Finite Group Databasebeta

← C2×#562×D47 #27123152

Subgroups — C2×#562×D47 #27123152

Order 12032.

8102 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689871C211yesmaximal, characteristic, complemented
2C2×#15689870C214yesmaximal, complemented
3C2×#15689869C214yesmaximal, complemented
4C2×#15689868C214yesmaximal, complemented
5C2×#15689867C212yesmaximal, complemented
6#562×D47C2132yesmaximal, direct product factor
7C2×#125×D47C211yesmaximal, characteristic, complemented
8C2×#124×D47C212yesmaximal, complemented
9C2×#123×D47C214yesmaximal, complemented
10C2×C22⋊Q8×D47C214yesmaximal, complemented
11C2×#121×D47C214yesmaximal, complemented
12C2×C47×#562C211yesmaximal, characteristic, complemented
13C22×Q8×D47C2212yes—
14C22×D4×D47C2214yes—
15C22×D4×D47C2212yes—
16C23×C4×D47C2214yes—
17#15689871C22116yescomplemented
18#15689870C22164yescomplemented
19#15689869C22164yescomplemented
20#15689868C22164yescomplemented
21#15689867C22132yescomplemented
22C2×#13094016C2211yescharacteristic, complemented
23C2×#13094015C2212yescomplemented
24C2×#13094014C2214yescomplemented
25#125×D47C22116yescomplemented
26C2×#13094013C2212yescomplemented
27C2×#13094012C2212yescomplemented
28C2×#13094011C2212yescomplemented
29C2×#13094010C2214yescomplemented
30C2×#13094010C2214yescomplemented
31#124×D47C22132yescomplemented
32C2×#13094009C2214yescomplemented
33C2×#13094009C2214yescomplemented
34C2×#13094008C2214yescomplemented
35C2×#13094007C2214yescomplemented
36C2×#13094006C2214yescomplemented
37C2×#13094006C2214yescomplemented
38C2×#13094005C2214yescomplemented
39#123×D47C22164yescomplemented
40C2×#13094004C2214yescomplemented
41C2×#13094003C2214yescomplemented
42C2×#13094002C2214yescomplemented
43C2×#13094002C2214yescomplemented
44C2×#13094001C2214yescomplemented
45C2×#13094001C2214yescomplemented
46C2×#13094000C2214yescomplemented
47C22⋊Q8×D47C22164yescomplemented
48C2×#13093999C2214yescomplemented
49C2×#13093998C2214yescomplemented
50C2×#13093997C2214yescomplemented
51C2×#13093997C2214yescomplemented
52C2×#13093996C2214yescomplemented
53C2×#13093996C2214yescomplemented
54C2×#13093995C2214yescomplemented
55#121×D47C22164yescomplemented
56C2×C4⋊C4×D47C2214yes—
57C2×C4⋊C4×D47C2214yes—
58C2×C4⋊C4×D47C2212yes—
59C2×C22⋊C4×D47C2214yes—
60C2×C22⋊C4×D47C2214yes—
61C2×C22⋊C4×D47C2214yes—
62C2×C42×D47C2211yescharacteristic
63C47×#562C22116yescomplemented
64C2×#125×C47C2211yescharacteristic, complemented
65C2×#124×C47C2212yescomplemented
66C2×#123×C47C2214yescomplemented
67C2×C22⋊Q8×C47C2214yescomplemented
68C2×#121×C47C2214yescomplemented
69C24×D47C2314yes—
70C22×Dic94C2312yes—
71C22×Dic94C2314yes—
72C2×Q8×D47—48no—
73C2×Q8×D47C23116yes—
74C22×D188C2312yes—
75C22×D188C2314yes—
76C22×C22⋊D47C2314yes—
77C22×C22⋊D47C2314yes—
78C22×C22⋊D47C2314yes—
79C2×D4×D47—416no—
80C2×D4×D47—48no—
81C2×D4×D47C23132yes—
82C2×D4×D47C23116yes—
83C23×Dic47C2314yes—
84C22×C4×D47—416no—
85C22×C4×D47C2311yescharacteristic
86C22×C4×D47C2312yes—
87C22×C4×D47C2314yes—
88C22×C4×D47C2314yes—
89C22×C4×D47C23132yes—
90C22×C4×D47C2314yes—
91C22×C4×D47C2314yes—
92#13094016C2318yescomplemented
93#13094015C23116yescomplemented
94#13094014C23132yescomplemented
95#13094013C23116yescomplemented
96#13094012C23116yescomplemented
97#13094011C23116yescomplemented
98#13094010C23132yescomplemented
99#13094010C23132yescomplemented
100#13094009C23132yescomplemented
101#13094009C23132yescomplemented
102#13094008C23132yescomplemented
103#13094007C23132yescomplemented
104#13094006C23132yescomplemented
105#13094006C23132yescomplemented
106#13094005C23132yescomplemented
107#13094004C23132yescomplemented
108#13094003C23132yescomplemented
109#13094002C23132yescomplemented
110#13094002C23132yescomplemented
111#13094001C23132yescomplemented
112#13094001C23132yescomplemented
113#13094000C23132yescomplemented
114#13093999C23132yescomplemented
115#13093998C23132yescomplemented
116#13093997C23132yescomplemented
117#13093997C23132yescomplemented
118#13093996C23132yescomplemented
119#13093996C23132yescomplemented
120#13093995C23132yescomplemented
121C2×C4⋊Dic47C2314yes—
122C2×C4⋊Dic47C2314yes—
123C2×C4⋊Dic47C2312yes—
124C2×Dic47⋊C4C2314yes—
125C2×Dic47⋊C4C2314yes—
126C2×Dic47⋊C4C2314yes—
127C2×Dic47⋊C4C2314yes—
128C2×Dic47⋊C4C2314yes—
129C4⋊C4×D47C23132yes—
130C4⋊C4×D47C23132yes—
131C4⋊C4×D47C23116yes—
132C2×C22⋊Dic47C2314yes—
133C2×C22⋊Dic47C2314yes—
134C2×C22⋊Dic47C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C22⋊C4×D47C23132yes—
142C22⋊C4×D47C23132yes—
143C22⋊C4×D47C23132yes—
144C2×C4×Dic47C2311yescharacteristic
145C2×C4×Dic47C2312yes—
146C42×D47C2318yes—
147C22×Q8×C47C2312yes—
148C22×D4×C47C2314yes—
149C22×D4×C47C2312yes—
150C23×C4×C47C2314yes—
151#125×C47C2318yescomplemented
152#124×C47C23116yescomplemented
153#123×C47C23132yescomplemented
154C22⋊Q8×C47C23132yescomplemented
155#121×C47C23132yescomplemented
156C2×C4⋊C4×C47C2314yes—
157C2×C4⋊C4×C47C2314yes—
158C2×C4⋊C4×C47C2312yes—
159C2×C22⋊C4×C47C2314yes—
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162C2×C42×C47C2311yescharacteristic
163C24×C47C2414yes—
164C23×D47—216no—
165C23×D47—216no—
166C23×D47—216no—
167C23×D47C24116yes—
168C23×D47C2414yes—
169C23×D47C2411yescharacteristic
170C2×Q8×C47—44no—
171C2×Q8×C47C2418yes—
172C2×D4×C47—44no—
173C2×D4×C47—48no—
174C2×D4×C47C24116yes—
175C2×D4×C47C2418yes—
176C22×C4×C47—48no—
177C22×C4×C47C2411yescharacteristic
178C22×C4×C47C2412yes—
179C22×C4×C47C2414yes—
180C22×C4×C47C2414yes—
181C22×C4×C47C24116yes—
182C2×C22⋊D47—48no—
183C2×C22⋊D47—48no—
184C2×C22⋊D47—48no—
185C2×C22⋊D47C24116yes—
186C2×C22⋊D47C24116yes—
187C2×C22⋊D47C24116yes—
188C22×Dic47—48no—
189C22×Dic47C2411yescharacteristic
190C22×Dic47C2412yes—
191C22×Dic47C2414yes—
192C22×Dic47C2414yes—
193C22×Dic47C24116yes—
194Q8×D47—432no—
195D4×D47—464no—
196D4×D47—432no—
197C2×D188—44no—
198C2×D188—48no—
199C2×D188C2418yes—
200C2×D188C24116yes—
201C2×C4×D47—216no—
202C2×C4×D47—216no—
203C2×C4×D47—28no—
204C2×C4×D47—24no—
205C2×C4×D47—464no—
206C2×C4×D47—48no—
207C2×C4×D47—48no—
208C2×C4×D47C2414yes—
209C2×C4×D47C2418yes—
210C2×C4×D47C24116yes—
211C2×C4×D47C24116yes—
212C2×C4×D47C24116yes—
213C2×C4×D47C24116yes—
214C2×Dic94—44no—
215C2×Dic94—48no—
216C2×Dic94C2418yes—
217C2×Dic94C24116yes—
218C4⋊C4×C47C24116yes—
219C4⋊C4×C47C24116yes—
220C4⋊C4×C47C2418yes—
221C22⋊C4×C47C24116yes—
222C22⋊C4×C47C24116yes—
223C22⋊C4×C47C24116yes—
224C42×C47C2414yes—
225C22⋊Dic47C24116yes—
226C22⋊Dic47C24116yes—
227C22⋊Dic47C24116yes—
228(C2×D47)⋊C4C24116yes—
229(C2×D47)⋊C4C24116yes—
230(C2×D47)⋊C4C24116yes—
231(C2×D47)⋊C4C24116yes—
232(C2×D47)⋊C4C24116yes—
233(C2×D47)⋊C4C24116yes—
234C4⋊Dic47C24116yes—
235C4⋊Dic47C24116yes—
236C4⋊Dic47C2418yes—
237Dic47⋊C4C24116yes—
238Dic47⋊C4C24116yes—
239Dic47⋊C4C24116yes—
240Dic47⋊C4C24116yes—
241Dic47⋊C4C24116yes—
242C4×Dic47C2414yes—
243C4×Dic47C2418yes—
244C23×C47—28no—
245C23×C47—28no—
246C23×C47—28no—
247C23×C47C2518yes—
248C23×C47C2511yescharacteristic
249C22×D47—28no—
250C22×D47—28no—
251C22×D47—28no—
252C22×D47—232no—
253C22×D47—232no—
254C22×D47—232no—
255C22×D47—464no—
256C22×D47H(5,𝔽2)18yes—
257C22×D472−1+414yes—
258C22×D47C2518yes—
259C22×D47C2512yes—
260Q8×C47—48no—
261D4×C47—48no—
262D4×C47—416no—
263C2×C4×C47—28no—
264C2×C4×C47—24no—
265C2×C4×C47—28no—
266C2×C4×C47—22no—
267C2×C4×C47—416no—
268C2×C4×C47C2514yes—
269C2×C4×C47C2512yes—
270C2×C4×C47C2518yes—
271C2×C4×C47C2518yes—
272C22⋊D47—416no—
273C22⋊D47—416no—
274C22⋊D47—416no—
275C2×Dic47—28no—
276C2×Dic47—24no—
277C2×Dic47—28no—
278C2×Dic47—22no—
279C2×Dic47—416no—
280C2×Dic47C2512yes—
281C2×Dic47C2514yes—
282C2×Dic47C2518yes—
283C2×Dic47C2518yes—
284D188—48no—
285D188—416no—
286C4×D47—232no—
287C4×D47—232no—
288C4×D47—216no—
289C4×D47—28no—
290C4×D47—416no—
291C4×D47—416no—
292Dic94—48no—
293Dic94—416no—
294C22×#562—471nomaximal, Sylow
295C22×C47—28no—
296C22×C47—28no—
297C22×C47—28no—
298C22×C47—416no—
299C22×C47C2×H(5,𝔽2)14yes—
300C22×C47C2×2−1+412yes—
301C22×C47C2611yescharacteristic
302C2×D47—28no—
303C2×D47—28no—
304C2×D47—28no—
305C2×D47—416no—
306C2×D47—464no—
307C2×D47#562116yesdirect product factor
308C2×D47C2×H(5,𝔽2)18yes—
309C2×D47C2×2−1+414yes—
310C4×C47—28no—
311C4×C47—24no—
312C4×C47—28no—
313C4×C47—22no—
314Dic47—28no—
315Dic47—24no—
316Dic47—28no—
317Dic47—22no—
318C2×#562—4732no—
319C2×#562—471no—
320C2×#562—472no—
321C2×#562—474no—
322C2×#562—474no—
323C2×#562—474no—
324C2×#562D4711yescharacteristic, direct product factor
325C22×#125—471no—
326C22×#124—472no—
327C22×#123—474no—
328C22×C22⋊Q8—474no—
329C22×#121—474no—
330C2×C47—48no—
331C2×C47C2×#56214yescomplemented
332C2×C47C22×H(5,𝔽2)12yes—
333C2×C47C22×2−1+411yescharacteristic
334D47—48no—
335D47C2×#56218yesdirect product factor
336C23×Q8—472no—
337C23×D4—474no—
338C23×D4—472no—
339C24×C4—474no—
340#562—4716no—
341#562—4732no—
342#562—4764no—
343#562—4764no—
344#562—4764no—
345#562C2×D47116yesdirect product factor
346C2×#125—4716no—
347C2×#125—474no—
348C2×#125—472no—
349C2×#125—471no—
350C2×#125C2×D4711yescharacteristic, complemented
351C2×#124—472no—
352C2×#124—472no—
353C2×#124—4732no—
354C2×#124—474no—
355C2×#124—474no—
356C2×#124—472no—
357C2×#124C2×D4712yescomplemented
358C2×#123—474no—
359C2×#123—474no—
360C2×#123—4764no—
361C2×#123—474no—
362C2×#123—474no—
363C2×#123—474no—
364C2×#123—474no—
365C2×#123—474no—
366C2×#123C2×D4714yescomplemented
367C2×C22⋊Q8—474no—
368C2×C22⋊Q8—474no—
369C2×C22⋊Q8—4764no—
370C2×C22⋊Q8—474no—
371C2×C22⋊Q8—474no—
372C2×C22⋊Q8—474no—
373C2×C22⋊Q8—474no—
374C2×C22⋊Q8—474no—
375C2×C22⋊Q8C2×D4714yescomplemented
376C2×#121—474no—
377C2×#121—474no—
378C2×#121—474no—
379C2×#121—474no—
380C2×#121—4764no—
381C2×#121—474no—
382C2×#121—474no—
383C2×#121—474no—
384C2×#121C2×D4714yescomplemented
385C22×C4⋊C4—474no—
386C22×C4⋊C4—474no—
387C22×C4⋊C4—472no—
388C22×C22⋊C4—474no—
389C22×C22⋊C4—474no—
390C22×C22⋊C4—474no—
391C22×C42—471no—
392C47C22×#56211yescharacteristic, complemented, Sylow
393C25—474no—
394C22×Q8—4716no—
395C22×Q8—474no—
396C22×Q8—472no—
397C22×Q8—1888no—
398C22×Q8C22×D4712yes—
399C22×D4—474no—
400C22×D4—474no—
401C22×D4—474no—
402C22×D4—4732no—
403C22×D4—4716no—
404C22×D4—474no—
405C22×D4—472no—
406C22×D4—18816no—
407C22×D4—1888no—
408C22×D4C22×D4714yes—
409C22×D4C22×D4712yes—
410C23×C4—474no—
411C23×C4—471no—
412C23×C4—474no—
413C23×C4—472no—
414C23×C4—474no—
415C23×C4—474no—
416C23×C4—474no—
417C23×C4—4732no—
418C23×C4—18816no—
419C23×C4C22×D4714yes—
420#125—4732no—
421#125—4716no—
422#125—478no—
423#125C22×D4718yescomplemented
424#124—4716no—
425#124—4716no—
426#124—4732no—
427#124—4732no—
428#124—4716no—
429#124C22×D47116yescomplemented
430#123—4732no—
431#123—4732no—
432#123—4732no—
433#123—4732no—
434#123—4732no—
435#123—4732no—
436#123—4732no—
437#123C22×D47132yescomplemented
438C22⋊Q8—4732no—
439C22⋊Q8—4732no—
440C22⋊Q8—4732no—
441C22⋊Q8—4732no—
442C22⋊Q8—4732no—
443C22⋊Q8—4732no—
444C22⋊Q8—4732no—
445C22⋊Q8C22×D47132yescomplemented
446#121—4732no—
447#121—4732no—
448#121—4732no—
449#121—4732no—
450#121—4732no—
451#121—4732no—
452#121—4732no—
453#121C22×D47132yescomplemented
454C2×C4⋊C4—474no—
455C2×C4⋊C4—474no—
456C2×C4⋊C4—474no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—472no—
462C2×C4⋊C4—4732no—
463C2×C4⋊C4—4732no—
464C2×C4⋊C4—4716no—
465C2×C4⋊C4C22×D4714yes—
466C2×C4⋊C4C22×D4714yes—
467C2×C4⋊C4C22×D4712yes—
468C2×C22⋊C4—474no—
469C2×C22⋊C4—474no—
470C2×C22⋊C4—474no—
471C2×C22⋊C4—474no—
472C2×C22⋊C4—474no—
473C2×C22⋊C4—474no—
474C2×C22⋊C4—474no—
475C2×C22⋊C4—474no—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—4732no—
478C2×C22⋊C4—4732no—
479C2×C22⋊C4—4732no—
480C2×C22⋊C4C22×D4714yes—
481C2×C22⋊C4C22×D4714yes—
482C2×C22⋊C4C22×D4714yes—
483C2×C42—472no—
484C2×C42—471no—
485C2×C42—478no—
486C2×C42C22×D4711yescharacteristic
487C24—471no—
488C24—4716no—
489C24—474no—
490C24—9416no—
491C24—9416no—
492C24—9416no—
493C24C23×D4714yes—
494C2×Q8—44no—
495C2×Q8—4716no—
496C2×Q8—478no—
497C2×Q8—1888no—
498C2×Q8—1884no—
499C2×Q8—18832no—
500C2×Q8C23×D4718yes—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—4716no—
504C2×D4—4716no—
505C2×D4—4716no—
506C2×D4—4716no—
507C2×D4—478no—
508C2×D4—1888no—
509C2×D4—1884no—
510C2×D4—18864no—
511C2×D4—18832no—
512C2×D4—1888no—
513C2×D4—1888no—
514C2×D4—1888no—
515C2×D4C23×D47116yes—
516C2×D4C23×D4718yes—
517C22×C4—48no—
518C22×C4—471no—
519C22×C4—472no—
520C22×C4—474no—
521C22×C4—474no—
522C22×C4—4716no—
523C22×C4—474no—
524C22×C4—478no—
525C22×C4—4716no—
526C22×C4—4716no—
527C22×C4—4716no—
528C22×C4—4716no—
529C22×C4—944no—
530C22×C4—9416no—
531C22×C4—9416no—
532C22×C4—948no—
533C22×C4—1888no—
534C22×C4—1888no—
535C22×C4—18864no—
536C22×C4—1888no—
537C22×C4C23×D4711yescharacteristic
538C22×C4C23×D4712yes—
539C22×C4C23×D4714yes—
540C22×C4C23×D4714yes—
541C22×C4C23×D47116yes—
542C4⋊C4—4716no—
543C4⋊C4—4716no—
544C4⋊C4—4716no—
545C4⋊C4—4716no—
546C4⋊C4—4716no—
547C4⋊C4—4716no—
548C4⋊C4—4716no—
549C4⋊C4—478no—
550C4⋊C4C23×D47116yes—
551C4⋊C4C23×D47116yes—
552C4⋊C4C23×D4718yes—
553C22⋊C4—4716no—
554C22⋊C4—4716no—
555C22⋊C4—4716no—
556C22⋊C4—4716no—
557C22⋊C4—4716no—
558C22⋊C4—4716no—
559C22⋊C4—4716no—
560C22⋊C4—4716no—
561C22⋊C4—4716no—
562C22⋊C4C23×D47116yes—
563C22⋊C4C23×D47116yes—
564C22⋊C4C23×D47116yes—
565C42—478no—
566C42—474no—
567C42C23×D4714yes—
568C23—28no—
569C23—28no—
570C23—28no—
571C23—478no—
572C23—474no—
573C23—472no—
574C23—478no—
575C23—9432no—
576C23—9432no—
577C23—9432no—
578C23—948no—
579C23—948no—
580C23—948no—
581C23—18864no—
582C23C24×D4718yes—
583C23C24×D4711yescharacteristic
584Q8—48no—
585Q8—18816no—
586Q8—1888no—
587D4—416no—
588D4—48no—
589D4—18816no—
590D4—1888no—
591D4—18816no—
592D4—18816no—
593D4—18816no—
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—416no—
599C2×C4—472no—
600C2×C4—474no—
601C2×C4—478no—
602C2×C4—478no—
603C2×C4—948no—
604C2×C4—9432no—
605C2×C4—9432no—
606C2×C4—9416no—
607C2×C4—948no—
608C2×C4—948no—
609C2×C4—944no—
610C2×C4—942no—
611C2×C4—18816no—
612C2×C4—18816no—
613C2×C4—18816no—
614C2×C4C24×D4712yes—
615C2×C4C24×D4714yes—
616C2×C4C24×D4718yes—
617C2×C4C24×D4718yes—
618C22—28no—
619C22—28no—
620C22—28no—
621C22—416no—
622C22—478no—
623C22—474no—
624C22—4716no—
625C22—948no—
626C22—948no—
627C22—948no—
628C22—18864no—
629C22—18816no—
630C22H(5,𝔽2)×D4714yes—
631C222−1+4×D4712yes—
632C22C25×D4711yescharacteristic
633C4—28no—
634C4—28no—
635C4—24no—
636C4—22no—
637C4—948no—
638C4—948no—
639C4—944no—
640C4—942no—
641C2—48no—
642C2—478no—
643C2—1888no—
644C2#562×D4714yesdirect product factor
645C2C2×H(5,𝔽2)×D4712yes—
646C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#562C2
socleC23×C47C25
hypercenterC2×#562D47
hypocenterC47C22×#562
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#562

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#15689871C2semidirect
2. C2×#15689870C2semidirect
3. C2×#15689869C2semidirect
4. C2×#15689868C2semidirect
5. C2×#15689867C2semidirect
6. #562×D47C2direct (N × H)
7. C2×#125×D47C2semidirect
8. C2×#124×D47C2semidirect
9. C2×#123×D47C2semidirect
10. C2×C22⋊Q8×D47C2semidirect
11. C2×#121×D47C2semidirect
12. C2×C47×#562C2semidirect
17. #15689871C22semidirect
18. #15689870C22semidirect
19. #15689869C22semidirect
20. #15689868C22semidirect
21. #15689867C22semidirect
22. C2×#13094016C22semidirect
23. C2×#13094015C22semidirect
24. C2×#13094014C22semidirect
25. #125×D47C22semidirect
26. C2×#13094013C22semidirect
27. C2×#13094012C22semidirect
28. C2×#13094011C22semidirect
29. C2×#13094010C22semidirect
30. C2×#13094010C22semidirect
31. #124×D47C22semidirect
32. C2×#13094009C22semidirect
33. C2×#13094009C22semidirect
34. C2×#13094008C22semidirect
35. C2×#13094007C22semidirect
36. C2×#13094006C22semidirect
37. C2×#13094006C22semidirect
38. C2×#13094005C22semidirect
39. #123×D47C22semidirect
40. C2×#13094004C22semidirect
41. C2×#13094003C22semidirect
42. C2×#13094002C22semidirect
43. C2×#13094002C22semidirect
44. C2×#13094001C22semidirect
45. C2×#13094001C22semidirect
46. C2×#13094000C22semidirect
47. C22⋊Q8×D47C22semidirect
48. C2×#13093999C22semidirect
49. C2×#13093998C22semidirect
50. C2×#13093997C22semidirect
51. C2×#13093997C22semidirect
52. C2×#13093996C22semidirect
53. C2×#13093996C22semidirect
54. C2×#13093995C22semidirect
55. #121×D47C22semidirect
63. C47×#562C22semidirect
64. C2×#125×C47C22semidirect
65. C2×#124×C47C22semidirect
66. C2×#123×C47C22semidirect
67. C2×C22⋊Q8×C47C22semidirect
68. C2×#121×C47C22semidirect
92. #13094016C23semidirect
93. #13094015C23semidirect
94. #13094014C23semidirect
95. #13094013C23semidirect
96. #13094012C23semidirect
97. #13094011C23semidirect
98. #13094010C23semidirect
99. #13094010C23semidirect
100. #13094009C23semidirect
101. #13094009C23semidirect
102. #13094008C23semidirect
103. #13094007C23semidirect
104. #13094006C23semidirect
105. #13094006C23semidirect
106. #13094005C23semidirect
107. #13094004C23semidirect
108. #13094003C23semidirect
109. #13094002C23semidirect
110. #13094002C23semidirect
111. #13094001C23semidirect
112. #13094001C23semidirect
113. #13094000C23semidirect
114. #13093999C23semidirect
115. #13093998C23semidirect
116. #13093997C23semidirect
117. #13093997C23semidirect
118. #13093996C23semidirect
119. #13093996C23semidirect
120. #13093995C23semidirect
151. #125×C47C23semidirect
152. #124×C47C23semidirect
153. #123×C47C23semidirect
154. C22⋊Q8×C47C23semidirect
155. #121×C47C23semidirect
307. C2×D47#562direct (N × H)
324. C2×#562D47direct (N × H)
331. C2×C47C2×#562semidirect
335. D47C2×#562direct (N × H)
345. #562C2×D47direct (N × H)
350. C2×#125C2×D47semidirect
357. C2×#124C2×D47semidirect
366. C2×#123C2×D47semidirect
375. C2×C22⋊Q8C2×D47semidirect
384. C2×#121C2×D47semidirect
392. C47C22×#562semidirect
423. #125C22×D47semidirect
429. #124C22×D47semidirect
437. #123C22×D47semidirect
445. C22⋊Q8C22×D47semidirect
453. #121C22×D47semidirect
644. C2#562×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898712
C2×#156898702
C2×#156898692
C2×#156898682
C2×#156898672
#562×D472
C2×#125×D472
C2×#124×D472
C2×#123×D472
C2×C22⋊Q8×D472
C2×#121×D472
C2×C47×#5622
C22×#56247