Finite Group Databasebeta

← #15633851

Subgroups — #15633851

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082470C211yesmaximal, characteristic, complemented
2#13081443C214yesmaximal, complemented
3#13081408C214yesmaximal, complemented
4#13081369C214yesmaximal, complemented
5#13081323C214yesmaximal, complemented
6#13078975C212yesmaximal, complemented
7#13078964C211yesmaximal, characteristic, complemented
8#13078474C212yesmaximal, complemented
9#13078409C211yesmaximal, characteristic, complemented
10#13078119C212yesmaximal, complemented
11#13078080C211yesmaximal, characteristic, complemented
12#13077557C211yesmaximal, characteristic, complemented
13#13077448C212yesmaximal, complemented
14C2×#10622627C211yesmaximal, characteristic, complemented
15C11×#3501C211yesmaximal, characteristic, complemented
16C11×#554—21no—
17C11×#554—22no—
18C11×#554C2212yescomplemented
19C11×#554C2214yescomplemented
20D4×Q8×C11—21no—
21D4×Q8×C11C2212yescomplemented
22C11×#544C2212yes—
23C11×#543—22no—
24C11×#533C2211yescharacteristic
25C11×#533C2211yescharacteristic
26C2×C11×C22⋊Q8—22no—
27C11×#518C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66985C2212yes—
30C22×#4323C2211yescharacteristic
31#10623265—21no—
32#10623257—21no—
33#10623226—22no—
34#10623175—22no—
35#10623158—22no—
36#10623116C2214yescomplemented
37#10623115C2212yescomplemented
38#10623108C2212yescomplemented
39#10623056C2212yes—
40#10623054C2212yes—
41#10623008C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44#10622707C2214yescomplemented
45#10622702C2212yescomplemented
46#10622702C2212yescomplemented
47#10622702C2214yescomplemented
48#10622701C2214yescomplemented
49#10622700C2212yescomplemented
50#10622697C2212yescomplemented
51#10622697C2214yescomplemented
52#10622682C2212yescomplemented
53#10622681C2214yescomplemented
54#10622680C2214yescomplemented
55#10622680C2212yescomplemented
56#10622679C2214yescomplemented
57#10622679C2214yescomplemented
58#10622676C2214yescomplemented
59#10622637C2214yescomplemented
60#10622637C2214yescomplemented
61#10622632C2212yescomplemented
62#10622631C2214yescomplemented
63C4×#4324C2214yescomplemented
64#10622629C2214yes—
65#10622629C2214yes—
66#10622629C2214yescomplemented
67#10622628C2214yes—
68#10622628C2214yes—
69#10622628C2212yescomplemented
70#10622627C2214yes—
71#10622627C2214yes—
72#10622627C2214yescomplemented
73C4×#4323C2214yescomplemented
74#10622615C2212yes—
75#10622615C2212yes—
76#10622614C2212yes—
77#10622612C2212yes—
78#10622610C2212yes—
79#10622608C2212yes—
80#10622579C2212yes—
81C2×#66873C2211yescharacteristic
82C2×#66872C2211yescharacteristic
83#10622537C2211yescharacteristic
84C2×#66867C2211yescharacteristic
85C22×Q8×C11—22no—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C2×#4343—22no—
89C2×#4339C2312yes—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8D411yescharacteristic
94C11×C4⋊Q8D411yescharacteristic
95C11×C4⋊Q8C2311yescharacteristic
96C11×C4⋊Q8C2311yescharacteristic
97C11×C4⋊Q8C2314yes—
98C11×#125—22no—
99C11×#125D412yes—
100C11×#125C2312yes—
101C11×#125C2314yes—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—24no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—24no—
108C11×C22⋊Q8—24no—
109C11×C22⋊Q8—24no—
110C11×C22⋊Q8—24no—
111C11×C22⋊Q8—24no—
112C11×C22⋊Q8D412yes—
113C11×C22⋊Q8D412yes—
114C4×Q8×C11—21no—
115C4×Q8×C11—21no—
116C4×Q8×C11C2312yes—
117C4×Q8×C11C2312yes—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11C2312yes—
123C4×D4×C11C2312yes—
124C4×D4×C11C2314yes—
125C4×D4×C11C2314yes—
126C11×#117C2312yes—
127C11×#117C2312yes—
128C2×C11×C4⋊C4—24no—
129C2×C11×C4⋊C4—22no—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—24no—
133C2×C42×C11C2311yescharacteristic
134#67000—24no—
135#66999—22no—
136C2×#4324C2314yes—
137#66985—28no—
138C2×#4323—24no—
139C2×#4323C2314yes—
140C2×#4323C2314yes—
141#66983—21no—
142#66983—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×#4318C2312yes—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66951—24no—
149#66948—22no—
150#66948—22no—
151#66948—22no—
152#66948—24no—
153#66947—24no—
154#66947—24no—
155#66946—24no—
156#66945—22no—
157#66945—22no—
158C4⋊C4×D11—22no—
159#66935—24no—
160(C22⋊D11)⋊C4—24no—
161#66928C2312yes—
162#66928C2314yes—
163#66927C2311yescharacteristic
164#66927C2314yes—
165C4×D44—21no—
166C4×D44—21no—
167C4×D44—21no—
168C4×D44—21no—
169C4×D44C2312yes—
170C4×D44C2312yes—
171C4×D44C2314yes—
172#66922C2311yescharacteristic
173C4×Dic22C2314yes—
174#66896C2314yes—
175#66874C2314yes—
176#66874C2312yes—
177#66874C2312yes—
178#66874C2312yes—
179#66874C2312yes—
180#66873C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184#66873C2312yes—
185#66873C2312yes—
186#66873C2312yes—
187#66873C2312yes—
188#66872C2314yes—
189#66872C2314yes—
190#66871C2314yes—
191C4⋊(C11⋊C8)C2312yes—
192C4⋊(C11⋊C8)C2312yes—
193C4⋊(C11⋊C8)C2314yes—
194C4⋊(C11⋊C8)C2314yes—
195#66867C2312yes—
196#66867C2312yes—
197#66867C2314yes—
198C4×C11⋊C8C2314yes—
199#61332—111nomaximal, Sylow
200C24×C11—21no—
201C23×D11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—21no—
204C2×Q8×C11—24no—
205C2×Q8×C11—84no—
206C2×Q8×C11C2×D412yes—
207C2×Q8×C11C2×D412yes—
208C2×D4×C11—21no—
209C2×D4×C11—22no—
210C2×D4×C11#4114yescomplemented
211C2×D4×C11C2412yes—
212C22×C4×C11—21no—
213C22×C4×C11—22no—
214C22×C4×C11—24no—
215C22×C4×C11—24no—
216C22×C4×C11—22no—
217C22×C4×C11—82no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—22no—
222C22×Dic11—21no—
223#4343—84no—
224#4339—24no—
225#4339—24no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—24no—
230C2×D44—24no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44C2412yes—
234C2×D44C2412yes—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—24no—
239C2×C4×D11—82no—
240C2×Dic22C2412yes—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4C2×D412yes—
250C11×C4⋊C4C2×D412yes—
251C11×C4⋊C4C2×D412yes—
252C11×C4⋊C4C2×D414yes—
253C11×C4⋊C4C2×D412yes—
254C11×C4⋊C4C2×D414yes—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4C2×D414yes—
264C42×C11—22no—
265C42×C11C2×D411yescharacteristic
266C42×C11C2×D411yescharacteristic
267C42×C11C2414yes—
268C42×C11C2411yescharacteristic
269C42×C11C2411yescharacteristic
270#4324—28no—
271#4323—28no—
272#4323—28no—
273(C2×D11)⋊C4—22no—
274(C2×D11)⋊C4—22no—
275(C2×D11)⋊C4—22no—
276(C2×D11)⋊C4—22no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285C4×Dic11—24no—
286#4318—24no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2414yes—
291C2×C11⋊C8C2412yes—
292#3506—111no—
293#3501D1111yescharacteristic, complemented
294#3376—114no—
295#3373—114no—
296#3370—114no—
297#3366—114no—
298#3136—112no—
299#3135—111no—
300#3084—112no—
301#3077—111no—
302#3041—112no—
303#3036—111no—
304#2961—111no—
305#2946—112no—
306C2×#442—111no—
307C23×C11—22no—
308C23×C11—24no—
309C23×C11—81no—
310C23×C11—81no—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—81no—
316C22×D11—81no—
317Q8×C11—42no—
318Q8×C11—42no—
319Q8×C11—42no—
320Q8×C11—81no—
321Q8×C11—84no—
322D4×C11—24no—
323D4×C11—22no—
324D4×C11C2×#4114yes—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—44no—
331C2×C4×C11—84no—
332C2×C4×C11—82no—
333C2×C4×C11—84no—
334C2×C4×C11—81no—
335C2×C4×C11C22×D414yes—
336C2×C4×C11C22×D414yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4112yes—
343C2×C4×C112−1+412yes—
344C2×C4×C11C2511yescharacteristic
345C22⋊D11—44no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—81no—
349D44—22no—
350D44—22no—
351D44—22no—
352D44—22no—
353D44—42no—
354D44—42no—
355D44—81no—
356D44—84no—
357D44—84no—
358C4×D11—44no—
359C4×D11—44no—
360C4×D11—82no—
361C4×D11—84no—
362Dic22—22no—
363Dic22—22no—
364C11⋊C8—22no—
365C11⋊C8—24no—
366C11⋊C8—22no—
367C2×AGL(1,ℤ/8)—112no—
368C22×D8—111no—
369#559—114no—
370#556—112no—
371#555—221no—
372#554—21no—
373#554—22no—
374#554C2×D1114yescomplemented
375#554C2×D1112yescomplemented
376#553—222no—
377#550—112no—
378D4×Q8—21no—
379D4×Q8C2×D1112yescomplemented
380#547—221no—
381#544C2×D1112yes—
382#543—22no—
383#538—222no—
384#535—112no—
385#533C2×D1111yescharacteristic
386#533C2×D1111yescharacteristic
387#532—111no—
388#525—222no—
389C2×C22⋊Q8—22no—
390#520—112no—
391#518C2×D1112yes—
392C2×C4×D4—111no—
393C2×C4×D4C2×D1111yescharacteristic
394#491—112no—
395#490—112no—
396#490—114no—
397#489—112no—
398#489—112no—
399#489—114no—
400#488—114no—
401#486—114no—
402#479—114no—
403#478—114no—
404#478—114no—
405#476—112no—
406#476—114no—
407#475—114no—
408#474—112no—
409#463—114no—
410#463—114no—
411#463—114no—
412#461—112no—
413#459—112no—
414#459—114no—
415#459—114no—
416#446—114no—
417#446—114no—
418#442—114no—
419#442—114no—
420#442—114no—
421#440—114no—
422C4×SD16—114no—
423C4×D8—114no—
424#428—112no—
425C2×#106—111no—
426#424—112no—
427#423—111no—
428#418—112no—
429#417—112no—
430#416—112no—
431#416—112no—
432C2×#102—111no—
433C2×#102—111no—
434#405—112no—
435C2×#97—111no—
436C22×C11—21no—
437C22×C11—21no—
438C22×C11—24no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—84no—
442C22×C11#54812yes—
443C22×C11C23×D411yescharacteristic
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—84no—
451C4×C11—21no—
452C4×C11—21no—
453C4×C11—21no—
454C4×C11—21no—
455C4×C11—24no—
456C4×C11—24no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11#54812yes—
461C4×C11C22×#4111yescharacteristic
462C4×C11C2×2−1+411yescharacteristic
463Dic11—42no—
464Dic11—42no—
465C2×#41—112no—
466C2×#41—222no—
467C22×Q8—22no—
468C22×D4—111no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—221no—
472AGL(1,ℤ/8)—228no—
473C2×SD16—114no—
474C2×D8—114no—
475C2×D8—114no—
476C2×D8—224no—
477C2×M16—112no—
478C22×C8—111no—
479C22×C8—111no—
480C4⋊Q8—22no—
481C4⋊Q8—111no—
482C4⋊Q8C22⋊D1111yescharacteristic
483C4⋊Q8C22⋊D1111yescharacteristic
484C4⋊Q8C22×D1111yescharacteristic
485C4⋊Q8C22×D1111yescharacteristic
486C4⋊Q8C22×D1114yes—
487#127—111no—
488#127—114no—
489#126—224no—
490#125—22no—
491#125C22⋊D1112yes—
492#125C22×D1112yes—
493#125C22×D1114yes—
494#124—112no—
495#124—114no—
496#124—224no—
497#123—224no—
498#123—224no—
499C22⋊Q8—22no—
500C22⋊Q8—24no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—22no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—222no—
510C22⋊Q8C22⋊D1112yes—
511C22⋊Q8C22⋊D1112yes—
512#121—221no—
513#121—221no—
514#121—222no—
515#121—222no—
516#121—222no—
517#121—224no—
518#120—224no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8—114no—
522C4×Q8C22×D1112yes—
523C4×Q8C22×D1112yes—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—112no—
529C4×D4—112no—
530C4×D4—114no—
531C4×D4—224no—
532C4×D4—224no—
533C4×D4—221no—
534C4×D4—221no—
535C4×D4—221no—
536C4×D4—221no—
537C4×D4C22×D1112yes—
538C4×D4C22×D1112yes—
539C4×D4C22×D1114yes—
540C4×D4C22×D1114yes—
541#117—222no—
542#117—222no—
543#117C22×D1112yes—
544#117C22×D1112yes—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—221no—
553C2×C42C22×D1111yescharacteristic
554#107—114no—
555#106—114no—
556#106—114no—
557C4⋊C8—112no—
558C4⋊C8—112no—
559C4⋊C8—114no—
560C4⋊C8—114no—
561#103—112no—
562#103—112no—
563#103—112no—
564#103—112no—
565#103—114no—
566#102—114no—
567#102—114no—
568#102—112no—
569#102—112no—
570#102—112no—
571#102—112no—
572#102—114no—
573#102—114no—
574#102—114no—
575#97—112no—
576#97—112no—
577#97—114no—
578C4×C8—114no—
579C2×C11—22no—
580C2×C11—44no—
581C2×C11C2×#54811yescharacteristic
582C2×C11#358511yescharacteristic
583C2×C11#358511yescharacteristic
584D11—82no—
585D11—82no—
586C24—21no—
587C24—221no—
588#41—224no—
589#41—224no—
590#41—884no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—24no—
594C2×Q8—84no—
595C2×Q8—112no—
596C2×Q8C2×C22⋊D1112yes—
597C2×Q8C2×C22⋊D1112yes—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—112no—
601C2×D4—112no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—224no—
608C2×D4—221no—
609C2×D4—224no—
610C2×D4#434314yescomplemented
611C2×D4C23×D1112yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—82no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—224no—
622C22×C4—222no—
623C22×C4—882no—
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627SD16—228no—
628D8—228no—
629D8—228no—
630M16—224no—
631C2×C8—112no—
632C2×C8—114no—
633C2×C8—112no—
634C2×C8—222no—
635C2×C8—222no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—112no—
645C4⋊C4—221no—
646C4⋊C4—224no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4C2×C22⋊D1114yes—
650C4⋊C4C2×C22⋊D1112yes—
651C4⋊C4C2×C22⋊D1112yes—
652C4⋊C4C2×C22⋊D1112yes—
653C4⋊C4C2×C22⋊D1112yes—
654C4⋊C4C2×C22⋊D1114yes—
655C4⋊C4C23×D1112yes—
656C4⋊C4C23×D1112yes—
657C4⋊C4C23×D1112yes—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—222no—
664C22⋊C4—222no—
665C22⋊C4—224no—
666C22⋊C4—224no—
667C22⋊C4—222no—
668C22⋊C4—224no—
669C22⋊C4—222no—
670C22⋊C4C2×C22⋊D1114yes—
671C42—22no—
672C42—224no—
673C42C2×C22⋊D1111yescharacteristic
674C42C2×C22⋊D1111yescharacteristic
675C42C23×D1114yes—
676C42C23×D1111yescharacteristic
677C42C23×D1111yescharacteristic
678C11#6133211yescharacteristic, complemented, Sylow
679C23—22no—
680C23—24no—
681C23—81no—
682C23—81no—
683C23—222no—
684C23—222no—
685C23—442no—
686C23—881no—
687C23—881no—
688C23C22×C22⋊D1111yescharacteristic
689Q8—42no—
690Q8—42no—
691Q8—42no—
692Q8—81no—
693Q8—84no—
694Q8—222no—
695Q8—222no—
696D4—24no—
697D4—22no—
698D4—222no—
699D4—222no—
700D4—222no—
701D4—222no—
702D4—442no—
703D4—444no—
704D4—442no—
705D4—884no—
706D4—881no—
707D4—884no—
708D4C2×#434314yes—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—44no—
715C2×C4—84no—
716C2×C4—82no—
717C2×C4—84no—
718C2×C4—81no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—444no—
722C2×C4—444no—
723C2×C4—882no—
724C2×C4—884no—
725C2×C4—881no—
726C2×C4C2×#434312yes—
727C2×C4#6704012yes—
728C2×C4C22×C22⋊D1114yes—
729C2×C4C22×C22⋊D1111yescharacteristic
730C2×C4C22×C22⋊D1111yescharacteristic
731C2×C4C22×C22⋊D1111yescharacteristic
732C2×C4C22×C22⋊D1111yescharacteristic
733C2×C4C22×C22⋊D1114yes—
734C2×C4C22×C22⋊D1111yescharacteristic
735C2×C4C24×D1111yescharacteristic
736C8—222no—
737C8—224no—
738C8—222no—
739C22—21no—
740C22—21no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—84no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—884no—
752C22#1062334812yes—
753C22C23×C22⋊D1111yescharacteristic
754C4—21no—
755C4—21no—
756C4—24no—
757C4—21no—
758C4—21no—
759C4—24no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—442no—
764C4—442no—
765C4#1062334812yes—
766C4C22×#434311yescharacteristic
767C4C2×#6704011yescharacteristic
768C2—22no—
769C2—44no—
770C2—882no—
771C2—882no—
772C2C2×#1062334811yescharacteristic
773C2#1308339511yescharacteristic
774C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3501C2
socleC22×C11C23×D4
hypercenter#3501D11
hypocenterC11#61332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13082470C2semidirect
2. #13081443C2semidirect
3. #13081408C2semidirect
4. #13081369C2semidirect
5. #13081323C2semidirect
6. #13078975C2semidirect
7. #13078964C2semidirect
8. #13078474C2semidirect
9. #13078409C2semidirect
10. #13078119C2semidirect
11. #13078080C2semidirect
12. #13077557C2semidirect
13. #13077448C2semidirect
14. C2×#10622627C2semidirect
15. C11×#3501C2semidirect
18. C11×#554C22semidirect
19. C11×#554C22semidirect
21. D4×Q8×C11C22semidirect
36. #10623116C22semidirect
37. #10623115C22semidirect
38. #10623108C22semidirect
44. #10622707C22semidirect
45. #10622702C22semidirect
46. #10622702C22semidirect
47. #10622702C22semidirect
48. #10622701C22semidirect
49. #10622700C22semidirect
50. #10622697C22semidirect
51. #10622697C22semidirect
52. #10622682C22semidirect
53. #10622681C22semidirect
54. #10622680C22semidirect
55. #10622680C22semidirect
56. #10622679C22semidirect
57. #10622679C22semidirect
58. #10622676C22semidirect
59. #10622637C22semidirect
60. #10622637C22semidirect
61. #10622632C22semidirect
62. #10622631C22semidirect
63. C4×#4324C22semidirect
66. #10622629C22semidirect
69. #10622628C22semidirect
72. #10622627C22semidirect
73. C4×#4323C22semidirect
210. C2×D4×C11#41semidirect
293. #3501D11semidirect
374. #554C2×D11semidirect
375. #554C2×D11semidirect
379. D4×Q8C2×D11semidirect
610. C2×D4#4343semidirect
678. C11#61332semidirect

Maximal subgroups

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

subgroupindex
#130824702
#130814432
#130814082
#130813692
#130813232
#130789752
#130789642
#130784742
#130784092
#130781192
#130780802
#130775572
#130774482
C2×#106226272
C11×#35012
#6133211