—41no—
83C22×D4×C47—41no—
84C22×D4×C47—41no—
85C22×D4×C47—41no—
86C22×D4×C47—44no—
87C22×D4×C47—44no—
88C22×D4×C47D411yescharacteristic
89C22×D4×C47D414yes—
90C22×D4×C47C2311yescharacteristic
91C22×D4×C47C2311yescharacteristic
92C22×D4×C47C2311yescharacteristic
93C23×C4×C47—21no—
94C23×C4×C47—21no—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C2×SD16×C47—22no—
98C2×SD16×C47—22no—
99C2×SD16×C47—22no—
100C2×SD16×C47—22no—
101C2×SD16×C47—22no—
102C2×SD16×C47—22no—
103C2×SD16×C47—41no—
104C2×SD16×C47—41no—
105C2×SD16×C47—41no—
106C22×C8×C47—22no—
107C22×C8×C47—22no—
108C22×C8×C47—41no—
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113#127×C47—22no—
114#127×C47—22no—
115C22⋊Q8×C47—22no—
116C22⋊Q8×C47—22no—
117C22⋊Q8×C47—22no—
118C22⋊Q8×C47—41no—
119#121×C47—28no—
120#121×C47—22no—
121#121×C47—22no—
122#121×C47—22no—
123#121×C47D414yes—
124#120×C47—28no—
125#120×C47—28no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47—22no—
129C4×D4×C47—22no—
130C2×C4⋊C4×C47—22no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47—41no—
136C2×C4⋊C4×C47D411yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47D411yescharacteristic
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C42×C47C2311yescharacteristic
150#106×C47—22no—
151#103×C47—22no—
152#102×C47—22no—
153#102×C47—22no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—22no—
158#102×C47—22no—
159#102×C47—41no—
160#102×C47D414yescomplemented
161C22⋊C8×C47—22no—
162C22⋊C8×C47—22no—
163C22⋊C8×C47—41no—
164#95×C47—21no—
165#95×C47—21no—
166#95×C47—21no—
167#95×C47—21no—
168C24×C47—21no—
169C24×C47—24no—
170C24×C47—21no—
171C24×C47—21no—
172C24×C47—24no—
173C24×C47—42no—
174C24×C47—42no—
175C24×C47—42no—
176C24×C47—42no—
177C24×C47—42no—
178C24×C47—42no—
179C24×C47—42no—
180C24×C47—42no—
181C24×C47—81no—
182C24×C47—81no—
183C24×C47—81no—
184C24×C47—81no—
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—28no—
196C2×D4×C47—24no—
197C2×D4×C47—24no—
198C2×D4×C47—24no—
199C2×D4×C47—24no—
200C2×D4×C47—24no—
201C2×D4×C47—24no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—21no—
214C2×D4×C47—21no—
215C2×D4×C47—44no—
216C2×D4×C47—44no—
217C2×D4×C47—44no—
218C2×D4×C47—42no—
219C2×D4×C47—42no—
220C2×D4×C47—42no—
221C2×D4×C47—42no—
222C2×D4×C47—42no—
223C2×D4×C47—44no—
224C2×D4×C47—44no—
225C2×D4×C47—432no—
226C2×D4×C47—44no—
227C2×D4×C47—42no—
228C2×D4×C47—42no—
229C2×D4×C47—42no—
230C2×D4×C47—42no—
231C2×D4×C47—44no—
232C2×D4×C47—42no—
233C2×D4×C47—81no—
234C2×D4×C47—81no—
235C2×D4×C47SD1614yescomplemented
236C2×D4×C47C2×D412yes—
237C2×D4×C47C2×D412yes—
238C2×D4×C47C2×D412yes—
239C2×D4×C47C2×D412yes—
240C2×D4×C47#4112yes—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—24no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—42no—
258C22×C4×C47—42no—
259C22×C4×C47—42no—
260C22×C4×C47—42no—
261C22×C4×C47—81no—
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D412yes—
266C22×C4×C47C2×D412yes—
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2411yescharacteristic
269SD16×C47—44no—
270SD16×C47—44no—
271SD16×C47—44no—
272C2×C8×C47—21no—
273C2×C8×C47—21no—
274C2×C8×C47—21no—
275C2×C8×C47—21no—
276C2×C8×C47—21no—
277C2×C8×C47—21no—
278C2×C8×C47—21no—
279C2×C8×C47—21no—
280C2×C8×C47—21no—
281C2×C8×C47—21no—
282C2×C8×C47—21no—
283C2×C8×C47—44no—
284C2×C8×C47C2×D412yescomplemented
285C4⋊C4×C47—22no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47—42no—
293C4⋊C4×C47—42no—
294C4⋊C4×C47—42no—
295C4⋊C4×C47—81no—
296C4⋊C4×C47C2×D412yes—
297C4⋊C4×C47C2×D412yescomplemented
298C22⋊C4×C47—24no—
299C22⋊C4×C47—24no—
300C22⋊C4×C47—22no—
301C22⋊C4×C47—24no—
302C22⋊C4×C47—22no—
303C22⋊C4×C47—42no—
304C22⋊C4×C47—42no—
305C22⋊C4×C47—81no—
306C42×C47—21no—
307C42×C47—21no—
308C23×C47—21no—
309C23×C47—21no—
310C23×C47—21no—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—22no—
314C23×C47—21no—
315C23×C47—22no—
316C23×C47—21no—
317C23×C47—22no—
318C23×C47—21no—
319C23×C47—21no—
320C23×C47—21no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47—48no—
324C23×C47—48no—
325C23×C47—48no—
326C23×C47—41no—
327C23×C47—41no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—41no—
333C23×C47—41no—
334C23×C47—41no—
335C23×C47—41no—
336C23×C47—41no—
337C23×C47—41no—
338C23×C47—41no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—41no—
342C23×C47—48no—
343C23×C47—84no—
344C23×C47—84no—
345C23×C47—84no—
346C23×C47—84no—
347C23×C47—84no—
348C23×C47—84no—
349C23×C47—84no—
350C23×C47—84no—
351C23×C47—84no—
352C23×C47—84no—
353C23×C47#12012yes—
354C23×C47C2×SD1612yes—
355C23×C47C2×SD1612yes—
356C23×C47AGL(1,ℤ/8)12yes—
357C23×C47C22×D411yescharacteristic
358Q8×C47—41no—
359Q8×C47—41no—
360Q8×C47—41no—
361Q8×C47—41no—
362D4×C47—28no—
363D4×C47—22no—
364D4×C47—22no—
365D4×C47—22no—
366D4×C47—22no—
367D4×C47—22no—
368D4×C47—22no—
369D4×C47—22no—
370D4×C47—48no—
371D4×C47—48no—
372D4×C47—48no—
373D4×C47—48no—
374D4×C47—48no—
375D4×C47—41no—
376D4×C47—41no—
377D4×C47—41no—
378D4×C47—41no—
379D4×C47—84no—
380D4×C47#12114yes—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—21no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—21no—
397C2×C4×C47—48no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—41no—
414C2×C4×C47—41no—
415C2×C4×C47—84no—
416C2×C4×C47#12012yes—
417C2×C4×C47C2×SD1612yes—
418C2×C4×C47C22×D411yescharacteristic
419C2×C4×C47C22×D411yescharacteristic
420C2×C4×C47C22×D411yescharacteristic
421C2×C4×C47C2×#4111yescharacteristic
422C2×C4×C47H(5,𝔽2)11yescharacteristic
423C2×C4×C47H(5,𝔽2)11yescharacteristic
424C8×C47—22no—
425C8×C47—41no—
426C8×C47—41no—
427C8×C47—41no—
428#24432C4711yesmaximal, characteristic, direct product factor, Sylow
429C22×C47—22no—
430C22×C47—22no—
431C22×C47—22no—
432C22×C47—22no—
433C22×C47—22no—
434C22×C47—22no—
435C22×C47—24no—
436C22×C47—22no—
437C22×C47—22no—
438C22×C47—22no—
439C22×C47—41no—
440C22×C47—42no—
441C22×C47—41no—
442C22×C47—42no—
443C22×C47—41no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47—42no—
447C22×C47—41no—
448C22×C47—42no—
449C22×C47—42no—
450C22×C47—42no—
451C22×C47—42no—
452C22×C47—42no—
453C22×C47—42no—
454C22×C47—42no—
455C22×C47—816no—
456C22×C47—816no—
457C22×C47—81no—
458C22×C47—81no—
459C22×C47—81no—
460C22×C47—81no—
461C22×C47—81no—
462C22×C47—81no—
463C22×C47—81no—
464C22×C47—81no—
465C22×C47#45014yescomplemented
466C22×C47C2×#12011yescharacteristic
467C22×C47D4211yescharacteristic
468C22×C47#54611yescharacteristic
469C22×C47C22×SD1611yescharacteristic
470C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C47#57611yescharacteristic
472C22×C47#57711yescharacteristic
473C4×C47—22no—
474C4×C47—22no—
475C4×C47—41no—
476C4×C47—42no—
477C4×C47—42no—
478C4×C47—41no—
479C4×C47—81no—
480C4×C47—81no—
481C4×C47—81no—
482C4×C47C2×#12111yescharacteristic
483C4×C47#53411yescharacteristic
484C4×C47D4211yescharacteristic
485C4×C47#54611yescharacteristic
486C2×D42C2×C4711yescharacteristic
487C2×#465C2×C4711yescharacteristic, complemented
488C2×#450C2×C4711yescharacteristic, complemented
489C2×#450C2×C4711yescharacteristic, complemented
490C22×#102C2×C4711yescharacteristic, complemented
491#2417C2×C4711yescharacteristic, complemented
492#2041C2×C4711yescharacteristic, complemented
493#2034C2×C4711yescharacteristic, complemented
494#2014C2×C4711yescharacteristic, complemented
495#2000C2×C4711yescharacteristic, complemented
496#1877C2×C4711yescharacteristic, complemented
497#1874C2×C4711yescharacteristic, complemented
498#1869C2×C4711yescharacteristic, complemented
499#1864C2×C4711yescharacteristic, complemented
500#1786C2×C4711yescharacteristic, complemented
501C2×C47—24no—
502C2×C47—42no—
503C2×C47—44no—
504C2×C47—82no—
505C2×C47—82no—
506C2×C47#241011yescharacteristic
507C2×C47C2×#45011yescharacteristic
508C2×C47#301211yescharacteristic
509C2×C47#326411yescharacteristic
510C2×C47D4×SD1611yescharacteristic
511C2×C47#329511yescharacteristic
512C2×C47#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C4711yescharacteristic
515C23×D4C22×C4711yescharacteristic
516C22×SD16C22×C4711yescharacteristic
517C22×SD16C22×C4711yescharacteristic, complemented
518C22×SD16C22×C4711yescharacteristic, complemented
519C23×C8C22×C4711yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C4711yescharacteristic
523C2×C22⋊Q8C22×C4711yescharacteristic, complemented
524C2×C22⋊Q8C22×C4711yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C4711yescharacteristic
527C2×#121C22×C4711yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C4711yescharacteristic
531C2×C4×D4C22×C4711yescharacteristic
532C22×C4⋊C4C22×C4711yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C4711yescharacteristic, complemented
537C2×#103C22×C4711yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C4711yescharacteristic
540C2×#102C22×C4711yescharacteristic
541C2×#102C22×C4711yescharacteristic
542C2×#102C22×C4711yescharacteristic, complemented
543C2×#102C22×C4711yescharacteristic, complemented
544C2×#102C22×C4711yescharacteristic, complemented
545C2×#102C22×C4711yescharacteristic, complemented
546C2×#102C22×C4711yescharacteristic, complemented
547C2×#102C22×C4711yescharacteristic, complemented
548C2×C22⋊C8C22×C4711yescharacteristic, complemented
549C2×C22⋊C8C22×C4711yescharacteristic, complemented
550C2×C22⋊C8C22×C4711yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C4711yescharacteristic, complemented
554#389C22×C4711yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C4711yescharacteristic, complemented
558#340C22×C4711yescharacteristic, complemented
559#340C22×C4711yescharacteristic, complemented
560#336C22×C4711yescharacteristic, complemented
561#336C22×C4711yescharacteristic, complemented
562C47#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C4711yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C4711yescharacteristic
587C22×D4D4×C4714yes—
588C22×D4C23×C4711yescharacteristic
589C22×D4C23×C4711yescharacteristic
590C22×D4C23×C4711yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C4711yescharacteristic
594C23×C4C23×C4711yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C4711yescharacteristic
608C22×C8C23×C4711yescharacteristic
609C22×C8C23×C4711yescharacteristic
610C22×C8C23×C4711yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C4714yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C4711yescharacteristic
635C2×C4⋊C4C23×C4711yescharacteristic
636C2×C4⋊C4C23×C4711yescharacteristic
637C2×C4⋊C4C23×C4711yescharacteristic
638C2×C4⋊C4C23×C4711yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C4711yescharacteristic
646C2×C22⋊C4D4×C4711yescharacteristic
647C2×C42C23×C4711yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C4714yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C4711yescharacteristic
684C24C2×D4×C4711yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C4714yescomplemented
734C2×D4C2×D4×C4712yes—
735C2×D4C2×D4×C4712yes—
736C2×D4C2×D4×C4712yes—
737C2×D4C2×D4×C4712yes—
738C2×D4#41×C4712yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C4711yescharacteristic
761C22×C4C2×D4×C4711yescharacteristic
762C22×C4C2×D4×C4711yescharacteristic
763C22×C4C2×D4×C4712yes—
764C22×C4C2×D4×C4712yes—
765C22×C4C2×D4×C4711yescharacteristic
766C22×C4C24×C4711yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C4712yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C4712yes—
795C4⋊C4C2×D4×C4712yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C4712yes—
852C23C2×SD16×C4712yes—
853C23C2×SD16×C4712yes—
854C23AGL(1,ℤ/8)×C4712yes—
855C23C22×D4×C4711yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C4714yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C4712yes—
915C2×C4C2×SD16×C4712yes—
916C2×C4C22×D4×C4711yescharacteristic
917C2×C4C22×D4×C4711yescharacteristic
918C2×C4C22×D4×C4711yescharacteristic
919C2×C4C2×#41×C4711yescharacteristic
920C2×C4H(5,𝔽2)×C4711yescharacteristic
921C2×C4H(5,𝔽2)×C4711yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—24no—
934C22—22no—
935C22—22no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—41no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C47×#45014yescomplemented
963C22C2×#120×C4711yescharacteristic
964C22D42×C4711yescharacteristic
965C22C47×#54611yescharacteristic
966C22C22×SD16×C4711yescharacteristic
967C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
968C22C47×#57611yescharacteristic
969C22C47×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C4711yescharacteristic
980C4C47×#53411yescharacteristic
981C4D42×C4711yescharacteristic
982C4C47×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C47×#241011yescharacteristic
989C2C2×C47×#45011yescharacteristic
990C2C47×#301211yescharacteristic
991C2C47×#326411yescharacteristic
992C2D4×SD16×C4711yescharacteristic
993C2C47×#329511yescharacteristic
994C2C47×#331011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×D42×C47C2
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
2. C2×C47×#465C2semidirect
3. C2×C47×#450C2semidirect
4. C2×C47×#450C2semidirect
5. C22×#102×C47C2semidirect
6. C47×#2417C2semidirect
7. C47×#2041C2semidirect
8. C47×#2034C2semidirect
9. C47×#2014C2semidirect
10. C47×#2000C2semidirect
11. C47×#1877C2semidirect
12. C47×#1874C2semidirect
13. C47×#1869C2semidirect
14. C47×#1864C2semidirect
15. C47×#1786C2semidirect
20. C22×SD16×C47C22semidirect
21. C22×SD16×C47C22semidirect
22. C23×C8×C47C22semidirect
26. C2×C22⋊Q8×C47C22semidirect
27. C2×C22⋊Q8×C47C22semidirect
35. C22×C4⋊C4×C47C22semidirect
39. C2×#106×C47C22semidirect
40. C2×#103×C47C22semidirect
45. C2×#102×C47C22semidirect
46. C2×#102×C47C22semidirect
47. C2×#102×C47C22semidirect
48. C2×#102×C47C22semidirect
49. C2×#102×C47C22semidirect
50. C2×#102×C47C22semidirect
51. C2×C22⋊C8×C47C22semidirect
52. C2×C22⋊C8×C47C22semidirect
53. C2×C22⋊C8×C47C22semidirect
56. C47×#391C22semidirect
57. C47×#389C22semidirect
60. C47×#380C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
160. #102×C47D4semidirect
235. C2×D4×C47SD16semidirect
284. C2×C8×C47C2×D4semidirect
297. C4⋊C4×C47C2×D4semidirect
428. #24432C47direct (N × H)
465. C22×C47#450semidirect
487. C2×#465C2×C47semidirect
488. C2×#450C2×C47semidirect
489. C2×#450C2×C47semidirect
490. C22×#102C2×C47semidirect
491. #2417C2×C47semidirect
492. #2041C2×C47semidirect
493. #2034C2×C47semidirect
494. #2014C2×C47semidirect
495. #2000C2×C47semidirect
496. #1877C2×C47semidirect
497. #1874C2×C47semidirect
498. #1869C2×C47semidirect
499. #1864C2×C47semidirect
500. #1786C2×C47semidirect
517. C22×SD16C22×C47semidirect
518. C22×SD16C22×C47semidirect
519. C23×C8C22×C47semidirect
523. C2×C22⋊Q8C22×C47semidirect
524. C2×C22⋊Q8C22×C47semidirect
532. C22×C4⋊C4C22×C47semidirect
536. C2×#106C22×C47semidirect
537. C2×#103C22×C47semidirect
542. C2×#102C22×C47semidirect
543. C2×#102C22×C47semidirect
544. C2×#102C22×C47semidirect
545. C2×#102C22×C47semidirect
546. C2×#102C22×C47semidirect
547. C2×#102C22×C47semidirect
548. C2×C22⋊C8C22×C47semidirect
549. C2×C22⋊C8C22×C47semidirect
550. C2×C22⋊C8C22×C47semidirect
553. #391C22×C47semidirect
554. #389C22×C47semidirect
557. #380C22×C47semidirect
558. #340C22×C47semidirect
559. #340C22×C47semidirect
560. #336C22×C47semidirect
561. #336C22×C47semidirect
562. C47#24432direct (N × H)
658. #102D4×C47semidirect
733. C2×D4SD16×C47semidirect
782. C2×C8C2×D4×C47semidirect
795. C4⋊C4C2×D4×C47semidirect
962. C22C47×#450semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C472
C2×C47×#4652
C2×C47×#4502
C22×#102×C472
C47×#24172
C47×#20412
C47×#20342
C47×#20142
C47×#20002
C47×#18772
C47×#18742
C47×#18692
C47×#18642
C47×#17862
#2443247