Finite Group Databasebeta

← #27124852

Subgroups — #27124852

Order 12032.

7286 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#20257143C218yesmaximal, complemented
2#20257126C218yesmaximal, complemented
3#20257109C214yesmaximal, complemented
4#20257098C214yesmaximal, complemented
5#20257087C214yesmaximal, complemented
6#20257078C214yesmaximal, complemented
7#20256955C2116yesmaximal, complemented
8#20256780C214yesmaximal, complemented
9#20256721C211yesmaximal, characteristic, complemented
10#20256685C214yesmaximal, complemented
11C2×#15689635C212yesmaximal, complemented
12#20256589C212yesmaximal, complemented
13C2×#117×D47C211yesmaximal, characteristic, complemented
14C47×#3458C211yesmaximal, characteristic, complemented
15C22×#10625350C2212yes—
16C23×C4×D47C2211yescharacteristic
17#15689847C22116yescomplemented
18#15689839C22116yescomplemented
19#15689834C22116yescomplemented
20#15689826C22116yescomplemented
21#15689826C22116yescomplemented
22#15689815C22132yescomplemented
23#15689811C22116yescomplemented
24#15689811C22116yescomplemented
25#15689800C22132yescomplemented
26#15689800C22132yescomplemented
27#15689776C22116yescomplemented
28#15689764C22132yescomplemented
29#15689747C22116yescomplemented
30#15689736C2218yescomplemented
31#15689729C2218yescomplemented
32#15689722C22116yescomplemented
33#15689713C22116yescomplemented
34#15689704C2214yescomplemented
35#15689699C2214yescomplemented
36#15689692C2214yescomplemented
37#15689685C2214yes—
38#15689678C2218yescomplemented
39#15689674C2218yescomplemented
40#15689673C2214yescomplemented
41#15689660C22116yescomplemented
42#15689660C22132yescomplemented
43#15689659C22116yescomplemented
44#15689658C22116yescomplemented
45#15689636C22116yescomplemented
46#15689635C2218yes—
47#15689635C2218yes—
48#15689635C2214yescomplemented
49#15689635C2214yescomplemented
50#15689635C2214yescomplemented
51#15689635C2214yescomplemented
52#15689635C2218yescomplemented
53C2×#13094008C2214yes—
54C2×#13094004C2214yescomplemented
55C2×#13093999C2214yescomplemented
56C2×#13093994C2214yes—
57#15689604C2218yescomplemented
58#15689603C2218yescomplemented
59#15689600C2214yescomplemented
60#15689597C2214yescomplemented
61#15689596C2218yes—
62C4×#10625354C22116yescomplemented
63C4×#10625350C2218yescomplemented
64#15689591C2218yescomplemented
65C2×C4×D188C2218yescomplemented
66C2×#13093983C2211yescharacteristic
67C2×#13093982C2212yescomplemented
68C2×#13093981C2212yescomplemented
69C2×#13093980C2212yes—
70#117×D47C2218yescomplemented
71#117×D47C2218yescomplemented
72#117×D47C2218yescomplemented
73C2×C4⋊C4×D47C2212yescomplemented
74C2×C22⋊C4×D47C2212yes—
75C2×C42×D47C2212yescomplemented
76C47×#544C2214yescomplemented
77C47×#544C2218yescomplemented
78C47×#543C2214yes—
79C47×#533C2214yescomplemented
80C47×#533C2218yescomplemented
81C2×#117×C47C2211yescharacteristic
82C2×#117×C47C2212yes—
83C24×D47C2311yescharacteristic
84C2×#10625354C23116yes—
85C2×#10625350—216no—
86C2×#10625350C2314yes—
87C2×#10625350C2314yes—
88C2×#10625350C2314yes—
89C2×#10625350C2314yes—
90C22×Dic94C2312yes—
91C22×D188C2312yes—
92C22×D188C2318yes—
93C22×C22⋊D47C2314yes—
94C23×Dic47C2311yescharacteristic
95C22×C4×D47—28no—
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2311yescharacteristic
98C22×C4×D47C2314yes—
99C22×C4×D47C2314yes—
100C22×C4×D47C2314yes—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2311yescharacteristic
103C22×C4×D47C2314yes—
104#13094024C2314yescomplemented
105#13094021C2314yescomplemented
106#13094019C23132yes—
107#13094019C23132yescomplemented
108#13094019C23132yescomplemented
109#13094015C23132yescomplemented
110#13094015C23116yescomplemented
111#13094013C23132yes—
112#13094013C23116yescomplemented
113#13094012C2318yescomplemented
114#13094009C23132yes—
115#13094009C23132yes—
116#13094009C23132yescomplemented
117#13094008C23116yes—
118#13094008C23116yes—
119#13094008C2318yes—
120#13094008C2318yes—
121#13094004C2318yes—
122#13094004C2318yes—
123#13094004C2318yes—
124#13094004C2318yes—
125#13094004C23116yescomplemented
126#13094000C23116yes—
127#13094000C23132yescomplemented
128#13093999C2318yes—
129#13093999C23132yes—
130#13093999C23116yes—
131#13093999C2318yes—
132#13093999C2318yes—
133#13093999C2318yes—
134#13093999C23116yescomplemented
135#13093998C23116yes—
136#13093994C23116yes—
137#13093994C23116yes—
138#13093994C2318yes—
139#13093994C2318yes—
140Q8×Dic47C23116yescomplemented
141C4×Dic94C23116yescomplemented
142#13093989C23116yescomplemented
143C4×D188C23116yes—
144C4×D188C23116yes—
145C4×D188C23116yes—
146C4×D188C23116yes—
147C4×D188C23116yescomplemented
148C4×D188C23116yescomplemented
149#13093986C23132yes—
150#13093986C23116yescomplemented
151#13093986C23116yescomplemented
152C4×C22⋊D47C23132yes—
153(C22⋊D47)⋊C4C23132yes—
154#13093983C2314yes—
155#13093983C2314yes—
156#13093982C23116yes—
157#13093982C2318yes—
158#13093982C2318yes—
159#13093982C23132yescomplemented
160#13093982C23116yescomplemented
161#13093981C2318yes—
162#13093981C2318yes—
163#13093981C23116yescomplemented
164#13093980C23116yes—
165#13093980C23116yes—
166C2×C4⋊Dic47C2318yes—
167C2×C4⋊Dic47C2312yes—
168C2×Dic47⋊C4C2314yes—
169C4⋊C4×D47C2318yes—
170C4⋊C4×D47C2318yes—
171C4⋊C4×D47C23116yescomplemented
172C2×C22⋊Dic47C2312yes—
173C2×(C2×D47)⋊C4C2318yes—
174C2×(C2×D47)⋊C4C2318yes—
175C2×(C2×D47)⋊C4C2314yes—
176C22⋊C4×D47C23116yes—
177C22⋊C4×D47C23116yes—
178C2×C4×Dic47C2314yes—
179C2×C4×Dic47C2312yes—
180C42×D47C2318yes—
181C42×D47C2318yes—
182C42×D47C23116yescomplemented
183C23×C4×C47C2311yescharacteristic
184C4⋊Q8×C47C2318yescomplemented
185C4⋊Q8×C47C23116yescomplemented
186#125×C47C2318yescomplemented
187#125×C47C23116yescomplemented
188C22⋊Q8×C47C23132yes—
189C22⋊Q8×C47C23116yes—
190C4×Q8×C47C23116yescomplemented
191#117×C47C2314yes—
192#117×C47C2314yes—
193#117×C47C2314yes—
194#117×C47C2314yes—
195#117×C47C2314yes—
196#117×C47C2314yes—
197C2×C4⋊C4×C47C2312yes—
198C2×C4⋊C4×C47C2314yes—
199C2×C22⋊C4×C47C2312yes—
200C2×C22⋊C4×C47C2314yes—
201C2×C42×C47C2312yes—
202C2×C42×C47C2314yes—
203C24×C47C2411yescharacteristic
204C23×D47—24no—
205C23×D47—44no—
206C23×D47C2411yescharacteristic
207C23×D47C2414yes—
208C23×D47C2414yes—
209C23×D47C2411yescharacteristic
210C2×Q8×C47C24116yes—
211C22×C4×C47#4118yescomplemented
212C22×C4×C47C2414yes—
213C22×C4×C47C2418yes—
214C22×C4×C47C2411yescharacteristic
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C22×C4×C47C2412yes—
218C2×C22⋊D47—216no—
219C2×C22⋊D47C2418yes—
220C2×C22⋊D47C2418yes—
221C22×Dic47—24no—
222C22×Dic47C2411yescharacteristic
223C22×Dic47C2414yes—
224C22×Dic47C2414yes—
225C22×Dic47C2411yescharacteristic
226C22×Dic47C2414yes—
227#10625354—432no—
228#10625350—216no—
229#10625350—216no—
230#10625350—216no—
231#10625350—216no—
232C2×D188—28no—
233C2×D188—416no—
234C2×D188C24116yes—
235C2×D188C2414yes—
236C2×D188C2414yes—
237C2×D188C24116yes—
238C2×D188C24116yes—
239C2×C4×D47—216no—
240C2×C4×D47—216no—
241C2×C4×D47—24no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—24no—
245C2×C4×D47—216no—
246C2×C4×D47—48no—
247C2×C4×D47C2412yes—
248C2×C4×D47C2412yes—
249C2×C4×D47C2418yes—
250C2×C4×D47C2418yes—
251C2×C4×D47C2414yes—
252C2×C4×D47C2418yes—
253C2×C4×D47C2412yes—
254C2×C4×D47C2412yes—
255C2×C4×D47C2414yes—
256C2×C4×D47C2418yes—
257C2×C4×D47C24132yes—
258C2×Dic94—28no—
259C2×Dic94C2414yes—
260C2×Dic94C2414yes—
261C4⋊C4×C47C2418yes—
262C4⋊C4×C47C2418yes—
263C4⋊C4×C47C2418yes—
264C4⋊C4×C47C24116yes—
265C4⋊C4×C47C24132yes—
266C22⋊C4×C47C2418yes—
267C22⋊C4×C47C2418yes—
268C22⋊C4×C47C2418yes—
269C42×C47C2414yes—
270C42×C47C2418yes—
271C42×C47C2414yes—
272C42×C47C2418yes—
273C22⋊Dic47C2418yes—
274(C2×D47)⋊C4C24116yes—
275(C2×D47)⋊C4C24132yes—
276(C2×D47)⋊C4C24116yes—
277(C2×D47)⋊C4C24116yes—
278(C2×D47)⋊C4C24116yes—
279(C2×D47)⋊C4C24116yes—
280(C2×D47)⋊C4C24132yes—
281C4⋊Dic47C2418yes—
282C4⋊Dic47C24116yes—
283C4⋊Dic47C24116yes—
284C4⋊Dic47C24116yes—
285Dic47⋊C4C24116yes—
286Dic47⋊C4C24132yes—
287C4×Dic47C2414yes—
288C4×Dic47C2418yes—
289C4×Dic47C2418yes—
290C4×Dic47C2414yes—
291C4×Dic47C24132yes—
292C23×C47—42no—
293C23×C47C2×#4114yes—
294C23×C47C2512yes—
295C23×C47C2511yescharacteristic
296C22×D47—22no—
297C22×D47—24no—
298C22×D47—28no—
299C22×D47—22no—
300C22×D47—28no—
301C22×D47—28no—
302C22×D47—44no—
303C22×D47—42no—
304C22×D47—48no—
305C22×D47—416no—
306C22×D47C2512yes—
307C22×D47C2518yes—
308C22×D47C2512yes—
309Q8×C47—416no—
310C2×C4×C47—44no—
311C2×C4×C47—48no—
312C2×C4×C47C2×#4118yes—
313C2×C4×C47C2×#4118yes—
314C2×C4×C47C2×#4114yes—
315C2×C4×C47C2×#4114yes—
316C2×C4×C47C2518yes—
317C2×C4×C47C25116yes—
318C2×C4×C47C2511yescharacteristic
319C2×C4×C47C2512yes—
320C2×C4×C47C2511yescharacteristic
321C22⋊D47—216no—
322C22⋊D47—216no—
323C2×Dic47—28no—
324C2×Dic47—28no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—44no—
328C2×Dic47C2518yes—
329C2×Dic47C2512yes—
330C2×Dic47C2518yes—
331C2×Dic47C2512yes—
332D188—232no—
333D188—28no—
334D188—28no—
335D188—416no—
336D188—416no—
337C4×D47—216no—
338C4×D47—24no—
339C4×D47—24no—
340C4×D47—28no—
341C4×D47—28no—
342C4×D47—24no—
343C4×D47—24no—
344C4×D47—216no—
345C4×D47—216no—
346C4×D47—48no—
347C4×D47—432no—
348Dic94—28no—
349Dic94—28no—
350#62814—471nomaximal, Sylow
351C22×C47—22no—
352C22×C47—24no—
353C22×C47—44no—
354C22×C47C22×#4114yes—
355C22×C47C22×#4112yes—
356C22×C47C2611yescharacteristic
357C2×D47—28no—
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—28no—
362C2×D47—216no—
363C2×D47—24no—
364C2×D47—416no—
365C2×D47—44no—
366C2×D47—88no—
367C2×D47#58514yes—
368C4×C47—28no—
369C4×C47—216no—
370C4×C47C22×#4112yes—
371C4×C47C22×#4114yes—
372C4×C47C22×#4112yes—
373Dic47—28no—
374Dic47—22no—
375Dic47—22no—
376Dic47—28no—
377#3495—478no—
378#3494—478no—
379#3493—474no—
380#3492—474no—
381#3491—474no—
382#3490—474no—
383#3475—4716no—
384#3458D4711yescharacteristic, complemented
385#3455—474no—
386#3449—471no—
387#3444—474no—
388C2×#525—472no—
389#3428—472no—
390C22×#117—471no—
391C2×C47—22no—
392C2×C47—24no—
393C2×C47C23×#4111yescharacteristic
394C2×C47C2×#58512yes—
395D47—24no—
396D47—42no—
397D47—48no—
398C22×#41—472no—
399C24×C4—471no—
400#556—4716no—
401#555—4716no—
402#554—4716no—
403#553—4716no—
404#553—4716no—
405#552—4716no—
406#552—4716no—
407#552—4732no—
408#551—4732no—
409#551—4732no—
410#547—4716no—
411#546—4732no—
412#544C2×D4714yescomplemented
413#544C2×D4718yescomplemented
414#543C2×D4714yes—
415#542—4716no—
416#541—478no—
417#540—478no—
418#539—4716no—
419#538—4716no—
420#537—474no—
421#536—474no—
422#535—474no—
423#534—474no—
424#533—478no—
425#533C2×D4714yescomplemented
426#533C2×D4718yescomplemented
427#532—478no—
428#532—474no—
429#529—4716no—
430#529—4716no—
431#529—4716no—
432#529—4732no—
433#525—4716no—
434#525—474no—
435#525—474no—
436#525—478no—
437#525—478no—
438#525—474no—
439#525—474no—
440#525—478no—
441C2×#123—474no—
442C2×C22⋊Q8—474no—
443C2×#121—474no—
444C2×#120—474no—
445#520—478no—
446#520—478no—
447#519—474no—
448#518—474no—
449#518—478no—
450C4×#41—4716no—
451C4×#41—478no—
452C4×#41—478no—
453C2×C4×D4—478no—
454C2×#117—471no—
455C2×#117—478no—
456C2×#117—478no—
457C2×#117—478no—
458C2×#117—472no—
459C2×#117—472no—
460C2×#117—472no—
461C2×#117C2×D4711yescharacteristic
462C2×#117C2×D4712yes—
463C22×C4⋊C4—472no—
464C22×C22⋊C4—472no—
465C22×C42—472no—
466C47#6281411yescharacteristic, complemented, Sylow
467C25—471no—
468C2×#41—4716no—
469C2×#41—474no—
470C2×#41—474no—
471C2×#41—474no—
472C2×#41—474no—
473C2×#41—9416no—
474C22×Q8—472no—
475C22×D4—474no—
476C22×D4—472no—
477C22×D4—478no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—474no—
481C23×C4—474no—
482C23×C4—474no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—474no—
487C23×C4—948no—
488C23×C4C22×D4711yescharacteristic
489C4⋊Q8—474no—
490C4⋊Q8C22×D4718yescomplemented
491C4⋊Q8C22×D47116yescomplemented
492#127—474no—
493#126—4732no—
494#126—4732no—
495#126—4732no—
496#125—4716no—
497#125—4732no—
498#125C22×D4718yescomplemented
499#125C22×D47116yescomplemented
500#124—4716no—
501#124—4732no—
502#124—478no—
503#123—4732no—
504#123—4732no—
505#123—4732no—
506#123—478no—
507#123—478no—
508#123—4716no—
509#123—4716no—
510C22⋊Q8—4716no—
511C22⋊Q8—4732no—
512C22⋊Q8—478no—
513C22⋊Q8—478no—
514C22⋊Q8—478no—
515C22⋊Q8—478no—
516C22⋊Q8—4716no—
517C22⋊Q8C22×D47116yes—
518C22⋊Q8C22×D47132yes—
519#121—4716no—
520#121—478no—
521#121—478no—
522#121—478no—
523#121—478no—
524#121—4716no—
525#121—4716no—
526#121—4732no—
527#120—478no—
528#120—478no—
529#120—4716no—
530#120—4716no—
531C4×Q8—4716no—
532C4×Q8—4716no—
533C4×Q8—4716no—
534C4×Q8C22×D47116yescomplemented
535C4×D4—4732no—
536C4×D4—4716no—
537C4×D4—4732no—
538C4×D4—4716no—
539C4×D4—4732no—
540C4×D4—4716no—
541C4×D4—4716no—
542C4×D4—4716no—
543C4×D4—4716no—
544C4×D4—4716no—
545C4×D4—4716no—
546#117—474no—
547#117—474no—
548#117—478no—
549#117—478no—
550#117—4716no—
551#117—4716no—
552#117—4732no—
553#117—4716no—
554#117—4716no—
555#117—478no—
556#117—478no—
557#117—4716no—
558#117C22×D4714yes—
559#117C22×D4714yes—
560#117C22×D4714yes—
561#117C22×D4714yes—
562#117C22×D4714yes—
563#117C22×D4714yes—
564C2×C4⋊C4—472no—
565C2×C4⋊C4—474no—
566C2×C4⋊C4—478no—
567C2×C4⋊C4—478no—
568C2×C4⋊C4—478no—
569C2×C4⋊C4—4716no—
570C2×C4⋊C4C22×D4712yes—
571C2×C4⋊C4C22×D4714yes—
572C2×C22⋊C4—472no—
573C2×C22⋊C4—474no—
574C2×C22⋊C4—478no—
575C2×C22⋊C4—478no—
576C2×C22⋊C4—4716no—
577C2×C22⋊C4—4716no—
578C2×C22⋊C4C22×D4712yes—
579C2×C22⋊C4C22×D4714yes—
580C2×C42—472no—
581C2×C42—474no—
582C2×C42—478no—
583C2×C42—478no—
584C2×C42—4716no—
585C2×C42C22×D4712yes—
586C2×C42C22×D4714yes—
587C24—471no—
588C24—474no—
589C24—474no—
590C24—471no—
591C24—944no—
592C24—1884no—
593C24C23×D4711yescharacteristic
594#41—9416no—
595#41—9416no—
596#41—9416no—
597#41—9416no—
598#41—18832no—
599C2×Q8—474no—
600C2×Q8—474no—
601C2×Q8—948no—
602C2×Q8C23×D47116yes—
603C2×D4—478no—
604C2×D4—478no—
605C2×D4—4716no—
606C2×D4—474no—
607C2×D4—474no—
608C2×D4—4716no—
609C2×D4—4716no—
610C2×D4—9416no—
611C2×D4—948no—
612C2×D4—18816no—
613C22×C4—471no—
614C22×C4—474no—
615C22×C4—474no—
616C22×C4—471no—
617C22×C4—474no—
618C22×C4—472no—
619C22×C4—478no—
620C22×C4—474no—
621C22×C4—478no—
622C22×C4—474no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—478no—
626C22×C4—472no—
627C22×C4—478no—
628C22×C4—4732no—
629C22×C4—944no—
630C22×C4—9416no—
631C22×C4—9416no—
632C22×C4—944no—
633C22×C4—944no—
634C22×C4—944no—
635C22×C4—944no—
636C22×C4—9416no—
637C22×C4—1888no—
638C22×C4#1062535418yescomplemented
639C22×C4C23×D4714yes—
640C22×C4C23×D4718yes—
641C22×C4C23×D4711yescharacteristic
642C22×C4C23×D4712yes—
643C22×C4C23×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C4⋊C4—4716no—
646C4⋊C4—4732no—
647C4⋊C4—478no—
648C4⋊C4—4716no—
649C4⋊C4—4716no—
650C4⋊C4—4716no—
651C4⋊C4C23×D4718yes—
652C4⋊C4C23×D4718yes—
653C4⋊C4C23×D4718yes—
654C4⋊C4C23×D47116yes—
655C4⋊C4C23×D47132yes—
656C22⋊C4—478no—
657C22⋊C4—4716no—
658C22⋊C4—4716no—
659C22⋊C4—4732no—
660C22⋊C4—4716no—
661C22⋊C4—4716no—
662C22⋊C4—4716no—
663C22⋊C4—4732no—
664C22⋊C4C23×D4718yes—
665C22⋊C4C23×D4718yes—
666C22⋊C4C23×D4718yes—
667C42—478no—
668C42—474no—
669C42—478no—
670C42—4732no—
671C42—474no—
672C42C23×D4714yes—
673C42C23×D4718yes—
674C42C23×D4714yes—
675C42C23×D4718yes—
676C23—42no—
677C23—472no—
678C23—472no—
679C23—478no—
680C23—944no—
681C23—948no—
682C23—942no—
683C23—948no—
684C23—948no—
685C23—942no—
686C23—1888no—
687C23—1882no—
688C23—1884no—
689C23—18816no—
690C23C2×#1062535414yes—
691C23C24×D4712yes—
692C23C24×D4711yescharacteristic
693Q8—416no—
694Q8—948no—
695Q8—948no—
696D4—9432no—
697D4—9416no—
698D4—9416no—
699D4—948no—
700D4—948no—
701D4—18816no—
702D4—18816no—
703C2×C4—44no—
704C2×C4—48no—
705C2×C4—472no—
706C2×C4—478no—
707C2×C4—478no—
708C2×C4—472no—
709C2×C4—9416no—
710C2×C4—948no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—948no—
714C2×C4—944no—
715C2×C4—944no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—944no—
719C2×C4—944no—
720C2×C4—9416no—
721C2×C4—9416no—
722C2×C4—1888no—
723C2×C4—18832no—
724C2×C4—1884no—
725C2×C4C2×#1062535418yes—
726C2×C4C2×#1062535418yes—
727C2×C4C2×#1062535414yes—
728C2×C4C2×#1062535414yes—
729C2×C4C24×D4718yes—
730C2×C4C24×D47116yes—
731C2×C4C24×D4711yescharacteristic
732C2×C4C24×D4712yes—
733C2×C4C24×D4711yescharacteristic
734C22—22no—
735C22—24no—
736C22—44no—
737C22—474no—
738C22—948no—
739C22—942no—
740C22—942no—
741C22—942no—
742C22—948no—
743C22—9416no—
744C22—944no—
745C22—3768no—
746C22—18816no—
747C22—1884no—
748C22C22×#1062535414yes—
749C22C22×#1062535412yes—
750C22C25×D4711yescharacteristic
751C4—28no—
752C4—216no—
753C4—942no—
754C4—942no—
755C4—948no—
756C4—948no—
757C4C22×#1062535412yes—
758C4C22×#1062535414yes—
759C4C22×#1062535412yes—
760C2—22no—
761C2—24no—
762C2—944no—
763C2—1888no—
764C2—1882no—
765C2C23×#1062535411yescharacteristic
766C2#585×D4712yes—
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC47×#3458C2
hypercenter#3458D47
hypocenterC47#62814
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #20257143C2semidirect
2. #20257126C2semidirect
3. #20257109C2semidirect
4. #20257098C2semidirect
5. #20257087C2semidirect
6. #20257078C2semidirect
7. #20256955C2semidirect
8. #20256780C2semidirect
9. #20256721C2semidirect
10. #20256685C2semidirect
11. C2×#15689635C2semidirect
12. #20256589C2semidirect
13. C2×#117×D47C2semidirect
14. C47×#3458C2semidirect
17. #15689847C22semidirect
18. #15689839C22semidirect
19. #15689834C22semidirect
20. #15689826C22semidirect
21. #15689826C22semidirect
22. #15689815C22semidirect
23. #15689811C22semidirect
24. #15689811C22semidirect
25. #15689800C22semidirect
26. #15689800C22semidirect
27. #15689776C22semidirect
28. #15689764C22semidirect
29. #15689747C22semidirect
30. #15689736C22semidirect
31. #15689729C22semidirect
32. #15689722C22semidirect
33. #15689713C22semidirect
34. #15689704C22semidirect
35. #15689699C22semidirect
36. #15689692C22semidirect
38. #15689678C22semidirect
39. #15689674C22semidirect
40. #15689673C22semidirect
41. #15689660C22semidirect
42. #15689660C22semidirect
43. #15689659C22semidirect
44. #15689658C22semidirect
45. #15689636C22semidirect
48. #15689635C22semidirect
49. #15689635C22semidirect
50. #15689635C22semidirect
51. #15689635C22semidirect
52. #15689635C22semidirect
54. C2×#13094004C22semidirect
55. C2×#13093999C22semidirect
57. #15689604C22semidirect
58. #15689603C22semidirect
59. #15689600C22semidirect
60. #15689597C22semidirect
62. C4×#10625354C22semidirect
63. C4×#10625350C22semidirect
64. #15689591C22semidirect
65. C2×C4×D188C22semidirect
67. C2×#13093982C22semidirect
68. C2×#13093981C22semidirect
70. #117×D47C22semidirect
71. #117×D47C22semidirect
72. #117×D47C22semidirect
73. C2×C4⋊C4×D47C22semidirect
75. C2×C42×D47C22semidirect
76. C47×#544C22semidirect
77. C47×#544C22semidirect
79. C47×#533C22semidirect
80. C47×#533C22semidirect
104. #13094024C23semidirect
105. #13094021C23semidirect
107. #13094019C23semidirect
108. #13094019C23semidirect
109. #13094015C23semidirect
110. #13094015C23semidirect
112. #13094013C23semidirect
113. #13094012C23semidirect
116. #13094009C23semidirect
125. #13094004C23semidirect
127. #13094000C23semidirect
134. #13093999C23semidirect
140. Q8×Dic47C23semidirect
141. C4×Dic94C23semidirect
142. #13093989C23semidirect
147. C4×D188C23semidirect
148. C4×D188C23semidirect
150. #13093986C23semidirect
151. #13093986C23semidirect
159. #13093982C23semidirect
160. #13093982C23semidirect
163. #13093981C23semidirect
171. C4⋊C4×D47C23semidirect
182. C42×D47C23semidirect
184. C4⋊Q8×C47C23semidirect
185. C4⋊Q8×C47C23semidirect
186. #125×C47C23semidirect
187. #125×C47C23semidirect
190. C4×Q8×C47C23semidirect
211. C22×C4×C47#41semidirect
384. #3458D47semidirect
412. #544C2×D47semidirect
413. #544C2×D47semidirect
425. #533C2×D47semidirect
426. #533C2×D47semidirect
466. C47#62814semidirect
490. C4⋊Q8C22×D47semidirect
491. C4⋊Q8C22×D47semidirect
498. #125C22×D47semidirect
499. #125C22×D47semidirect
534. C4×Q8C22×D47semidirect
638. C22×C4#10625354semidirect

Maximal subgroups

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

subgroupindex
#202571432
#202571262
#202571092
#202570982
#202570872
#202570782
#202569552
#202567802
#202567212
#202566852
C2×#156896352
#202565892
C2×#117×D472
C47×#34582
#6281447