Finite Group Databasebeta

← C47×#24424 #26064122

Subgroups — C47×#24424 #26064122

Order 12032.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C47C211yesmaximal, characteristic, complemented
2C2×C47×#466C211yesmaximal, characteristic, complemented
3C2×C47×#447C211yesmaximal, characteristic, complemented
4C2×C47×#447C211yesmaximal, characteristic, complemented
5C22×#102×C47C211yesmaximal, characteristic, complemented
6C47×#2416C211yesmaximal, characteristic, complemented
7C47×#2041C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#2011C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1869C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C47—21no—
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic, complemented
21C22×D8×C47C2211yescharacteristic, complemented
22C23×C8×C47C2211yescharacteristic, complemented
23D42×C47—24no—
24D42×C47—24no—
25C2×#127×C47C2211yescharacteristic
26C2×#121×C47—21no—
27C2×#121×C47—21no—
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic, complemented
31C2×#121×C47C2211yescharacteristic, complemented
32C2×#120×C47—21no—
33C2×#120×C47—21no—
34C2×C4×D4×C47C2211yescharacteristic
35C2×C4×D4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic, complemented
37C47×#466—24no—
38C47×#447—24no—
39C47×#447—24no—
40C2×#107×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×#102×C47C2211yescharacteristic, complemented
52C2×C22⋊C8×C47C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C2×C22⋊C8×C47C2211yescharacteristic, complemented
55C47×#396—21no—
56C47×#394—21no—
57C47×#390C2211yescharacteristic, complemented
58C47×#389C2211yescharacteristic, complemented
59C47×#386—21no—
60C47×#380C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47—21no—
66C25×C47—21no—
67C22×D4×C47—22no—
68C22×D4×C47—22no—
69C22×D4×C47—28no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—22no—
73C22×D4×C47—22no—
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—22no—
82C22×D4×C47—21no—
83C22×D4×C47—41no—
84C22×D4×C47—41no—
85C22×D4×C47—41no—
86C22×D4×C47—41no—
87C22×D4×C47—44no—
88C22×D4×C47—44no—
89C22×D4×C47D411yescharacteristic
90C22×D4×C47D414yescomplemented
91C22×D4×C47C2311yescharacteristic
92C22×D4×C47C2311yescharacteristic
93C22×D4×C47C2311yescharacteristic
94C22×D4×C47C2311yescharacteristic
95C23×C4×C47—21no—
96C23×C4×C47—21no—
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C2×D8×C47—22no—
100C2×D8×C47—22no—
101C2×D8×C47—22no—
102C2×D8×C47—22no—
103C2×D8×C47—22no—
104C2×D8×C47—22no—
105C2×D8×C47—41no—
106C2×D8×C47—41no—
107C2×D8×C47—41no—
108C22×C8×C47—22no—
109C22×C8×C47—22no—
110C22×C8×C47—41no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115#127×C47—22no—
116#127×C47—22no—
117#121×C47—28no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—22no—
122#121×C47—22no—
123#121×C47—22no—
124#121×C47—41no—
125#121×C47—44no—
126#121×C47D414yescomplemented
127#120×C47—28no—
128#120×C47—28no—
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47—22no—
132C4×D4×C47—22no—
133C2×C4⋊C4×C47—22no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47—21no—
136C2×C4⋊C4×C47—41no—
137C2×C4⋊C4×C47D411yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
148C2×C22⋊C4×C47—21no—
149C2×C22⋊C4×C47—21no—
150C2×C22⋊C4×C47D411yescharacteristic
151C2×C22⋊C4×C47D411yescharacteristic
152C2×C42×C47C2311yescharacteristic
153#107×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—22no—
160#102×C47—22no—
161#102×C47—22no—
162#102×C47—41no—
163#102×C47D414yescomplemented
164C22⋊C8×C47—22no—
165C22⋊C8×C47—22no—
166C22⋊C8×C47—41no—
167#95×C47—21no—
168#95×C47—21no—
169C24×C47—21no—
170C24×C47—24no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—24no—
174C24×C47—21no—
175C24×C47—42no—
176C24×C47—42no—
177C24×C47—42no—
178C24×C47—42no—
179C24×C47—42no—
180C24×C47—42no—
181C24×C47—42no—
182C24×C47—42no—
183C24×C47—81no—
184C24×C47—81no—
185C24×C47—81no—
186C24×C47—81no—
187C24×C47C2×D411yescharacteristic
188C24×C47C2×D411yescharacteristic
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—28no—
192C2×D4×C47—24no—
193C2×D4×C47—24no—
194C2×D4×C47—24no—
195C2×D4×C47—24no—
196C2×D4×C47—24no—
197C2×D4×C47—24no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
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—21no—
216C2×D4×C47—21no—
217C2×D4×C47—44no—
218C2×D4×C47—44no—
219C2×D4×C47—44no—
220C2×D4×C47—42no—
221C2×D4×C47—42no—
222C2×D4×C47—42no—
223C2×D4×C47—42no—
224C2×D4×C47—42no—
225C2×D4×C47—42no—
226C2×D4×C47—44no—
227C2×D4×C47—44no—
228C2×D4×C47—432no—
229C2×D4×C47—44no—
230C2×D4×C47—42no—
231C2×D4×C47—42no—
232C2×D4×C47—42no—
233C2×D4×C47—42no—
234C2×D4×C47—44no—
235C2×D4×C47—42no—
236C2×D4×C47—42no—
237C2×D4×C47—42no—
238C2×D4×C47—42no—
239C2×D4×C47—42no—
240C2×D4×C47—81no—
241C2×D4×C47—81no—
242C2×D4×C47—81no—
243C2×D4×C47D814yescomplemented
244C2×D4×C47C2×D412yes—
245C2×D4×C47C2×D412yes—
246C2×D4×C47C2×D412yes—
247C2×D4×C47C2×D412yes—
248C2×D4×C47#4112yes—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—24no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—42no—
265C22×C4×C47—42no—
266C22×C4×C47—42no—
267C22×C4×C47—42no—
268C22×C4×C47—81no—
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D412yes—
273C22×C4×C47C2×D412yes—
274C22×C4×C47C2×D411yescharacteristic
275C22×C4×C47C2411yescharacteristic
276D8×C47—44no—
277D8×C47—44no—
278D8×C47—44no—
279C2×C8×C47—21no—
280C2×C8×C47—21no—
281C2×C8×C47—21no—
282C2×C8×C47—21no—
283C2×C8×C47—21no—
284C2×C8×C47—21no—
285C2×C8×C47—21no—
286C2×C8×C47—21no—
287C2×C8×C47—21no—
288C2×C8×C47—21no—
289C2×C8×C47—21no—
290C2×C8×C47—44no—
291C2×C8×C47C2×D412yescomplemented
292C4⋊C4×C47—22no—
293C4⋊C4×C47—21no—
294C4⋊C4×C47—21no—
295C4⋊C4×C47—21no—
296C4⋊C4×C47—21no—
297C4⋊C4×C47—21no—
298C4⋊C4×C47—21no—
299C4⋊C4×C47—42no—
300C4⋊C4×C47—42no—
301C4⋊C4×C47C2×D412yes—
302C4⋊C4×C47C2×D412yescomplemented
303C22⋊C4×C47—24no—
304C22⋊C4×C47—24no—
305C22⋊C4×C47—22no—
306C22⋊C4×C47—24no—
307C22⋊C4×C47—22no—
308C22⋊C4×C47—42no—
309C22⋊C4×C47—42no—
310C22⋊C4×C47—42no—
311C22⋊C4×C47—42no—
312C22⋊C4×C47—81no—
313C42×C47—21no—
314C42×C47—21no—
315C23×C47—21no—
316C23×C47—21no—
317C23×C47—21no—
318C23×C47—21no—
319C23×C47—21no—
320C23×C47—22no—
321C23×C47—21no—
322C23×C47—22no—
323C23×C47—21no—
324C23×C47—22no—
325C23×C47—21no—
326C23×C47—21no—
327C23×C47—21no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—48no—
331C23×C47—48no—
332C23×C47—48no—
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—41no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47—41no—
349C23×C47—48no—
350C23×C47—41no—
351C23×C47—41no—
352C23×C47—41no—
353C23×C47—41no—
354C23×C47—41no—
355C23×C47—41no—
356C23×C47—41no—
357C23×C47—84no—
358C23×C47—84no—
359C23×C47—84no—
360C23×C47—84no—
361C23×C47—84no—
362C23×C47—84no—
363C23×C47—84no—
364C23×C47—84no—
365C23×C47—84no—
366C23×C47—84no—
367C23×C47#12012yes—
368C23×C47C2×D812yes—
369C23×C47C2×D812yes—
370C23×C47AGL(1,ℤ/8)12yes—
371C23×C47C22×D411yescharacteristic
372D4×C47—28no—
373D4×C47—22no—
374D4×C47—22no—
375D4×C47—22no—
376D4×C47—22no—
377D4×C47—22no—
378D4×C47—22no—
379D4×C47—22no—
380D4×C47—48no—
381D4×C47—48no—
382D4×C47—48no—
383D4×C47—48no—
384D4×C47—48no—
385D4×C47—41no—
386D4×C47—41no—
387D4×C47—41no—
388D4×C47—41no—
389D4×C47—41no—
390D4×C47—41no—
391D4×C47—41no—
392D4×C47—41no—
393D4×C47—84no—
394D4×C47—84no—
395D4×C47—84no—
396D4×C47#12114yescomplemented
397C2×C4×C47—21no—
398C2×C4×C47—21no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—22no—
405C2×C4×C47—21no—
406C2×C4×C47—21no—
407C2×C4×C47—22no—
408C2×C4×C47—21no—
409C2×C4×C47—22no—
410C2×C4×C47—21no—
411C2×C4×C47—21no—
412C2×C4×C47—21no—
413C2×C4×C47—48no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—41no—
427C2×C4×C47—41no—
428C2×C4×C47—84no—
429C2×C4×C47#12012yes—
430C2×C4×C47C2×D812yes—
431C2×C4×C47C22×D411yescharacteristic
432C2×C4×C47C22×D411yescharacteristic
433C2×C4×C47C22×D411yescharacteristic
434C2×C4×C47C2×#4111yescharacteristic
435C2×C4×C47H(5,𝔽2)11yescharacteristic
436C2×C4×C47H(5,𝔽2)11yescharacteristic
437C8×C47—22no—
438C8×C47—41no—
439C8×C47—41no—
440C8×C47—41no—
441#24424C4711yesmaximal, characteristic, direct product factor, Sylow
442C22×C47—22no—
443C22×C47—22no—
444C22×C47—22no—
445C22×C47—22no—
446C22×C47—22no—
447C22×C47—22no—
448C22×C47—24no—
449C22×C47—22no—
450C22×C47—22no—
451C22×C47—22no—
452C22×C47—41no—
453C22×C47—42no—
454C22×C47—41no—
455C22×C47—42no—
456C22×C47—41no—
457C22×C47—42no—
458C22×C47—42no—
459C22×C47—42no—
460C22×C47—41no—
461C22×C47—42no—
462C22×C47—42no—
463C22×C47—42no—
464C22×C47—42no—
465C22×C47—42no—
466C22×C47—42no—
467C22×C47—42no—
468C22×C47—816no—
469C22×C47—816no—
470C22×C47—81no—
471C22×C47—81no—
472C22×C47—81no—
473C22×C47—81no—
474C22×C47—81no—
475C22×C47—81no—
476C22×C47—81no—
477C22×C47—81no—
478C22×C47—81no—
479C22×C47—81no—
480C22×C47—81no—
481C22×C47—81no—
482C22×C47—81no—
483C22×C47—81no—
484C22×C47—81no—
485C22×C47#44714yescomplemented
486C22×C47C2×#12011yescharacteristic
487C22×C47D4211yescharacteristic
488C22×C47#54611yescharacteristic
489C22×C47C22×D811yescharacteristic
490C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
491C22×C47#57611yescharacteristic
492C22×C47#57711yescharacteristic
493C4×C47—22no—
494C4×C47—22no—
495C4×C47—41no—
496C4×C47—42no—
497C4×C47—41no—
498C4×C47—42no—
499C4×C47—81no—
500C4×C47—81no—
501C4×C47C2×#12111yescharacteristic
502C4×C47#53411yescharacteristic
503C4×C47D4211yescharacteristic
504C4×C47#54611yescharacteristic
505C2×D42C2×C4711yescharacteristic, complemented
506C2×#466C2×C4711yescharacteristic, complemented
507C2×#447C2×C4711yescharacteristic, complemented
508C2×#447C2×C4711yescharacteristic, complemented
509C22×#102C2×C4711yescharacteristic, complemented
510#2416C2×C4711yescharacteristic, complemented
511#2041C2×C4711yescharacteristic, complemented
512#2033C2×C4711yescharacteristic, complemented
513#2011C2×C4711yescharacteristic, complemented
514#1999C2×C4711yescharacteristic, complemented
515#1879C2×C4711yescharacteristic, complemented
516#1874C2×C4711yescharacteristic, complemented
517#1869C2×C4711yescharacteristic, complemented
518#1862C2×C4711yescharacteristic, complemented
519#1786C2×C4711yescharacteristic, complemented
520C2×C47—24no—
521C2×C47—42no—
522C2×C47—44no—
523C2×C47—82no—
524C2×C47—82no—
525C2×C47—161no—
526C2×C47#241011yescharacteristic
527C2×C47C2×#44711yescharacteristic
528C2×C47#301211yescharacteristic
529C2×C47#326511yescharacteristic
530C2×C47D4×D811yescharacteristic
531C2×C47#329411yescharacteristic
532C2×C47#331811yescharacteristic
533C23×D4—21no—
534C23×D4C22×C4711yescharacteristic
535C23×D4C22×C4711yescharacteristic
536C22×D8C22×C4711yescharacteristic
537C22×D8C22×C4711yescharacteristic, complemented
538C22×D8C22×C4711yescharacteristic, complemented
539C23×C8C22×C4711yescharacteristic, complemented
540D42—24no—
541D42—24no—
542C2×#127C22×C4711yescharacteristic
543C2×#121—21no—
544C2×#121—21no—
545C2×#121C22×C4711yescharacteristic
546C2×#121C22×C4711yescharacteristic
547C2×#121C22×C4711yescharacteristic, complemented
548C2×#121C22×C4711yescharacteristic, complemented
549C2×#120—21no—
550C2×#120—21no—
551C2×C4×D4C22×C4711yescharacteristic
552C2×C4×D4C22×C4711yescharacteristic
553C22×C4⋊C4C22×C4711yescharacteristic, complemented
554#466—24no—
555#447—24no—
556#447—24no—
557C2×#107C22×C4711yescharacteristic, complemented
558C2×#102—24no—
559C2×#102C22×C4711yescharacteristic
560C2×#102C22×C4711yescharacteristic
561C2×#102C22×C4711yescharacteristic
562C2×#102C22×C4711yescharacteristic, complemented
563C2×#102C22×C4711yescharacteristic, complemented
564C2×#102C22×C4711yescharacteristic, complemented
565C2×#102C22×C4711yescharacteristic, complemented
566C2×#102C22×C4711yescharacteristic, complemented
567C2×#102C22×C4711yescharacteristic, complemented
568C2×#102C22×C4711yescharacteristic, complemented
569C2×C22⋊C8C22×C4711yescharacteristic, complemented
570C2×C22⋊C8C22×C4711yescharacteristic, complemented
571C2×C22⋊C8C22×C4711yescharacteristic, complemented
572#396—21no—
573#394—21no—
574#390C22×C4711yescharacteristic, complemented
575#389C22×C4711yescharacteristic, complemented
576#386—21no—
577#380C22×C4711yescharacteristic, complemented
578#340C22×C4711yescharacteristic, complemented
579#340C22×C4711yescharacteristic, complemented
580#336C22×C4711yescharacteristic, complemented
581#336C22×C4711yescharacteristic, complemented
582C47#2442411yescharacteristic, direct product factor, Sylow
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C4711yescharacteristic
608C22×D4D4×C4714yescomplemented
609C22×D4C23×C4711yescharacteristic
610C22×D4C23×C4711yescharacteristic
611C22×D4C23×C4711yescharacteristic
612C22×D4C23×C4711yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C4711yescharacteristic
616C23×C4C23×C4711yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C4711yescharacteristic
630C22×C8C23×C4711yescharacteristic
631C22×C8C23×C4711yescharacteristic
632C22×C8C23×C4711yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C4714yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C4711yescharacteristic
656C2×C4⋊C4C23×C4711yescharacteristic
657C2×C4⋊C4C23×C4711yescharacteristic
658C2×C4⋊C4C23×C4711yescharacteristic
659C2×C4⋊C4C23×C4711yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C4711yescharacteristic
669C2×C22⋊C4D4×C4711yescharacteristic
670C2×C42C23×C4711yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C4714yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C4711yescharacteristic
706C24C2×D4×C4711yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C4714yescomplemented
762C2×D4C2×D4×C4712yes—
763C2×D4C2×D4×C4712yes—
764C2×D4C2×D4×C4712yes—
765C2×D4C2×D4×C4712yes—
766C2×D4#41×C4712yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C4711yescharacteristic
788C22×C4C2×D4×C4711yescharacteristic
789C22×C4C2×D4×C4711yescharacteristic
790C22×C4C2×D4×C4712yes—
791C22×C4C2×D4×C4712yes—
792C22×C4C2×D4×C4711yescharacteristic
793C22×C4C24×C4711yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C4712yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C4712yes—
820C4⋊C4C2×D4×C4712yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—48no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C4712yes—
886C23C2×D8×C4712yes—
887C23C2×D8×C4712yes—
888C23AGL(1,ℤ/8)×C4712yes—
889C23C22×D4×C4711yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C4714yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C4712yes—
948C2×C4C2×D8×C4712yes—
949C2×C4C22×D4×C4711yescharacteristic
950C2×C4C22×D4×C4711yescharacteristic
951C2×C4C22×D4×C4711yescharacteristic
952C2×C4C2×#41×C4711yescharacteristic
953C2×C4H(5,𝔽2)×C4711yescharacteristic
954C2×C4H(5,𝔽2)×C4711yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—24no—
967C22—22no—
968C22—22no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—42no—
976C22—41no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22C47×#44714yescomplemented
1003C22C2×#120×C4711yescharacteristic
1004C22D42×C4711yescharacteristic
1005C22C47×#54611yescharacteristic
1006C22C22×D8×C4711yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
1008C22C47×#57611yescharacteristic
1009C22C47×#57711yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C4711yescharacteristic
1019C4C47×#53411yescharacteristic
1020C4D42×C4711yescharacteristic
1021C4C47×#54611yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2C47×#241011yescharacteristic
1029C2C2×C47×#44711yescharacteristic
1030C2C47×#301211yescharacteristic
1031C2C47×#326511yescharacteristic
1032C2D4×D8×C4711yescharacteristic
1033C2C47×#329411yescharacteristic
1034C2C47×#331811yescharacteristic
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×D42×C47C2semidirect
2. C2×C47×#466C2semidirect
3. C2×C47×#447C2semidirect
4. C2×C47×#447C2semidirect
5. C22×#102×C47C2semidirect
6. C47×#2416C2semidirect
7. C47×#2041C2semidirect
8. C47×#2033C2semidirect
9. C47×#2011C2semidirect
10. C47×#1999C2semidirect
11. C47×#1879C2semidirect
12. C47×#1874C2semidirect
13. C47×#1869C2semidirect
14. C47×#1862C2semidirect
15. C47×#1786C2semidirect
20. C22×D8×C47C22semidirect
21. C22×D8×C47C22semidirect
22. C23×C8×C47C22semidirect
30. C2×#121×C47C22semidirect
31. C2×#121×C47C22semidirect
36. C22×C4⋊C4×C47C22semidirect
40. C2×#107×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×#102×C47C22semidirect
52. C2×C22⋊C8×C47C22semidirect
53. C2×C22⋊C8×C47C22semidirect
54. C2×C22⋊C8×C47C22semidirect
57. C47×#390C22semidirect
58. C47×#389C22semidirect
60. C47×#380C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
90. C22×D4×C47D4semidirect
126. #121×C47D4semidirect
163. #102×C47D4semidirect
243. C2×D4×C47D8semidirect
291. C2×C8×C47C2×D4semidirect
302. C4⋊C4×C47C2×D4semidirect
396. D4×C47#121semidirect
441. #24424C47direct (N × H)
485. C22×C47#447semidirect
505. C2×D42C2×C47semidirect
506. C2×#466C2×C47semidirect
507. C2×#447C2×C47semidirect
508. C2×#447C2×C47semidirect
509. C22×#102C2×C47semidirect
510. #2416C2×C47semidirect
511. #2041C2×C47semidirect
512. #2033C2×C47semidirect
513. #2011C2×C47semidirect
514. #1999C2×C47semidirect
515. #1879C2×C47semidirect
516. #1874C2×C47semidirect
517. #1869C2×C47semidirect
518. #1862C2×C47semidirect
519. #1786C2×C47semidirect
537. C22×D8C22×C47semidirect
538. C22×D8C22×C47semidirect
539. C23×C8C22×C47semidirect
547. C2×#121C22×C47semidirect
548. C2×#121C22×C47semidirect
553. C22×C4⋊C4C22×C47semidirect
557. C2×#107C22×C47semidirect
562. C2×#102C22×C47semidirect
563. C2×#102C22×C47semidirect
564. C2×#102C22×C47semidirect
565. C2×#102C22×C47semidirect
566. C2×#102C22×C47semidirect
567. C2×#102C22×C47semidirect
568. C2×#102C22×C47semidirect
569. C2×C22⋊C8C22×C47semidirect
570. C2×C22⋊C8C22×C47semidirect
571. C2×C22⋊C8C22×C47semidirect
574. #390C22×C47semidirect
575. #389C22×C47semidirect
577. #380C22×C47semidirect
578. #340C22×C47semidirect
579. #340C22×C47semidirect
580. #336C22×C47semidirect
581. #336C22×C47semidirect
582. C47#24424direct (N × H)
608. C22×D4D4×C47semidirect
644. #121D4×C47semidirect
681. #102D4×C47semidirect
761. C2×D4D8×C47semidirect
809. C2×C8C2×D4×C47semidirect
820. C4⋊C4C2×D4×C47semidirect
914. D4#121×C47semidirect
1002. C22C47×#447semidirect

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×#4662
C2×C47×#4472
C22×#102×C472
C47×#24162
C47×#20412
C47×#20332
C47×#20112
C47×#19992
C47×#18792
C47×#18742
C47×#18692
C47×#18622
C47×#17862
#2442447