Finite Group Databasebeta

← C2×#20256779 #27123133

Subgroups — C2×#20256779 #27123133

Order 12032.

7302 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256779C2132yesmaximal, direct product factor
2C2×#15689746C212yesmaximal, complemented
3C2×#15689745C212yesmaximal, complemented
4C2×#15689734C211yesmaximal, characteristic, complemented
5C2×#15689729C211yesmaximal, characteristic, complemented
6C2×#15689728C211yesmaximal, characteristic, complemented
7C2×#15689721C214yesmaximal, complemented
8C2×#15689712C214yesmaximal, complemented
9C2×#15689679C211yesmaximal, characteristic, complemented
10C2×#15689674C211yesmaximal, characteristic, complemented
11C2×#15689658C214yesmaximal, complemented
12C2×#15689656C214yesmaximal, complemented
13C2×#15689636C212yesmaximal, complemented
14C2×C4×#10625354C212yesmaximal, complemented
15C2×#117×D47C211yesmaximal, characteristic, complemented
16C2×C47×#541C211yesmaximal, characteristic, complemented
17C22×#10625354C2212yes—
18C23×C4×D47C2211yescharacteristic
19#15689746C22132yescomplemented
20#15689745C22132yescomplemented
21#15689734C22116yescomplemented
22#15689729C22116yescomplemented
23#15689728C22116yescomplemented
24#15689721C22164yescomplemented
25#15689712C22164yescomplemented
26#15689679C22116yescomplemented
27#15689674C22116yescomplemented
28C2×#13094023C2212yescomplemented
29C2×#13094021C2211yescharacteristic, complemented
30#15689658C22164yescomplemented
31#15689656C22164yescomplemented
32C2×#13094019C2214yes—
33C2×#13094019C2214yescomplemented
34C2×#13094018C2214yescomplemented
35C2×#13094016C2211yescharacteristic, complemented
36C2×#13094014C2214yescomplemented
37C2×#13094013C2212yescomplemented
38C2×#13094012C2214yes—
39C2×#13094010C2214yes—
40#15689636C22132yescomplemented
41C2×#13094009C2214yes—
42C2×#13094009C2214yes—
43C2×#13094009C2214yescomplemented
44C2×#13094009C2214yescomplemented
45C2×#13094006C2214yes—
46C2×#13094004C2214yescomplemented
47C2×#13094002C2214yes—
48C2×#13094002C2214yescomplemented
49C2×#13094000C2212yes—
50C2×#13093999C2212yes—
51C2×#13093999C2214yes—
52C2×#13093999C2214yes—
53C2×#13093998C2212yes—
54C2×#13093997C2214yes—
55C2×#13093994C2214yes—
56C4×#10625354C22132yescomplemented
57C2×Q8×Dic47C2212yescomplemented
58C2×#13093989C2214yescomplemented
59C2×C4×D188C2214yes—
60C2×C4×D188C2212yescomplemented
61C2×#13093986C2214yes—
62C2×#13093986C2214yes—
63C2×#13093986C2212yescomplemented
64C2×#13093986C2214yescomplemented
65C2×(C22⋊D47)⋊C4C2214yes—
66C2×#13093983C2211yescharacteristic
67C2×#13093982C2212yes—
68C2×#13093982C2212yes—
69C2×#13093982C2214yescomplemented
70C2×#13093981C2211yescharacteristic
71C2×#13093981C2211yescharacteristic
72C2×#13093980C2212yes—
73#117×D47C22116yescomplemented
74C2×C4⋊C4×D47C2212yes—
75C2×C22⋊C4×D47C2212yes—
76C2×C42×D47C2211yescharacteristic
77C2×C42×D47C2211yescharacteristic
78C2×C42×D47C2214yescomplemented
79C47×#541C22116yescomplemented
80C2×C4⋊Q8×C47C2211yescharacteristic, complemented
81C2×#126×C47C2214yes—
82C2×#125×C47C2214yescomplemented
83C2×#125×C47C2211yescharacteristic, complemented
84C2×C22⋊Q8×C47C2212yes—
85C2×C4×Q8×C47C2212yescomplemented
86C2×#117×C47C2211yescharacteristic
87C24×D47C2311yescharacteristic
88C2×#10625354—216no—
89C2×#10625354C23116yes—
90C22×Dic94C2314yes—
91C22×D188C2314yes—
92C22×D188C2312yes—
93C22×D188C2314yes—
94C22×D188C2314yes—
95C22×C22⋊D47C2314yes—
96C23×Dic47C2311yescharacteristic
97C22×C4×D47—28no—
98C22×C4×D47C2314yes—
99C22×C4×D47C2311yescharacteristic
100C22×C4×D47C2318yes—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2311yescharacteristic
103C22×C4×D47C2312yes—
104C22×C4×D47C2312yes—
105C22×C4×D47C2314yes—
106C22×C4×D47C2314yes—
107C22×C4×D47C2311yescharacteristic
108#13094023C23116yescomplemented
109#13094021C2318yescomplemented
110#13094019C23132yes—
111#13094019C23132yescomplemented
112#13094018C23132yescomplemented
113#13094016C2318yescomplemented
114#13094014C23132yescomplemented
115#13094013C23116yescomplemented
116#13094012C23132yes—
117#13094010C23132yes—
118#13094009C23132yes—
119#13094009C23132yes—
120#13094009C23132yescomplemented
121#13094009C23132yescomplemented
122#13094006C23132yes—
123#13094004C23132yescomplemented
124#13094002C23132yes—
125#13094002C23132yescomplemented
126#13094000C23116yes—
127#13093999C23116yes—
128#13093999C23132yes—
129#13093999C23132yes—
130#13093998C23116yes—
131#13093997C23132yes—
132#13093994C23132yes—
133Q8×Dic47C23116yescomplemented
134#13093989C23132yescomplemented
135C4×D188C23132yes—
136C4×D188C23116yescomplemented
137#13093986C23132yes—
138#13093986C23132yes—
139#13093986C23116yescomplemented
140#13093986C23132yescomplemented
141(C22⋊D47)⋊C4C23132yes—
142#13093983C2318yes—
143#13093982C23116yes—
144#13093982C23116yes—
145#13093982C23132yescomplemented
146#13093981C2318yes—
147#13093981C2318yes—
148#13093980C23116yes—
149C2×C4⋊Dic47C2312yes—
150C2×C4⋊Dic47C2312yes—
151C2×C4⋊Dic47C2314yes—
152C2×Dic47⋊C4C2312yes—
153C2×Dic47⋊C4C2312yes—
154C2×Dic47⋊C4C2314yes—
155C2×Dic47⋊C4C2314yes—
156C2×Dic47⋊C4C2314yes—
157C4⋊C4×D47C23116yes—
158C2×C22⋊Dic47C2312yes—
159C2×(C2×D47)⋊C4C2312yes—
160C2×(C2×D47)⋊C4C2312yes—
161C2×(C2×D47)⋊C4C2314yes—
162C2×(C2×D47)⋊C4C2314yes—
163C2×(C2×D47)⋊C4C2314yes—
164C2×(C2×D47)⋊C4C2314yes—
165C2×(C2×D47)⋊C4C2314yes—
166C2×(C2×D47)⋊C4C2314yes—
167C2×(C2×D47)⋊C4C2314yes—
168C2×(C2×D47)⋊C4C2314yes—
169C22⋊C4×D47C23116yes—
170C2×C4×Dic47C2312yes—
171C2×C4×Dic47C2312yes—
172C2×C4×Dic47C2311yescharacteristic
173C2×C4×Dic47C2311yescharacteristic
174C2×C4×Dic47C2314yes—
175C2×C4×Dic47C2314yes—
176C42×D47C2318yes—
177C42×D47C2318yes—
178C42×D47C23132yescomplemented
179C22×Q8×C47C2312yes—
180C23×C4×C47C2311yescharacteristic
181C4⋊Q8×C47C2318yescomplemented
182#126×C47C23132yes—
183#125×C47C2318yescomplemented
184#125×C47C23132yescomplemented
185C22⋊Q8×C47C23116yes—
186C4×Q8×C47C23116yescomplemented
187#117×C47C2318yes—
188C2×C4⋊C4×C47C2312yes—
189C2×C4⋊C4×C47C2312yes—
190C2×C4⋊C4×C47C2314yes—
191C2×C4⋊C4×C47C2314yes—
192C2×C4⋊C4×C47C2314yes—
193C2×C4⋊C4×C47C2314yes—
194C2×C22⋊C4×C47C2312yes—
195C2×C22⋊C4×C47C2314yes—
196C2×C42×C47C2311yescharacteristic
197C2×C42×C47C2311yescharacteristic
198C2×C42×C47C2314yes—
199C24×C47C2411yescharacteristic
200C23×D47—24no—
201C23×D47—44no—
202C23×D47C2411yescharacteristic
203C23×D47C2414yes—
204C23×D47C2411yescharacteristic
205C23×D47C2414yes—
206C2×Q8×C47—28no—
207C2×Q8×C47C2418yes—
208C22×C4×C47—24no—
209C22×C4×C47C2412yes—
210C22×C4×C47C2414yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2414yes—
213C22×C4×C47C2411yescharacteristic
214C22×C4×C47C2414yes—
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—48no—
217C2×C22⋊D47C24116yes—
218C22×Dic47—24no—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2414yes—
222C22×Dic47C2411yescharacteristic
223C22×Dic47C2414yes—
224C22×Dic47C2411yescharacteristic
225#10625354—264no—
226C2×D188—216no—
227C2×D188—28no—
228C2×D188—48no—
229C2×D188—48no—
230C2×D188C24116yes—
231C2×D188C2418yes—
232C2×D188C24116yes—
233C2×D188C24116yes—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—24no—
237C2×C4×D47—216no—
238C2×C4×D47—232no—
239C2×C4×D47—44no—
240C2×C4×D47—48no—
241C2×C4×D47—48no—
242C2×C4×D47—44no—
243C2×C4×D47#4118yes—
244C2×C4×D47C24116yes—
245C2×C4×D47C2414yes—
246C2×C4×D47C2414yes—
247C2×C4×D47C2414yes—
248C2×C4×D47C2418yes—
249C2×C4×D47C2418yes—
250C2×C4×D47C24116yes—
251C2×C4×D47C24116yes—
252C2×C4×D47C2414yes—
253C2×Dic94—48no—
254C2×Dic94C24116yes—
255C4⋊C4×C47C2418yes—
256C4⋊C4×C47C2418yes—
257C4⋊C4×C47C24116yes—
258C4⋊C4×C47C24116yes—
259C4⋊C4×C47C24116yes—
260C4⋊C4×C47C24116yes—
261C22⋊C4×C47C2418yes—
262C22⋊C4×C47C24116yes—
263C42×C47C2414yes—
264C42×C47C2414yes—
265C42×C47C24116yes—
266C22⋊Dic47C2418yes—
267(C2×D47)⋊C4C2418yes—
268(C2×D47)⋊C4C2418yes—
269(C2×D47)⋊C4C24116yes—
270(C2×D47)⋊C4C24116yes—
271(C2×D47)⋊C4C24116yes—
272(C2×D47)⋊C4C24116yes—
273(C2×D47)⋊C4C24116yes—
274(C2×D47)⋊C4C24116yes—
275(C2×D47)⋊C4C24116yes—
276(C2×D47)⋊C4C24116yes—
277C4⋊Dic47C2418yes—
278C4⋊Dic47C2418yes—
279C4⋊Dic47C24116yes—
280Dic47⋊C4C2418yes—
281Dic47⋊C4C2418yes—
282Dic47⋊C4C24116yes—
283Dic47⋊C4C24116yes—
284Dic47⋊C4C24116yes—
285C4×Dic47C2418yes—
286C4×Dic47C2418yes—
287C4×Dic47C2414yes—
288C4×Dic47C2414yes—
289C4×Dic47C24116yes—
290C4×Dic47C24116yes—
291C23×C47—22no—
292C23×C47—24no—
293C23×C47C2512yes—
294C23×C47C2511yescharacteristic
295C22×D47—24no—
296C22×D47—22no—
297C22×D47—28no—
298C22×D47—28no—
299C22×D47—28no—
300C22×D47—24no—
301C22×D47—28no—
302C22×D47—48no—
303C22×D47—416no—
304C22×D47C2×#4114yes—
305C22×D47C2512yes—
306C22×D47C2518yes—
307C22×D47C2512yes—
308Q8×C47—216no—
309C2×C4×C47—22no—
310C2×C4×C47—28no—
311C2×C4×C47—28no—
312C2×C4×C47—24no—
313C2×C4×C47—24no—
314C2×C4×C47—28no—
315C2×C4×C47C2×#4114yes—
316C2×C4×C47C2514yes—
317C2×C4×C47C2518yes—
318C2×C4×C47C2514yes—
319C2×C4×C47C2518yes—
320C2×C4×C47C2512yes—
321C2×C4×C47C2512yes—
322C22⋊D47—416no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—28no—
326C2×Dic47—24no—
327C2×Dic47—28no—
328C2×Dic47C2×#4114yes—
329C2×Dic47C2514yes—
330C2×Dic47C2518yes—
331C2×Dic47C2514yes—
332C2×Dic47C2512yes—
333C2×Dic47C2512yes—
334D188—232no—
335D188—216no—
336D188—416no—
337D188—416no—
338C4×D47—28no—
339C4×D47—28no—
340C4×D47—28no—
341C4×D47—232no—
342C4×D47—48no—
343C4×D47—416no—
344C4×D47—416no—
345C4×D47—48no—
346C4×D47C2×#41116yes—
347Dic94—416no—
348C2×#3455—471nomaximal, Sylow
349C22×C47—22no—
350C22×C47—24no—
351C22×C47—44no—
352C22×C47C22×#4112yes—
353C22×C47#58514yes—
354C22×C47C2611yescharacteristic
355C2×D47—24no—
356C2×D47—28no—
357C2×D47—22no—
358C2×D47—28no—
359C2×D47—28no—
360C2×D47—28no—
361C2×D47—24no—
362C2×D47—416no—
363C2×D47—416no—
364C2×D47—44no—
365C2×D47C22×#4114yes—
366C4×C47—22no—
367C4×C47—28no—
368C4×C47—28no—
369C4×C47—24no—
370C4×C47—24no—
371C4×C47C22×#4114yes—
372Dic47—22no—
373Dic47—24no—
374Dic47—28no—
375Dic47—24no—
376Dic47C22×#4114yes—
377#3455—4732no—
378C2×#542—472no—
379C2×#542—472no—
380C2×#541—471no—
381C2×#541D4711yescharacteristic, complemented
382C2×#540—471no—
383C2×#540—471no—
384C2×#539—474no—
385C2×#538—474no—
386C2×#533—471no—
387C2×#532—471no—
388C2×#529—474no—
389C2×#529—474no—
390C2×#525—472no—
391C2×C4×#41—472no—
392C22×#117—471no—
393C2×C47—42no—
394C2×C47#345514yescomplemented
395C2×C47C23×#4111yescharacteristic
396C2×C47C2×#58512yes—
397D47—24no—
398D47—48no—
399D47—42no—
400C22×#41—472no—
401C24×C4—471no—
402#542—4732no—
403#542—4732no—
404#541—4716no—
405#541C2×D47116yescomplemented
406#540—4716no—
407#540—4716no—
408#539—4764no—
409#538—4764no—
410#533—4716no—
411#532—4716no—
412C2×C4⋊Q8—472no—
413C2×C4⋊Q8C2×D4711yescharacteristic, complemented
414C2×#127—471no—
415#529—4764no—
416#529—4764no—
417C2×#126—474no—
418C2×#126—474no—
419C2×#126—474no—
420C2×#126C2×D4714yes—
421C2×#125—474no—
422C2×#125—471no—
423C2×#125C2×D4714yescomplemented
424C2×#125C2×D4711yescharacteristic, complemented
425C2×#124—472no—
426C2×#124—474no—
427C2×#124—474no—
428#525—4732no—
429C2×#123—474no—
430C2×#123—474no—
431C2×#123—474no—
432C2×#123—474no—
433C2×#123—474no—
434C2×C22⋊Q8—472no—
435C2×C22⋊Q8—474no—
436C2×C22⋊Q8—474no—
437C2×C22⋊Q8—474no—
438C2×C22⋊Q8C2×D4712yes—
439C2×#121—472no—
440C2×#121—472no—
441C2×#121—474no—
442C2×#121—474no—
443C2×#121—474no—
444C2×#120—474no—
445C4×#41—4732no—
446C2×C4×Q8—472no—
447C2×C4×Q8—474no—
448C2×C4×Q8C2×D4712yescomplemented
449C2×C4×D4—474no—
450C2×C4×D4—472no—
451C2×C4×D4—474no—
452C2×C4×D4—474no—
453C2×C4×D4—474no—
454C2×C4×D4—474no—
455C2×C4×D4—472no—
456C2×#117—471no—
457C2×#117—4716no—
458C2×#117—472no—
459C2×#117—472no—
460C2×#117—474no—
461C2×#117—472no—
462C2×#117—471no—
463C2×#117—471no—
464C2×#117C2×D4711yescharacteristic
465C22×C4⋊C4—472no—
466C22×C22⋊C4—472no—
467C22×C42—471no—
468C22×C42—471no—
469C22×C42—474no—
470C47C2×#345511yescharacteristic, complemented, Sylow
471C25—471no—
472C2×#41—4716no—
473C2×#41—9416no—
474C22×Q8—474no—
475C22×Q8C22×D4712yes—
476C22×D4—474no—
477C22×D4—474no—
478C22×D4—472no—
479C22×D4—474no—
480C22×D4—474no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—478no—
487C23×C4—474no—
488C23×C4—472no—
489C23×C4—472no—
490C23×C4—474no—
491C23×C4—474no—
492C23×C4—948no—
493C23×C4C22×D4711yescharacteristic
494C4⋊Q8—4716no—
495C4⋊Q8C22×D4718yescomplemented
496#127—478no—
497#126—4732no—
498#126—4732no—
499#126—4732no—
500#126C22×D47132yes—
501#125—4732no—
502#125—478no—
503#125C22×D47132yescomplemented
504#125C22×D4718yescomplemented
505#124—4716no—
506#124—4732no—
507#124—4732no—
508#123—4732no—
509#123—4732no—
510#123—4732no—
511#123—4732no—
512#123—4732no—
513C22⋊Q8—4716no—
514C22⋊Q8—4732no—
515C22⋊Q8—4732no—
516C22⋊Q8—4732no—
517C22⋊Q8C22×D47116yes—
518#121—4716no—
519#121—4716no—
520#121—4732no—
521#121—4732no—
522#121—4732no—
523#120—4732no—
524C4×Q8—4716no—
525C4×Q8—4732no—
526C4×Q8C22×D47116yescomplemented
527C4×D4—4732no—
528C4×D4—4716no—
529C4×D4—4732no—
530C4×D4—4732no—
531C4×D4—4732no—
532C4×D4—4732no—
533C4×D4—4716no—
534#117—478no—
535#117—4716no—
536#117—4716no—
537#117—4732no—
538#117—4716no—
539#117—478no—
540#117—478no—
541#117C22×D4718yes—
542C2×C4⋊C4—472no—
543C2×C4⋊C4—472no—
544C2×C4⋊C4—472no—
545C2×C4⋊C4—472no—
546C2×C4⋊C4—474no—
547C2×C4⋊C4—474no—
548C2×C4⋊C4—474no—
549C2×C4⋊C4—474no—
550C2×C4⋊C4—4716no—
551C2×C4⋊C4C22×D4712yes—
552C2×C4⋊C4C22×D4712yes—
553C2×C4⋊C4C22×D4714yes—
554C2×C4⋊C4C22×D4714yes—
555C2×C4⋊C4C22×D4714yes—
556C2×C4⋊C4C22×D4714yes—
557C2×C22⋊C4—472no—
558C2×C22⋊C4—472no—
559C2×C22⋊C4—472no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C22⋊C4—474no—
563C2×C22⋊C4—474no—
564C2×C22⋊C4—474no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—474no—
567C2×C22⋊C4—474no—
568C2×C22⋊C4—4716no—
569C2×C22⋊C4C22×D4712yes—
570C2×C22⋊C4C22×D4714yes—
571C2×C42—472no—
572C2×C42—472no—
573C2×C42—474no—
574C2×C42—471no—
575C2×C42—471no—
576C2×C42—474no—
577C2×C42—478no—
578C2×C42—478no—
579C2×C42—4732no—
580C2×C42C22×D4711yescharacteristic
581C2×C42C22×D4711yescharacteristic
582C2×C42C22×D4714yes—
583C24—471no—
584C24—471no—
585C24—474no—
586C24—474no—
587C24—944no—
588C24—1884no—
589C24C23×D4711yescharacteristic
590#41—9464no—
591C2×Q8—28no—
592C2×Q8—4716no—
593C2×Q8—1888no—
594C2×Q8C23×D4718yes—
595C2×D4—4716no—
596C2×D4—4716no—
597C2×D4—478no—
598C2×D4—4716no—
599C2×D4—4716no—
600C2×D4—9416no—
601C2×D4—948no—
602C2×D4—1888no—
603C2×D4—1888no—
604C2×D4—1888no—
605C22×C4—24no—
606C22×C4—471no—
607C22×C4—478no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—472no—
611C22×C4—472no—
612C22×C4—474no—
613C22×C4—471no—
614C22×C4—4716no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—474no—
618C22×C4—478no—
619C22×C4—478no—
620C22×C4—4716no—
621C22×C4—4716no—
622C22×C4—944no—
623C22×C4—9432no—
624C22×C4—9416no—
625C22×C4—944no—
626C22×C4—944no—
627C22×C4—944no—
628C22×C4—1884no—
629C22×C4—1888no—
630C22×C4—1884no—
631C22×C4—1888no—
632C22×C4C23×D4714yes—
633C22×C4C23×D4712yes—
634C22×C4C23×D4714yes—
635C22×C4C23×D4714yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638C22×C4C23×D4711yescharacteristic
639C4⋊C4—478no—
640C4⋊C4—478no—
641C4⋊C4—4716no—
642C4⋊C4—4716no—
643C4⋊C4—4716no—
644C4⋊C4—478no—
645C4⋊C4—478no—
646C4⋊C4—4716no—
647C4⋊C4C23×D4718yes—
648C4⋊C4C23×D4718yes—
649C4⋊C4C23×D47116yes—
650C4⋊C4C23×D47116yes—
651C4⋊C4C23×D47116yes—
652C4⋊C4C23×D47116yes—
653C22⋊C4—478no—
654C22⋊C4—478no—
655C22⋊C4—478no—
656C22⋊C4—4716no—
657C22⋊C4—4716no—
658C22⋊C4—4716no—
659C22⋊C4—4716no—
660C22⋊C4—4716no—
661C22⋊C4—4716no—
662C22⋊C4—4716no—
663C22⋊C4—4716no—
664C22⋊C4C23×D4718yes—
665C22⋊C4C23×D47116yes—
666C42—478no—
667C42—478no—
668C42—4716no—
669C42—474no—
670C42—474no—
671C42—4716no—
672C42C23×D4714yes—
673C42C23×D4714yes—
674C42C23×D47116yes—
675C23—22no—
676C23—24no—
677C23—474no—
678C23—472no—
679C23—472no—
680C23—478no—
681C23—948no—
682C23—944no—
683C23—942no—
684C23—948no—
685C23—948no—
686C23—948no—
687C23—944no—
688C23—1888no—
689C23—18816no—
690C23C24×D4712yes—
691C23C24×D4711yescharacteristic
692Q8—216no—
693Q8—18816no—
694D4—9432no—
695D4—9416no—
696D4—18816no—
697D4—18816no—
698D4—18816no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—474no—
706C2×C4—472no—
707C2×C4—4716no—
708C2×C4—474no—
709C2×C4—474no—
710C2×C4—478no—
711C2×C4—472no—
712C2×C4—948no—
713C2×C4—9432no—
714C2×C4—948no—
715C2×C4—948no—
716C2×C4—942no—
717C2×C4—944no—
718C2×C4—948no—
719C2×C4—944no—
720C2×C4—948no—
721C2×C4—1888no—
722C2×C4—18816no—
723C2×C4—1888no—
724C2×C4—18816no—
725C2×C4#41×D4714yes—
726C2×C4C24×D4714yes—
727C2×C4C24×D4718yes—
728C2×C4C24×D4718yes—
729C2×C4C24×D4714yes—
730C2×C4C24×D4712yes—
731C2×C4C24×D4712yes—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—474no—
736C22—948no—
737C22—944no—
738C22—942no—
739C22—948no—
740C22—948no—
741C22—948no—
742C22—944no—
743C22—18816no—
744C22—1884no—
745C22—18816no—
746C22C2×#41×D4712yes—
747C22#1568996014yes—
748C22C25×D4711yescharacteristic
749C4—22no—
750C4—28no—
751C4—24no—
752C4—24no—
753C4—28no—
754C4—474no—
755C4—942no—
756C4—944no—
757C4—948no—
758C4—944no—
759C4C2×#41×D4714yes—
760C2—42no—
761C2—944no—
762C2—1882no—
763C2—1888no—
764C2#2025677914yesdirect product factor
765C2C22×#41×D4711yescharacteristic
766C2C2×#1568996012yes—
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#541C2
socleC23×C47C25
hypercenterC2×#541D47
hypocenterC47C2×#3455
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #20256779C2direct (N × H)
2. C2×#15689746C2semidirect
3. C2×#15689745C2semidirect
4. C2×#15689734C2semidirect
5. C2×#15689729C2semidirect
6. C2×#15689728C2semidirect
7. C2×#15689721C2semidirect
8. C2×#15689712C2semidirect
9. C2×#15689679C2semidirect
10. C2×#15689674C2semidirect
11. C2×#15689658C2semidirect
12. C2×#15689656C2semidirect
13. C2×#15689636C2semidirect
14. C2×C4×#10625354C2semidirect
15. C2×#117×D47C2semidirect
16. C2×C47×#541C2semidirect
19. #15689746C22semidirect
20. #15689745C22semidirect
21. #15689734C22semidirect
22. #15689729C22semidirect
23. #15689728C22semidirect
24. #15689721C22semidirect
25. #15689712C22semidirect
26. #15689679C22semidirect
27. #15689674C22semidirect
28. C2×#13094023C22semidirect
29. C2×#13094021C22semidirect
30. #15689658C22semidirect
31. #15689656C22semidirect
33. C2×#13094019C22semidirect
34. C2×#13094018C22semidirect
35. C2×#13094016C22semidirect
36. C2×#13094014C22semidirect
37. C2×#13094013C22semidirect
40. #15689636C22semidirect
43. C2×#13094009C22semidirect
44. C2×#13094009C22semidirect
46. C2×#13094004C22semidirect
48. C2×#13094002C22semidirect
56. C4×#10625354C22semidirect
57. C2×Q8×Dic47C22semidirect
58. C2×#13093989C22semidirect
60. C2×C4×D188C22semidirect
63. C2×#13093986C22semidirect
64. C2×#13093986C22semidirect
69. C2×#13093982C22semidirect
73. #117×D47C22semidirect
78. C2×C42×D47C22semidirect
79. C47×#541C22semidirect
80. C2×C4⋊Q8×C47C22semidirect
82. C2×#125×C47C22semidirect
83. C2×#125×C47C22semidirect
85. C2×C4×Q8×C47C22semidirect
108. #13094023C23semidirect
109. #13094021C23semidirect
111. #13094019C23semidirect
112. #13094018C23semidirect
113. #13094016C23semidirect
114. #13094014C23semidirect
115. #13094013C23semidirect
120. #13094009C23semidirect
121. #13094009C23semidirect
123. #13094004C23semidirect
125. #13094002C23semidirect
133. Q8×Dic47C23semidirect
134. #13093989C23semidirect
136. C4×D188C23semidirect
139. #13093986C23semidirect
140. #13093986C23semidirect
145. #13093982C23semidirect
178. C42×D47C23semidirect
181. C4⋊Q8×C47C23semidirect
183. #125×C47C23semidirect
184. #125×C47C23semidirect
186. C4×Q8×C47C23semidirect
381. C2×#541D47semidirect
394. C2×C47#3455semidirect
405. #541C2×D47semidirect
413. C2×C4⋊Q8C2×D47semidirect
423. C2×#125C2×D47semidirect
424. C2×#125C2×D47semidirect
448. C2×C4×Q8C2×D47semidirect
470. C47C2×#3455semidirect
495. C4⋊Q8C22×D47semidirect
503. #125C22×D47semidirect
504. #125C22×D47semidirect
526. C4×Q8C22×D47semidirect
764. C2#20256779direct (N × H)

Maximal subgroups

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

subgroupindex
#202567792
C2×#156897462
C2×#156897452
C2×#156897342
C2×#156897292
C2×#156897282
C2×#156897212
C2×#156897122
C2×#156896792
C2×#156896742
C2×#156896582
C2×#156896562
C2×#156896362
C2×C4×#106253542
C2×#117×D472
C2×C47×#5412
C2×#345547