Finite Group Databasebeta

← #15633767

Subgroups — #15633767

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082421C211yesmaximal, characteristic, complemented
2#13081452C214yesmaximal, complemented
3#13081426C212yesmaximal, complemented
4#13081415C212yesmaximal, complemented
5#13081308C212yesmaximal, complemented
6#13081297C214yesmaximal, complemented
7#13081290C212yesmaximal, complemented
8#13078981C212yesmaximal, complemented
9#13078938C211yesmaximal, characteristic
10#13078467C212yesmaximal, complemented
11#13078421C211yesmaximal, characteristic, complemented
12#13078142C212yesmaximal, complemented
13#13078084C211yesmaximal, characteristic
14#13077551C211yesmaximal, characteristic, complemented
15#13077455C212yesmaximal, complemented
16C2×C4×#4326C211yesmaximal, characteristic, complemented
17C11×#3507C211yesmaximal, characteristic
18C11×#559C2212yes—
19C11×#557C2212yes—
20C11×#556—21no—
21C11×#556C2214yes—
22C11×#554—21no—
23C11×#552—22no—
24C11×#539—22no—
25C11×#536C2212yes—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C11×#529—22no—
29C11×#520C2212yes—
30C2×C4×Q8×C11C2211yescharacteristic
31C2×#67004C2212yes—
32C22×#4326C2211yescharacteristic
33#10623253—21no—
34#10623252—21no—
35#10623216—22no—
36#10623154—22no—
37#10623153—22no—
38#10623098C2212yes—
39#10623098C2214yes—
40Q8×Dic22C2212yes—
41#10623050C2212yes—
42#10623047C2212yes—
43#10623001C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45#10622846C2212yes—
46#10622846C2212yes—
47#10622845C2212yes—
48#10622838C2212yes—
49C2×#66899C2211yescharacteristic
50#10622703C2212yes—
51#10622703C2214yes—
52#10622703C2214yes—
53#10622695C2214yes—
54#10622694C2211yescharacteristic
55#10622694C2211yescharacteristic
56#10622694C2214yes—
57#10622688C2212yes—
58#10622683C2211yescharacteristic
59#10622683C2211yescharacteristic
60#10622669C2212yes—
61#10622669C2212yes—
62#10622669C2214yes—
63#10622668C2214yes—
64#10622667C2214yes—
65#10622667C2214yes—
66#10622667C2214yes—
67#10622643C2214yes—
68C4×#4326C2212yes—
69C4×#4326C2212yes—
70C4×#4326C2212yes—
71C4×#4326C2212yes—
72C4×#4326C2214yes—
73#10622637C2212yes—
74#10622637C2212yes—
75Q8×C11⋊C8C2212yes—
76Q8×C11⋊C8C2212yes—
77#10622635C2214yes—
78#10622635C2214yes—
79#10622634C2212yes—
80#10622634C2214yes—
81#10622633C2212yes—
82#10622631C2214yes—
83C4×#4324C2214yes—
84#10622622C2214yes—
85#10622620C2214yes—
86#10622612C2212yes—
87#10622610C2212yes—
88C2×#66874C2211yescharacteristic
89#10622577C2212yes—
90C2×#66871C2211yescharacteristic
91#10622537C2211yescharacteristic
92C2×C4×C11⋊C8C2211yescharacteristic
93C2×C11×#41C2312yes—
94C22×Q8×C11C2311yescharacteristic
95C22×Dic22C2311yescharacteristic
96C11×C4⋊Q8D411yescharacteristic
97C11×C4⋊Q8D411yescharacteristic
98C11×C4⋊Q8C2311yescharacteristic
99C11×C4⋊Q8C2314yes—
100C11×#127C2311yescharacteristic
101C11×#126—24no—
102C11×#126—24no—
103C11×#125—22no—
104C11×#125—24no—
105C11×#125D412yes—
106C11×#124—22no—
107C11×#124C2312yes—
108C11×#124C2314yes—
109C11×#123—24no—
110C11×#123—24no—
111C11×C22⋊Q8—24no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8D412yes—
115C11×C22⋊Q8D412yes—
116C11×#121—21no—
117C11×#121—21no—
118C4×Q8×C11—22no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2314yes—
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2312yes—
126C4×D4×C11—22no—
127C4×D4×C11—24no—
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11C2314yes—
131C11×#117—22no—
132C11×#117—24no—
133C11×#117C2312yes—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C42×C11—21no—
138C2×C42×C11C2311yescharacteristic
139#67004—28no—
140Q8×Dic11—22no—
141#66997—22no—
142#66997—24no—
143C2×#4326—24no—
144C2×#4326C2312yes—
145C2×#4326C2312yes—
146C2×#4326C2314yes—
147C2×#4324C2314yes—
148#66979C2312yes—
149C2×C4⋊Dic11C2311yescharacteristic
150#66977—21no—
151#66977—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×#4318C2312yes—
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66943—22no—
158#66942—24no—
159#66942—24no—
160#66942—24no—
161#66941—22no—
162#66941—22no—
163#66941—24no—
164#66940—22no—
165#66940—22no—
166#66940—22no—
167#66940—24no—
168#66931—24no—
169#66930—24no—
170#66923C2312yes—
171#66923C2314yes—
172#66922C2311yescharacteristic
173#66922C2311yescharacteristic
174#66922C2314yes—
175C4×Dic22—21no—
176C4×Dic22—21no—
177C4×Dic22—21no—
178C4×Dic22—21no—
179C4×Dic22C2312yes—
180C4×Dic22C2312yes—
181C4×Dic22C2314yes—
182C4×Dic22C2314yes—
183#66899C2312yes—
184#66899C2312yes—
185#66899C2314yes—
186#66899C2314yes—
187#66899C2314yes—
188#66899C2312yes—
189#66899C2312yes—
190#66899C2312yes—
191#66899C2312yes—
192#66896C2314yes—
193#66896C2312yes—
194#66896C2312yes—
195#66896C2312yes—
196#66896C2312yes—
197#66874C2312yes—
198#66874C2312yes—
199#66872C2314yes—
200#66871C2312yes—
201#66871C2312yes—
202#66871C2314yes—
203C4⋊(C11⋊C8)C2312yes—
204C4⋊(C11⋊C8)C2312yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207#66867C2314yes—
208C4×C11⋊C8C2311yescharacteristic
209C4×C11⋊C8C2311yescharacteristic
210C4×C11⋊C8C2311yescharacteristic
211C4×C11⋊C8C2311yescharacteristic
212C4×C11⋊C8C2314yes—
213#61328—111nomaximal, Sylow
214C11×#41—24no—
215C11×#41—24no—
216C2×Q8×C11—21no—
217C2×Q8×C11—22no—
218C2×Q8×C11—22no—
219C2×Q8×C11C2×D412yes—
220C2×Q8×C11C2×D412yes—
221C2×Q8×C11C2412yes—
222C2×Q8×C11C2412yes—
223C2×D4×C11—22no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11C2412yes—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—22no—
230C22×C4×C11—24no—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C22×Dic11—21no—
235C22×Dic11—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—24no—
240C2×Dic22—22no—
241C2×Dic22#4114yes—
242C2×Dic22C2412yes—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4C2×D412yes—
252C11×C4⋊C4C2×D412yes—
253C11×C4⋊C4C2×D414yes—
254C11×C4⋊C4C2×D412yes—
255C11×C4⋊C4C2×D414yes—
256C11×C4⋊C4C2×D412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4C2×D414yes—
264C42×C11—22no—
265C42×C11—22no—
266C42×C11—24no—
267C42×C11C2×D411yescharacteristic
268C42×C11C2×D411yescharacteristic
269C42×C11C2411yescharacteristic
270C42×C11C2411yescharacteristic
271C42×C11C2414yes—
272C22⋊Dic11—22no—
273#4326—24no—
274#4326—24no—
275#4326—28no—
276#4324—28no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—24no—
281C4⋊Dic11C2412yes—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—22no—
285Dic11⋊C4—22no—
286Dic11⋊C4—22no—
287Dic11⋊C4—22no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292C4×Dic11—22no—
293C4×Dic11—22no—
294C4×Dic11—22no—
295C4×Dic11—24no—
296C4×Dic11—24no—
297#4318—24no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8C2411yescharacteristic
301C2×C11⋊C8C2411yescharacteristic
302C2×C11⋊C8C2411yescharacteristic
303C2×C11⋊C8C2411yescharacteristic
304C2×C11⋊C8C2414yes—
305#3507D1111yescharacteristic
306#3502—111no—
307#3377—114no—
308#3375—112no—
309#3374—112no—
310#3365—112no—
311#3364—114no—
312#3363—112no—
313#3137—112no—
314#3131—111no—
315#3083—112no—
316#3078—111no—
317#3044—112no—
318#3037—111no—
319#2960—111no—
320#2947—112no—
321C2×C4×Q16—111no—
322C23×C11—22no—
323C23×C11C22×D411yescharacteristic
324Q8×C11—24no—
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—42no—
330Q8×C11—42no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—44no—
334D4×C11—42no—
335D4×C11—81no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—41no—
341C2×C4×C11—42no—
342C2×C4×C11—44no—
343C2×C4×C11—84no—
344C2×C4×C11—81no—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D414yes—
347C2×C4×C11C22×D414yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4112yes—
353C2×C4×C112−1+412yes—
354C2×C4×C11C2511yescharacteristic
355C2×Dic11—24no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—81no—
361Dic22—24no—
362Dic22—22no—
363Dic22—42no—
364Dic22—81no—
365Dic22—84no—
366Dic22C2×#4114yes—
367C11⋊C8—21no—
368C11⋊C8—21no—
369C11⋊C8—24no—
370C11⋊C8—21no—
371C11⋊C8—21no—
372C2×#137—112no—
373C22×Q16—111no—
374#559C2×D1112yes—
375Q82—112no—
376Q82—221no—
377#557—114no—
378#557—112no—
379#557—221no—
380#557—222no—
381#557C2×D1112yes—
382#556—21no—
383#556C2×D1114yes—
384#554—21no—
385#552—22no—
386#544—112no—
387#544—222no—
388#539—22no—
389#536C2×D1112yes—
390#533—111no—
391#533—222no—
392#533C2×D1111yescharacteristic
393#532C2×D1111yescharacteristic
394#529—22no—
395#520C2×D1112yes—
396#519—112no—
397C2×C4×Q8—111no—
398C2×C4×Q8C2×D1111yescharacteristic
399#491—114no—
400#489—114no—
401#488—112no—
402#488—114no—
403#488—112no—
404#487—111no—
405#487—114no—
406#487—111no—
407#486—111no—
408#486—111no—
409#479—114no—
410#479—114no—
411#478—114no—
412#477—112no—
413#477—114no—
414#475—112no—
415#474—114no—
416#464—114no—
417#464—114no—
418#464—114no—
419#462—112no—
420#462—114no—
421#462—114no—
422#460—112no—
423#446—112no—
424#446—112no—
425C8×Q8—112no—
426C8×Q8—112no—
427#441—114no—
428#440—114no—
429C4×Q16—114no—
430C4×Q16—112no—
431C4×Q16—112no—
432C4×Q16—112no—
433C4×Q16—112no—
434C4×SD16—114no—
435#428—112no—
436C2×#107—111no—
437#424—112no—
438#423—111no—
439#419—112no—
440#417—112no—
441#416—112no—
442#416—112no—
443C2×#103—111no—
444C2×#103—111no—
445#405—112no—
446C2×C4×C8—111no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11#54812yes—
453C22×C11C23×D411yescharacteristic
454C4×C11—21no—
455C4×C11—21no—
456C4×C11—24no—
457C4×C11—21no—
458C4×C11—24no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11#54812yes—
463C4×C11#57812yes—
464C4×C11C22×#4111yescharacteristic
465C4×C11C2×2−1+411yescharacteristic
466Dic11—24no—
467Dic11—42no—
468Dic11—42no—
469Dic11—42no—
470C2×#41C22×D1112yes—
471C22×Q8—111no—
472C22×Q8C22×D1111yescharacteristic
473#137—228no—
474C2×Q16—112no—
475C2×Q16—112no—
476C2×Q16—114no—
477C2×Q16—224no—
478C2×SD16—114no—
479C2×M16—112no—
480C22×C8—111no—
481C22×C8—111no—
482C4⋊Q8—111no—
483C4⋊Q8—111no—
484C4⋊Q8—114no—
485C4⋊Q8—222no—
486C4⋊Q8—224no—
487C4⋊Q8—222no—
488C4⋊Q8—222no—
489C4⋊Q8—224no—
490C4⋊Q8C22⋊D1111yescharacteristic
491C4⋊Q8C22⋊D1111yescharacteristic
492C4⋊Q8C22×D1111yescharacteristic
493C4⋊Q8C22×D1114yes—
494#127C22×D1111yescharacteristic
495#126—24no—
496#126—24no—
497#125—22no—
498#125—24no—
499#125—112no—
500#125—114no—
501#125—224no—
502#125—222no—
503#125—224no—
504#125—224no—
505#125C22⋊D1112yes—
506#124—22no—
507#124C22×D1112yes—
508#124C22×D1114yes—
509#123—24no—
510#123—24no—
511C22⋊Q8—24no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—221no—
515C22⋊Q8—221no—
516C22⋊Q8—224no—
517C22⋊Q8C22⋊D1112yes—
518C22⋊Q8C22⋊D1112yes—
519#121—21no—
520#121—21no—
521C4×Q8—22no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8—112no—
525C4×Q8—112no—
526C4×Q8—114no—
527C4×Q8—114no—
528C4×Q8—222no—
529C4×Q8—222no—
530C4×Q8—222no—
531C4×Q8—224no—
532C4×Q8—222no—
533C4×Q8—221no—
534C4×Q8—221no—
535C4×Q8—221no—
536C4×Q8—221no—
537C4×Q8C22×D1112yes—
538C4×Q8C22×D1112yes—
539C4×Q8C22×D1114yes—
540C4×Q8C22×D1112yes—
541C4×Q8C22×D1112yes—
542C4×D4—22no—
543C4×D4—24no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4C22×D1114yes—
547#117—22no—
548#117—24no—
549#117—112no—
550#117—224no—
551#117C22×D1112yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C42—21no—
558C2×C42—221no—
559C2×C42C22×D1111yescharacteristic
560#107—112no—
561#107—112no—
562#107—114no—
563#106—114no—
564C4⋊C8—112no—
565C4⋊C8—112no—
566C4⋊C8—114no—
567C4⋊C8—114no—
568#103—112no—
569#103—112no—
570#103—112no—
571#103—112no—
572#103—112no—
573#103—112no—
574#103—114no—
575#103—114no—
576#103—114no—
577#103—112no—
578#103—112no—
579#102—112no—
580#102—112no—
581#102—112no—
582#102—112no—
583#102—114no—
584#97—114no—
585C4×C8—111no—
586C4×C8—111no—
587C4×C8—111no—
588C4×C8—111no—
589C4×C8—114no—
590C2×C11—22no—
591C2×C11—82no—
592C2×C11C2×#54811yescharacteristic
593C2×C11C2×#57811yescharacteristic
594C2×C11#358411yescharacteristic
595#41—24no—
596#41—24no—
597C2×Q8—21no—
598C2×Q8—22no—
599C2×Q8—22no—
600C2×Q8—114no—
601C2×Q8—112no—
602C2×Q8—222no—
603C2×Q8—221no—
604C2×Q8—221no—
605C2×Q8—221no—
606C2×Q8—224no—
607C2×Q8C2×C22⋊D1112yes—
608C2×Q8C2×C22⋊D1112yes—
609C2×Q8C23×D1112yes—
610C2×Q8C23×D1112yes—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4C23×D1112yes—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—24no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C23×D1111yescharacteristic
624Q16—224no—
625Q16—224no—
626Q16—228no—
627SD16—228no—
628M16—224no—
629C2×C8—111no—
630C2×C8—111no—
631C2×C8—111no—
632C2×C8—111no—
633C2×C8—114no—
634C2×C8—222no—
635C2×C8—222no—
636C4⋊C4—21no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—112no—
645C4⋊C4—112no—
646C4⋊C4—112no—
647C4⋊C4—221no—
648C4⋊C4—222no—
649C4⋊C4—222no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—222no—
653C4⋊C4—221no—
654C4⋊C4—224no—
655C4⋊C4—222no—
656C4⋊C4—224no—
657C4⋊C4—221no—
658C4⋊C4—224no—
659C4⋊C4C2×C22⋊D1112yes—
660C4⋊C4C2×C22⋊D1112yes—
661C4⋊C4C2×C22⋊D1114yes—
662C4⋊C4C2×C22⋊D1112yes—
663C4⋊C4C2×C22⋊D1114yes—
664C4⋊C4C2×C22⋊D1112yes—
665C4⋊C4C23×D1112yes—
666C22⋊C4—22no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—24no—
671C22⋊C4—222no—
672C22⋊C4C2×C22⋊D1114yes—
673C42—22no—
674C42—22no—
675C42—24no—
676C42—222no—
677C42—222no—
678C42—222no—
679C42—224no—
680C42—224no—
681C42C2×C22⋊D1111yescharacteristic
682C42C2×C22⋊D1111yescharacteristic
683C42C23×D1111yescharacteristic
684C42C23×D1111yescharacteristic
685C42C23×D1114yes—
686C11#6132811yescharacteristic, complemented, Sylow
687C23—22no—
688C23C22×C22⋊D1111yescharacteristic
689Q8—24no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—42no—
695Q8—42no—
696Q8—114no—
697Q8—224no—
698Q8—222no—
699Q8—442no—
700Q8—881no—
701Q8—884no—
702D4—22no—
703D4—22no—
704D4—44no—
705D4—42no—
706D4—81no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—84no—
715C2×C4—81no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—881no—
722C2×C4#41×D1112yes—
723C2×C4#6704312yes—
724C2×C4C22×C22⋊D1111yescharacteristic
725C2×C4C22×C22⋊D1114yes—
726C2×C4C22×C22⋊D1114yes—
727C2×C4C22×C22⋊D1111yescharacteristic
728C2×C4C22×C22⋊D1111yescharacteristic
729C2×C4C22×C22⋊D1111yescharacteristic
730C2×C4C22×C22⋊D1111yescharacteristic
731C2×C4C24×D1111yescharacteristic
732C8—221no—
733C8—221no—
734C8—224no—
735C8—221no—
736C8—221no—
737C22—21no—
738C22—21no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22#1062336212yes—
743C22C23×C22⋊D1111yescharacteristic
744C4—21no—
745C4—24no—
746C4—21no—
747C4—21no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—224no—
753C4—442no—
754C4—442no—
755C4—442no—
756C4#1062336212yes—
757C4#1062336912yes—
758C4C2×#41×D1111yescharacteristic
759C4C2×#6704311yescharacteristic
760C2—22no—
761C2—82no—
762C2C2×#1062336211yescharacteristic
763C2C2×#1062336911yescharacteristic
764C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3507C2
socleC22×C11C23×D4
prime radicalC11×#532C22
hypercenter#3507D11
hypocenterC11#61328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13082421C2semidirect
2. #13081452C2semidirect
3. #13081426C2semidirect
4. #13081415C2semidirect
5. #13081308C2semidirect
6. #13081297C2semidirect
7. #13081290C2semidirect
8. #13078981C2semidirect
10. #13078467C2semidirect
11. #13078421C2semidirect
12. #13078142C2semidirect
14. #13077551C2semidirect
15. #13077455C2semidirect
16. C2×C4×#4326C2semidirect
686. C11#61328semidirect

Maximal subgroups

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

subgroupindex
#130824212
#130814522
#130814262
#130814152
#130813082
#130812972
#130812902
#130789812
#130789382
#130784672
#130784212
#130781422
#130780842
#130775512
#130774552
C2×C4×#43262
C11×#35072
#6132811