Finite Group Databasebeta

← #15634605

Subgroups — #15634605

Order 2816.

1726 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#13082435C211yesmaximal, characteristic
2#13082426C211yesmaximal, characteristic, complemented
3#13081584C214yesmaximal, complemented
4#13081546C212yesmaximal, complemented
5#13081538C214yesmaximal, complemented
6#13081524C212yesmaximal, complemented
7Q16×Dic22C212yesmaximal, complemented
8#13081489C212yesmaximal, complemented
9#13079162C211yesmaximal, characteristic, complemented
10#13079154C212yesmaximal, complemented
11#13078471C212yesmaximal
12#13078460C212yesmaximal, complemented
13#13078404C211yesmaximal, characteristic
14C2×#10622634C211yesmaximal, characteristic, complemented
15#13077563C211yesmaximal, characteristic, complemented
16#13077460C212yesmaximal
17C4×C11×#137C211yesmaximal, characteristic
18C2×C11×#137C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21#10623358C2212yes—
22#10623343C2212yes—
23#10623101—21no—
24#10623101C2212yes—
25#10623101C2212yes—
26#10623100—22no—
27#10623100C2214yes—
28Q8×Dic22—21no—
29Q8×Dic22C2212yes—
30Q8×Dic22C2212yes—
31#10623074—22no—
32#10623074C2212yes—
33D4×Dic22—22no—
34D4×Dic22C2212yes—
35#10623050—22no—
36#10623050C2212yes—
37#10623031—22no—
38#10623031C2212yes—
39#10623001—22no—
40#10623001—21no—
41#10623001C2211yescharacteristic
42#10623001C2211yescharacteristic
43C2×#66922—21no—
44C2×#66922C2211yescharacteristic
45C11×#441C2212yes—
46C11×#440C2212yes—
47C4×C11×Q16C2212yes—
48C4×C11×SD16C2212yes—
49C11×#428C2211yescharacteristic
50C11×#419C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C4×C11×M16C2211yescharacteristic
53#10622846C2212yes—
54C2×#66899C2212yes—
55#10622797C2214yes—
56Q16×Dic11C2214yes—
57#10622777C2214yes—
58SD16×Dic11C2214yes—
59#10622735C2212yes—
60#10622734C2212yes—
61#10622734C2212yes—
62#10622732C2212yes—
63#10622635C2212yes—
64#10622634C2212yes—
65#10622634C2212yes—
66#10622634C2214yes—
67#10622634C2211yescharacteristic
68#10622633C2211yescharacteristic
69#10622622C2212yes—
70#10622621C2211yescharacteristic
71#10622620C2211yescharacteristic
72#10622611C2212yes—
73C2×#66871C2212yes—
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622489C2214yes—
76#10622487C2214yes—
77#10622471C2214yes—
78#10622469C2214yes—
79#10622412C2214yes—
80#10622412C2214yes—
81#10622409C2214yes—
82#10622407C2214yes—
83#10622407C2214yes—
84#10622404C2214yes—
85#10622376C2214yes—
86#10622372C2214yes—
87#10622315C2214yes—
88#10622314C2214yes—
89#10622295C2212yes—
90#10622293C2212yes—
91#10622292C2212yes—
92C8×Dic22C2212yes—
93C2×C11×#41C2311yescharacteristic
94C22×Q8×C11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22—22no—
97C11×#137Q818yescomplemented
98C2×C11×Q16C2312yes—
99C2×C11×SD16C2312yes—
100C2×C11×M16C2311yescharacteristic
101C2×C11×M16C2311yescharacteristic
102C4×Q8×C11—21no—
103C4×Q8×C11—21no—
104C4×Q8×C11C2311yescharacteristic
105C4×Q8×C11C2312yes—
106C4×Q8×C11C2312yes—
107C4×Q8×C11C2311yescharacteristic
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11C2311yescharacteristic
111C4×D4×C11C2311yescharacteristic
112C11×#117—21no—
113C11×#117C2311yescharacteristic
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119Q8×Dic11—22no—
120Q8×Dic11—22no—
121Q8×Dic11C2314yes—
122Q8×Dic11C2314yes—
123Q8×Dic11C2314yes—
124D4×Dic11—24no—
125D4×Dic11C2314yes—
126#66979—24no—
127#66979—22no—
128#66979C2312yes—
129#66979C2312yes—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11C2312yes—
134#66977—21no—
135#66977—21no—
136#66977—22no—
137#66977—24no—
138#66977—22no—
139#66977D412yes—
140#66977D412yes—
141C22×C11⋊C8C2312yes—
142#66943—24no—
143#66943—22no—
144#66943—24no—
145#66943—24no—
146#66943C2314yes—
147#66943C2314yes—
148#66941—24no—
149#66941—22no—
150#66941—24no—
151#66941—24no—
152#66941C2314yes—
153#66941C2314yes—
154#66931—24no—
155#66931—24no—
156#66931—24no—
157#66923—22no—
158#66923—24no—
159#66923D412yes—
160#66923C2312yes—
161#66922—22no—
162#66922—22no—
163#66922—21no—
164#66922—21no—
165#66922—22no—
166#66922—22no—
167#66922—22no—
168#66922D411yescharacteristic
169#66922D411yescharacteristic
170#66922C2312yes—
171#66922C2312yes—
172#66922C2311yescharacteristic
173#66922C2311yescharacteristic
174C4×Dic22—22no—
175C4×Dic22—22no—
176C4×Dic22—21no—
177C4×Dic22—21no—
178C4×Dic22—22no—
179C4×Dic22—22no—
180C4×Dic22—24no—
181C4×Dic22C2312yes—
182C4×Dic22C2312yes—
183C11×#107C2312yes—
184C11×#106C2312yes—
185C11×#103C2312yes—
186C11×#103C2312yes—
187C11×#103C2312yes—
188C11×#102C2312yes—
189C11×#97C2312yes—
190C4×C8×C11C2312yes—
191#66899C2314yes—
192#66899C2314yes—
193#66899C2312yes—
194#66899C2312yes—
195#66896C2312yes—
196#66896C2312yes—
197#66882C2314yes—
198#66882C2314yes—
199#66881C2314yes—
200#66881C2314yes—
201#66879C2314yes—
202Dic11⋊C8C2314yes—
203Dic11⋊C8C2314yes—
204C8×Dic11C2314yes—
205#66872C2312yes—
206#66872C2312yes—
207#66871C2314yes—
208#66871C2312yes—
209#66871C2314yes—
210#66871C2312yes—
211C4⋊(C11⋊C8)C2311yescharacteristic
212C4⋊(C11⋊C8)C2311yescharacteristic
213C4⋊(C11⋊C8)C2312yes—
214#61384—111nomaximal, Sylow
215C11×#41—22no—
216C11×#41C2×Q814yes—
217C2×Q8×C11—21no—
218C2×Q8×C11—22no—
219C2×Q8×C11C2×Q814yescomplemented
220C2×Q8×C11C2412yes—
221C2×Q8×C11C2411yescharacteristic
222C2×D4×C11—21no—
223C2×D4×C11C2411yescharacteristic
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C22×Dic11—24no—
233C22×Dic11—22no—
234C2×Dic22—24no—
235C2×Dic22—24no—
236C2×Dic22—21no—
237C2×Dic22—22no—
238C2×Dic22—21no—
239C2×Dic22—22no—
240C2×Dic22—82no—
241C2×Dic22—84no—
242C2×Dic22C2×D412yes—
243C2×Dic22C2×D412yes—
244C11×Q16C2×Q818yescomplemented
245C11×SD16C2×Q818yescomplemented
246C11×M16—22no—
247C11×M16C2×Q814yescomplemented
248C2×C8×C11C2412yes—
249C2×C8×C11C2412yes—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2411yescharacteristic
257C11×C4⋊C4C2411yescharacteristic
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C11×C22⋊C4—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—22no—
264C42×C11—22no—
265C42×C11—21no—
266C42×C11C2×D411yescharacteristic
267C42×C11C2×D411yescharacteristic
268C42×C11C2411yescharacteristic
269C42×C11C2411yescharacteristic
270C22⋊Dic11—24no—
271C22⋊Dic11—22no—
272C22⋊Dic11C2×D414yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—24no—
277C4⋊Dic11—24no—
278C4⋊Dic11—21no—
279C4⋊Dic11—22no—
280C4⋊Dic11—21no—
281C4⋊Dic11—22no—
282C4⋊Dic11—22no—
283C4⋊Dic11C2×D412yes—
284C4⋊Dic11C2×D412yes—
285C4⋊Dic11C2×D412yes—
286C4⋊Dic11C2×D412yes—
287C4⋊Dic11C2414yes—
288C4⋊Dic11C2412yes—
289C4⋊Dic11C2412yes—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—22no—
295Dic11⋊C4—22no—
296Dic11⋊C4C2×D414yes—
297Dic11⋊C4C2×D414yes—
298C4×Dic11—24no—
299C4×Dic11—24no—
300C4×Dic11—24no—
301C4×Dic11—22no—
302C4×Dic11C2414yes—
303C2×C11⋊C8—24no—
304C2×C11⋊C8C2412yes—
305C2×C11⋊C8C2412yes—
306#3503—111no—
307#3502—111no—
308#3390—114no—
309#3387—112no—
310#3386—114no—
311#3385—112no—
312Q8×Q16—112no—
313#3381—112no—
314#3165—111no—
315#3164—112no—
316#3083—112no—
317#3082—112no—
318#3076—111no—
319C2×#477—111no—
320#2962—111no—
321#2947—112no—
322C4×#137D1111yescharacteristic
323C23×C11—21no—
324C23×C11C22×D411yescharacteristic
325Q8×C11—24no—
326Q8×C11—22no—
327Q8×C11—21no—
328Q8×C11C22×Q814yes—
329Q8×C11C22×Q812yes—
330D4×C11—24no—
331D4×C11—21no—
332D4×C11C22×Q812yes—
333C2×C4×C11—24no—
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—21no—
339C2×C4×C11—22no—
340C2×C4×C11—21no—
341C2×C4×C11—41no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—81no—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×Q812yes—
351C2×C4×C112−1+412yes—
352C2×C4×C11C2511yescharacteristic
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—24no—
356C2×Dic11—84no—
357C2×Dic11—82no—
358C2×Dic11C22×D414yes—
359C2×Dic11C22×D414yes—
360Dic22—24no—
361Dic22—42no—
362Dic22—44no—
363Dic22—42no—
364Dic22—84no—
365Dic22—84no—
366Dic22—81no—
367Dic22—82no—
368C8×C11—22no—
369C8×C11C22×Q814yes—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C2×#137C2×D1111yescharacteristic
373Q82—112no—
374Q82—112no—
375Q82—221no—
376#557—112no—
377#557—114no—
378#557—112no—
379#557—222no—
380#557—221no—
381#554—112no—
382#554—222no—
383D4×Q8—112no—
384D4×Q8—222no—
385#544—112no—
386#544—112no—
387#544—222no—
388#544—222no—
389#533—111no—
390#533—111no—
391#533—222no—
392#533—221no—
393C2×C4⋊Q8—111no—
394C2×C4⋊Q8—221no—
395#520—112no—
396#519—112no—
397C4×#41C2×D1111yescharacteristic
398C2×C4×Q8C2×D1111yescharacteristic
399#501—114no—
400#501—114no—
401#501—114no—
402#500—114no—
403#500—112no—
404#499—114no—
405#498—112no—
406#479—112no—
407#479—114no—
408#479—114no—
409#479—114no—
410#478—112no—
411#478—114no—
412#477—112no—
413#477—112no—
414#477—114no—
415#477—111no—
416#477—114no—
417#477—114no—
418#476—111no—
419#475—111no—
420#475—114no—
421#474—111no—
422#474—114no—
423#446—114no—
424#446—112no—
425C8×Q8—112no—
426#441—114no—
427#441C2×D1112yes—
428#440—114no—
429#440C2×D1112yes—
430C4×Q16—114no—
431C4×Q16C2×D1112yes—
432C4×SD16—114no—
433C4×SD16C2×D1112yes—
434#428—112no—
435#428—112no—
436#428C2×D1111yescharacteristic
437#427—112no—
438C2×#107—112no—
439#424—112no—
440C2×C4⋊C8—111no—
441#419C2×D1111yescharacteristic
442#417C2×D1111yescharacteristic
443#416—112no—
444C2×#103—112no—
445#405—112no—
446C4×M16C2×D1111yescharacteristic
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11D4×Q812yes—
453C22×C11C23×D411yescharacteristic
454C4×C11—21no—
455C4×C11—21no—
456C4×C11—22no—
457C4×C11—24no—
458C4×C11—21no—
459C4×C11—41no—
460C4×C11—42no—
461C4×C11—41no—
462C4×C11D4×Q812yes—
463C4×C11#57812yes—
464C4×C11C23×Q811yescharacteristic
465C4×C11C2×2−1+411yescharacteristic
466Dic11—24no—
467Dic11—24no—
468Dic11—44no—
469Dic11—42no—
470Dic11—42no—
471C2×#41C22×D1111yescharacteristic
472C22×Q8—222no—
473C22×Q8—221no—
474C22×Q8C22×D1111yescharacteristic
475#137Dic2218yescomplemented
476C2×Q16C22×D1112yes—
477C2×SD16C22×D1112yes—
478C2×M16C22×D1111yescharacteristic
479C2×M16C22×D1111yescharacteristic
480C22×C8—112no—
481C4⋊Q8—114no—
482C4⋊Q8—114no—
483C4⋊Q8—111no—
484C4⋊Q8—111no—
485C4⋊Q8—112no—
486C4⋊Q8—112no—
487C4⋊Q8—111no—
488C4⋊Q8—111no—
489C4⋊Q8—222no—
490C4⋊Q8—222no—
491C4⋊Q8—222no—
492C4⋊Q8—222no—
493C4⋊Q8—222no—
494C4⋊Q8—222no—
495C4⋊Q8—224no—
496C4⋊Q8—224no—
497C4⋊Q8—224no—
498C4⋊Q8—221no—
499C4⋊Q8—221no—
500#125—114no—
501#125—114no—
502#125—112no—
503#125—112no—
504#125—222no—
505#125—224no—
506#125—222no—
507#125—224no—
508#125—224no—
509#125—224no—
510C22⋊Q8—112no—
511C22⋊Q8—112no—
512C22⋊Q8—224no—
513C22⋊Q8—224no—
514C22⋊Q8—224no—
515C22⋊Q8—224no—
516C22⋊Q8—222no—
517C22⋊Q8—222no—
518C22⋊Q8—221no—
519C22⋊Q8—221no—
520C4×Q8—21no—
521C4×Q8—21no—
522C4×Q8—112no—
523C4×Q8—112no—
524C4×Q8—114no—
525C4×Q8—114no—
526C4×Q8—114no—
527C4×Q8—222no—
528C4×Q8—224no—
529C4×Q8—222no—
530C4×Q8—222no—
531C4×Q8—222no—
532C4×Q8—222no—
533C4×Q8—222no—
534C4×Q8—221no—
535C4×Q8—221no—
536C4×Q8C22×D1112yes—
537C4×Q8C22×D1112yes—
538C4×Q8C22×D1111yescharacteristic
539C4×Q8C22×D1111yescharacteristic
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—114no—
543C4×D4—224no—
544C4×D4C22×D1111yescharacteristic
545C4×D4C22×D1111yescharacteristic
546#117—21no—
547#117—112no—
548#117—112no—
549#117—224no—
550#117—222no—
551#117C22×D1111yescharacteristic
552C2×C4⋊C4—21no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—222no—
555C2×C4⋊C4—222no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C42—21no—
559C2×C42—21no—
560C2×C42C22×D1111yescharacteristic
561#107—114no—
562#107—114no—
563#107—114no—
564#107—114no—
565#107—112no—
566#107—112no—
567#107C22×D1112yes—
568#106—114no—
569#106—114no—
570#106—112no—
571#106—112no—
572#106C22×D1112yes—
573C4⋊C8—114no—
574C4⋊C8—114no—
575C4⋊C8—111no—
576C4⋊C8—111no—
577C4⋊C8—112no—
578#103—114no—
579#103—114no—
580#103—112no—
581#103—112no—
582#103C22×D1112yes—
583#103C22×D1112yes—
584#103C22×D1112yes—
585#102—112no—
586#102—112no—
587#102C22×D1112yes—
588#97—114no—
589#97C22×D1112yes—
590C4×C8—114no—
591C4×C8C22×D1112yes—
592C2×C11—22no—
593C2×C11—42no—
594C2×C11C2×D4×Q811yescharacteristic
595C2×C11C2×#57811yescharacteristic
596C2×C11#358511yescharacteristic
597#41—22no—
598#41C2×Dic2214yes—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—112no—
602C2×Q8—112no—
603C2×Q8—224no—
604C2×Q8—224no—
605C2×Q8—221no—
606C2×Q8—222no—
607C2×Q8—221no—
608C2×Q8—222no—
609C2×Q8—882no—
610C2×Q8—884no—
611C2×Q8C2×Dic2214yescomplemented
612C2×Q8C23×D1112yes—
613C2×Q8C23×D1111yescharacteristic
614C2×D4—21no—
615C2×D4C23×D1111yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—224no—
622C22×C4—222no—
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626Q16C2×Dic2218yescomplemented
627SD16C2×Dic2218yescomplemented
628M16—22no—
629M16C2×Dic2214yescomplemented
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—224no—
633C2×C8C23×D1112yes—
634C2×C8C23×D1112yes—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—112no—
641C4⋊C4—112no—
642C4⋊C4—112no—
643C4⋊C4—114no—
644C4⋊C4—112no—
645C4⋊C4—114no—
646C4⋊C4—112no—
647C4⋊C4—112no—
648C4⋊C4—114no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C4⋊C4—224no—
655C4⋊C4—224no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—222no—
659C4⋊C4—222no—
660C4⋊C4—222no—
661C4⋊C4—222no—
662C4⋊C4—221no—
663C4⋊C4—222no—
664C4⋊C4—221no—
665C4⋊C4C23×D1112yes—
666C4⋊C4C23×D1111yescharacteristic
667C4⋊C4C23×D1111yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—114no—
672C22⋊C4—224no—
673C22⋊C4—222no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—22no—
678C42—22no—
679C42—114no—
680C42—224no—
681C42—224no—
682C42—224no—
683C42—222no—
684C42D4×D1111yescharacteristic
685C42D4×D1111yescharacteristic
686C42C23×D1111yescharacteristic
687C42C23×D1111yescharacteristic
688C11#6138411yescharacteristic, complemented, Sylow
689C23—21no—
690C23C2×D4×D1111yescharacteristic
691Q8—24no—
692Q8—22no—
693Q8—21no—
694Q8—224no—
695Q8—442no—
696Q8—444no—
697Q8—442no—
698Q8—882no—
699Q8—881no—
700Q8—884no—
701Q8—884no—
702Q8C22×Dic2214yes—
703Q8C22×Dic2212yes—
704D4—24no—
705D4—21no—
706D4C22×Dic2212yes—
707C2×C4—24no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—81no—
719C2×C4—114no—
720C2×C4—114no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—224no—
724C2×C4—884no—
725C2×C4—882no—
726C2×C4C22×Dic2212yes—
727C2×C4C2×D4×D1111yescharacteristic
728C2×C4C2×D4×D1111yescharacteristic
729C2×C4C2×D4×D1111yescharacteristic
730C2×C4C2×D4×D1111yescharacteristic
731C2×C4C2×D4×D1111yescharacteristic
732C2×C4#6704312yes—
733C2×C4C24×D1111yescharacteristic
734C8—22no—
735C8—222no—
736C8—222no—
737C8C22×Dic2214yes—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22D4×Dic2212yes—
744C22C22×D4×D1111yescharacteristic
745C4—21no—
746C4—21no—
747C4—22no—
748C4—24no—
749C4—21no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—224no—
754C4—224no—
755C4—444no—
756C4—442no—
757C4—442no—
758C4D4×Dic2212yes—
759C4#1062331012yes—
760C4C23×Dic2211yescharacteristic
761C4C2×#6704311yescharacteristic
762C2—22no—
763C2—42no—
764C2C2×D4×Dic2211yescharacteristic
765C2C2×#1062331011yescharacteristic
766C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#137C2
socleC22×C11C23×D4
prime radicalC2×C11×#41C23
hypercenterC4×#137D11
hypocenterC11#61384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. #13082426C2semidirect
3. #13081584C2semidirect
4. #13081546C2semidirect
5. #13081538C2semidirect
6. #13081524C2semidirect
7. Q16×Dic22C2semidirect
8. #13081489C2semidirect
9. #13079162C2semidirect
10. #13079154C2semidirect
12. #13078460C2semidirect
14. C2×#10622634C2semidirect
15. #13077563C2semidirect
97. C11×#137Q8semidirect
219. C2×Q8×C11C2×Q8semidirect
244. C11×Q16C2×Q8semidirect
245. C11×SD16C2×Q8semidirect
247. C11×M16C2×Q8semidirect
475. #137Dic22semidirect
611. C2×Q8C2×Dic22semidirect
626. Q16C2×Dic22semidirect
627. SD16C2×Dic22semidirect
629. M16C2×Dic22semidirect
688. C11#61384semidirect

Maximal subgroups

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

subgroupindex
#130824352
#130824262
#130815842
#130815462
#130815382
#130815242
Q16×Dic222
#130814892
#130791622
#130791542
#130784712
#130784602
#130784042
C2×#106226342
#130775632
#130774602
C4×C11×#1372
#6138411