Finite Group Databasebeta

← #15660676

Subgroups — #15660676

Order 2816.

6640 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082762C216yesmaximal, complemented
2#13082761C216yesmaximal, complemented
3#13082760C216yesmaximal, complemented
4#13082756C212yesmaximal, complemented
5#13082754C216yesmaximal, complemented
6#13082753C216yesmaximal, complemented
7#13082752C213yesmaximal, complemented
8#13082751C2112yesmaximal, complemented
9#13081911C213yesmaximal, complemented
10#13081910C216yesmaximal, complemented
11#13081908C216yesmaximal, complemented
12C11×#3529C211yesmaximal, characteristic, complemented
13C11×#563C2213yescomplemented
14C11×#562C2216yescomplemented
15C11×H(3,𝔽4)C2211yescharacteristic, complemented
16C11×#560C2216yescomplemented
17C11×#532C2213yes—
18C11×#529C2216yescomplemented
19C11×#525C2216yescomplemented
20#10623363C2216yes—
21#10623359C2213yescomplemented
22#10623359C2213yescomplemented
23#41×Dic11C2213yescomplemented
24#41×Dic11C2211yescharacteristic, complemented
25#10623322C2216yescomplemented
26C22×C4×Dic11C2212yescomplemented
27#10623266C2216yescomplemented
28#10623259C2216yescomplemented
29#10623251C2216yescomplemented
30#10623247C2216yes—
31#10623243C22112yescomplemented
32#10623243C22112yescomplemented
33#10623237C22112yescomplemented
34#10623237C22112yescomplemented
35#10623230C2216yescomplemented
36#10623222C2216yescomplemented
37#10623219C2216yescomplemented
38C11⋊#564C2216yescomplemented
39#10623215C2216yescomplemented
40#10623215C2216yescomplemented
41#10623214C2213yescomplemented
42#10623211C2216yescomplemented
43#10623211C2216yescomplemented
44#10623211C2216yescomplemented
45#10623203C2213yescomplemented
46#10623203C2216yescomplemented
47#10623199C2216yes—
48#10623198C22112yescomplemented
49#10623198C22112yescomplemented
50#10623197C2216yescomplemented
51#10623187C22112yescomplemented
52#10623182C22112yescomplemented
53#10623182C2216yescomplemented
54#10623180C22112yescomplemented
55#10623180C22112yescomplemented
56#10623180C22112yescomplemented
57#10623178C22112yescomplemented
58#10623177C22112yescomplemented
59#10623177C22112yescomplemented
60#10623158C2216yescomplemented
61#10623155C22112yescomplemented
62#10623153C22112yescomplemented
63#10623153C2216yescomplemented
64#10623152C22112yescomplemented
65#10623152C22112yescomplemented
66#10623152C22112yescomplemented
67#10623151C22112yescomplemented
68#10623151C22112yescomplemented
69#10623137C2216yescomplemented
70#10623137C22112yescomplemented
71#10623131C22112yescomplemented
72#10623131C22112yescomplemented
73#10623127C22112yes—
74#10623127C2216yes—
75#10623126C2216yescomplemented
76#10623126C22112yescomplemented
77#10623125C2216yescomplemented
78#10623117C22112yescomplemented
79#10623117C22112yescomplemented
80#10623109C2216yescomplemented
81C4×#4343C2212yescomplemented
82#10623088C22112yescomplemented
83#10623079C2216yes—
84#10623078C22112yescomplemented
85#10623069C22112yescomplemented
86#10623069C22112yescomplemented
87C4×#4341C2216yescomplemented
88C4×#4341C22112yescomplemented
89#10623059C22112yescomplemented
90#10623053C2216yescomplemented
91#10623048C2216yescomplemented
92#10623010C2216yescomplemented
93C2×C42×D11C2213yescomplemented
94#10623001C2213yescomplemented
95C2×C11×#41C2311yescharacteristic
96C2×C11×#41C2313yes—
97C23×C4×C11C2312yes—
98C23×Dic11C2314yes—
99C2×#4343C2312yes—
100C2×#4341C23112yes—
101C2×#4341C2316yes—
102C2×#4339C2316yes—
103C22×C4×D11C2313yes—
104C22×C4×D11C2316yes—
105C11×C4⋊Q8C2313yes—
106C11×#127C2313yes—
107C11×#126C23112yes—
108C11×#125C2316yes—
109C11×#124C2316yes—
110C11×#124C2313yes—
111C11×#124C2313yes—
112C11×#123C2316yes—
113C11×#123C2316yes—
114C11×#123C23112yes—
115C11×C22⋊Q8C23112yes—
116C11×C22⋊Q8C2316yes—
117C11×#121C23112yes—
118C11×#121C2316yes—
119C11×#121C23112yes—
120C11×#120C2316yes—
121C11×#120C2316yes—
122C4×Q8×C11C2312yes—
123C4×D4×C11C2316yes—
124C4×D4×C11C23112yes—
125C11×#117C2316yes—
126C2×C42×C11C2313yes—
127#67006C23112yes—
128#67000C2316yes—
129#66999C2316yes—
130#66999C2316yes—
131#66999C2316yes—
132Q8×Dic11C2312yes—
133Q8×Dic11C2316yes—
134Q8×Dic11C2312yes—
135#66997C2316yes—
136#66997C2316yes—
137#66993C2316yes—
138#66993C2316yes—
139#66992C23112yes—
140#66992C23112yes—
141#66992C23112yes—
142#66992C23112yes—
143#66992C23112yes—
144#66991C23112yes—
145#66991C2316yes—
146#66991C2316yes—
147#66991C2316yes—
148#66990C23112yes—
149#66990C2316yes—
150#66990C2316yes—
151#66989C23112yes—
152#66989C2316yes—
153#66988C23112yes—
154#66988C2316yes—
155#66988C23112yes—
156#66988C2316yes—
157D4×Dic11C23112yes—
158D4×Dic11C2316yes—
159D4×Dic11C2316yes—
160D4×Dic11C2316yes—
161D4×Dic11C23112yes—
162#66983C2316yes—
163#66983C23112yes—
164#66982C23112yes—
165#66982C23112yes—
166C4×C22⋊D11C23112yes—
167C4×C22⋊D11C23112yes—
168C4×C22⋊D11C23112yes—
169#66979C2313yes—
170#66979C2313yes—
171#66979C2316yes—
172#66977C23112yes—
173#66977C2316yes—
174#66977C23112yes—
175C2×C4×Dic11C2313yes—
176C2×C4×Dic11C2316yes—
177C2×C4×Dic11C2316yes—
178C2×C4×Dic11C2316yes—
179C2×C4×Dic11C23112yes—
180#66951C23112yes—
181#66951C23112yes—
182#66951C23112yes—
183#66950C2316yes—
184#66950C23112yes—
185#66949C23112yes—
186#66949C23112yes—
187#66949C23112yes—
188#66948C2316yes—
189#66947C23112yes—
190#66947C23112yes—
191#66946C2316yes—
192#66946C23112yes—
193#66945C2316yes—
194#66945C23112yes—
195#66945C2316yes—
196#66943C23112yes—
197#66943C23112yes—
198#66942C23112yes—
199#66942C23112yes—
200#66942C23112yes—
201#66942C23112yes—
202#66941C2316yes—
203#66941C23112yes—
204#66941C2316yes—
205#66940C23112yes—
206#66940C23112yes—
207#66940C2316yes—
208#66939C23112yes—
209#66939C23112yes—
210#66938C23112yes—
211#66938C23112yes—
212#66938C23112yes—
213#66938C23112yes—
214#66937C23112yes—
215#66937C23112yes—
216#66937C23112yes—
217#66936C23112yes—
218#66936C23112yes—
219#66936C23112yes—
220#66936C23112yes—
221#66935C23112yes—
222(C22⋊D11)⋊C4C23112yes—
223(C22⋊D11)⋊C4C23112yes—
224(C22⋊D11)⋊C4C23112yes—
225(C22⋊D11)⋊C4C23112yes—
226(C22⋊D11)⋊C4C23112yes—
227#66932C23112yes—
228#66932C23112yes—
229#66932C23112yes—
230#66932C23112yes—
231#66932C23112yes—
232#66931C23112yes—
233#66931C23112yes—
234#66931C23112yes—
235#66931C23112yes—
236#66931C23112yes—
237#66930C23112yes—
238#66930C23112yes—
239#66930C23112yes—
240#66929C23112yes—
241#66928C2316yes—
242C4×D44C2316yes—
243#66925C23112yes—
244C42×D11C2316yes—
245C42×D11C2316yes—
246C42×D11C2316yes—
247C42×D11C2316yes—
248#66923C2316yes—
249#66923C2316yes—
250#66922C2316yes—
251C4×Dic22C23112yes—
252C4×Dic22C2316yes—
253#62694—111nomaximal, Sylow
254C24×C11C2412yes—
255C23×D11C2413yes—
256C11×#41—42no—
257C11×#41—46no—
258C2×Q8×C11C2412yes—
259C2×Q8×C11C2413yes—
260C2×Q8×C11C2411yescharacteristic
261C2×D4×C11C2413yes—
262C2×D4×C11C2416yes—
263C2×D4×C11C2413yes—
264C2×D4×C11C2416yes—
265C2×D4×C11C24112yes—
266C22×C4×C11—44no—
267C22×C4×C11C2416yes—
268C22×C4×C11C2413yes—
269C22×C4×C11C2416yes—
270C22×C4×C11C2416yes—
271C2×C22⋊D11C24112yes—
272C2×C22⋊D11C24112yes—
273C2×C22⋊D11C24112yes—
274C2×C22⋊D11C24112yes—
275C22×Dic11—48no—
276C22×Dic11C24112yes—
277C22×Dic11C2416yes—
278C22×Dic11C24112yes—
279C22×Dic11C2413yes—
280#4343—44no—
281#4341—424no—
282#4341—412no—
283#4339—412no—
284C2×D44C2416yes—
285C2×D44C2416yes—
286C2×C4×D11—46no—
287C2×C4×D11—412no—
288C2×C4×D11C2416yes—
289C2×C4×D11C2416yes—
290C2×C4×D11C2416yes—
291C2×C4×D11C2416yes—
292C2×C4×D11C2416yes—
293C2×C4×D11C2416yes—
294C2×Dic22C24112yes—
295C2×Dic22C2416yes—
296C2×Dic22C2416yes—
297C11×C4⋊C4C2416yes—
298C11×C4⋊C4C24112yes—
299C11×C4⋊C4C24112yes—
300C11×C4⋊C4C2416yes—
301C11×C22⋊C4C24112yes—
302C11×C22⋊C4C24112yes—
303C11×C22⋊C4C24112yes—
304C11×C22⋊C4C2416yes—
305C11×C22⋊C4C2416yes—
306C42×C11C2416yes—
307C42×C11C2413yes—
308C42×C11C2413yes—
309C22⋊Dic11C24112yes—
310C22⋊Dic11C24112yes—
311C22⋊Dic11C24112yes—
312C22⋊Dic11C24112yes—
313C22⋊Dic11C2416yes—
314C22⋊Dic11C2416yes—
315(C2×D11)⋊C4C24112yes—
316(C2×D11)⋊C4C24112yes—
317(C2×D11)⋊C4C24112yes—
318(C2×D11)⋊C4C24112yes—
319(C2×D11)⋊C4C24112yes—
320(C2×D11)⋊C4C24112yes—
321C4⋊Dic11C24112yes—
322C4⋊Dic11C2416yes—
323C4⋊Dic11C2416yes—
324C4⋊Dic11C2416yes—
325C4⋊Dic11C2416yes—
326C4⋊Dic11C24112yes—
327Dic11⋊C4C24112yes—
328Dic11⋊C4C24112yes—
329Dic11⋊C4C24112yes—
330Dic11⋊C4C24112yes—
331Dic11⋊C4C24112yes—
332Dic11⋊C4C24112yes—
333Dic11⋊C4C24112yes—
334Dic11⋊C4C24112yes—
335C4×Dic11C2413yes—
336C4×Dic11C2416yes—
337C4×Dic11C2411yescharacteristic
338C4×Dic11C2416yes—
339C4×Dic11C2416yes—
340C4×Dic11C2416yes—
341C4×Dic11C2416yes—
342C4×Dic11C2416yes—
343C4×Dic11C24112yes—
344C4×Dic11C2416yes—
345C4×Dic11C2416yes—
346#3531—116no—
347#3531—116no—
348#3531—116no—
349#3529—116no—
350#3529—112no—
351#3529—1112no—
352#3529—113no—
353#3529—116no—
354#3529D1111yescharacteristic, complemented
355#3444—113no—
356#3444—116no—
357#3444—116no—
358C23×C11—44no—
359C23×C11—42no—
360C23×C11C2513yes—
361C23×C11C2516yes—
362C22×D11—43no—
363C22×D11—46no—
364C22×D11C2516yes—
365Q8×C11—42no—
366Q8×C11—43no—
367Q8×C11—41no—
368D4×C11—412no—
369D4×C11—46no—
370D4×C11—46no—
371D4×C11—43no—
372D4×C11—43no—
373C2×C4×C11—26no—
374C2×C4×C11—212no—
375C2×C4×C11—46no—
376C2×C4×C11—46no—
377C2×C4×C11C2516yes—
378C2×C4×C11C2516yes—
379C2×C4×C11C2513yes—
380C2×C4×C11C2516yes—
381C2×C4×C11C2511yescharacteristic
382C22⋊D11—412no—
383C22⋊D11—412no—
384C22⋊D11—412no—
385C22⋊D11—412no—
386C2×Dic11—212no—
387C2×Dic11—224no—
388C2×Dic11—43no—
389C2×Dic11—412no—
390C2×Dic11C2516yes—
391C2×Dic11C25112yes—
392C2×Dic11C2516yes—
393C2×Dic11C2512yes—
394D44—46no—
395D44—46no—
396C4×D11—212no—
397C4×D11—212no—
398C4×D11—212no—
399C4×D11—46no—
400C4×D11—46no—
401C4×D11—46no—
402Dic22—46no—
403Dic22—412no—
404Dic22—46no—
405#564—116no—
406#563—116no—
407#563—1112no—
408#563—1112no—
409#563—116no—
410#563—113no—
411#563—116no—
412#563—1112no—
413#563—116no—
414#563—1112no—
415#563—1112no—
416#563C2×D1113yescomplemented
417#562—116no—
418#562—116no—
419#562—1112no—
420#562—1112no—
421#562—1112no—
422#562—1112no—
423#562—1112no—
424#562—1112no—
425#562C2×D1116yescomplemented
426H(3,𝔽4)—113no—
427H(3,𝔽4)—116no—
428H(3,𝔽4)C2×D1111yescharacteristic, complemented
429#560—116no—
430#560—116no—
431#560—1112no—
432#560—1112no—
433#560—1112no—
434#560—116no—
435#560C2×D1116yescomplemented
436#533—116no—
437#533—116no—
438#533—116no—
439#533—1112no—
440#533—116no—
441#533—116no—
442#533—113no—
443#532—116no—
444#532—116no—
445#532—116no—
446#532—116no—
447#532—1112no—
448#532—116no—
449#532C2×D1113yes—
450#529—1112no—
451#529—1112no—
452#529—116no—
453#529—116no—
454#529—116no—
455#529—116no—
456#529—1112no—
457#529—1112no—
458#529—1112no—
459#529—1112no—
460#529—1112no—
461#529—1112no—
462#529—1112no—
463#529—1112no—
464#529—1112no—
465#529—1112no—
466#529—116no—
467#529C2×D1116yescomplemented
468#525—113no—
469#525—113no—
470#525—116no—
471#525—1112no—
472#525—116no—
473#525—1112no—
474#525—116no—
475#525—1112no—
476#525—1112no—
477#525—1112no—
478#525C2×D1116yescomplemented
479C4×#41—111no—
480C4×#41—113no—
481C4×#41—112no—
482C4×#41—1112no—
483C4×#41—116no—
484C4×#41—116no—
485C22×C42—112no—
486C22×C42—113no—
487C22×C11—26no—
488C22×C11—23no—
489C22×C11—26no—
490C22×C11—212no—
491C22×C11—48no—
492C22×C11C2611yescharacteristic
493C2×D11—26no—
494C2×D11—26no—
495C2×D11—26no—
496C2×D11—412no—
497C4×C11—26no—
498C4×C11—23no—
499C4×C11—26no—
500C4×C11—26no—
501C4×C11#58512yes—
502Dic11—26no—
503Dic11—26no—
504Dic11—212no—
505Dic11#58514yes—
506C2×#41—112no—
507C2×#41—1112no—
508C2×#41—116no—
509C2×#41—116no—
510C2×#41C22×D1111yescharacteristic
511C2×#41C22×D1113yes—
512C23×C4—114no—
513C23×C4—116no—
514C23×C4—113no—
515C23×C4C22×D1112yes—
516C4⋊Q8—116no—
517C4⋊Q8—116no—
518C4⋊Q8—116no—
519C4⋊Q8—116no—
520C4⋊Q8—1112no—
521C4⋊Q8—116no—
522C4⋊Q8C22×D1113yes—
523#127—116no—
524#127—116no—
525#127C22×D1113yes—
526#126—1112no—
527#126—1112no—
528#126—1112no—
529#126—1112no—
530#126—1112no—
531#126—1112no—
532#126—1112no—
533#126—1112no—
534#126—1112no—
535#126C22×D11112yes—
536#125—1112no—
537#125—1112no—
538#125—1112no—
539#125—1112no—
540#125—1112no—
541#125—1112no—
542#125—116no—
543#125—116no—
544#125C22×D1116yes—
545#124—116no—
546#124—116no—
547#124—1112no—
548#124—1112no—
549#124—1112no—
550#124—1112no—
551#124—1112no—
552#124—116no—
553#124C22×D1113yes—
554#124C22×D1113yes—
555#124C22×D1116yes—
556#123—116no—
557#123—116no—
558#123—1112no—
559#123—1112no—
560#123—1112no—
561#123—1112no—
562#123—1112no—
563#123—1112no—
564#123—1112no—
565#123—1112no—
566#123—1112no—
567#123—1112no—
568#123—1112no—
569#123—1112no—
570#123C22×D11112yes—
571#123C22×D1116yes—
572#123C22×D1116yes—
573C22⋊Q8—116no—
574C22⋊Q8—116no—
575C22⋊Q8—116no—
576C22⋊Q8—1112no—
577C22⋊Q8—1112no—
578C22⋊Q8—116no—
579C22⋊Q8—1112no—
580C22⋊Q8—1112no—
581C22⋊Q8—1112no—
582C22⋊Q8—116no—
583C22⋊Q8—1112no—
584C22⋊Q8—1112no—
585C22⋊Q8—1112no—
586C22⋊Q8—1112no—
587C22⋊Q8—1112no—
588C22⋊Q8—1112no—
589C22⋊Q8C22×D1116yes—
590C22⋊Q8C22×D11112yes—
591#121—116no—
592#121—116no—
593#121—1112no—
594#121—116no—
595#121—1112no—
596#121—1112no—
597#121—1112no—
598#121—1112no—
599#121—1112no—
600#121—1112no—
601#121—116no—
602#121—116no—
603#121—1112no—
604#121—1112no—
605#121—1112no—
606#121C22×D11112yes—
607#121C22×D1116yes—
608#121C22×D11112yes—
609#120—1112no—
610#120—116no—
611#120—116no—
612#120—1112no—
613#120—1112no—
614#120C22×D1116yes—
615#120C22×D1116yes—
616C4×Q8—112no—
617C4×Q8—116no—
618C4×Q8—112no—
619C4×Q8—116no—
620C4×Q8—1112no—
621C4×Q8—1112no—
622C4×Q8—116no—
623C4×Q8—1112no—
624C4×Q8C22×D1112yes—
625C4×D4—116no—
626C4×D4—1112no—
627C4×D4—116no—
628C4×D4—1112no—
629C4×D4—116no—
630C4×D4—1112no—
631C4×D4—1112no—
632C4×D4—1112no—
633C4×D4—116no—
634C4×D4—1112no—
635C4×D4—1112no—
636C4×D4—1112no—
637C4×D4—1112no—
638C4×D4—1112no—
639C4×D4—1112no—
640C4×D4—116no—
641C4×D4C22×D11112yes—
642C4×D4C22×D1116yes—
643#117—116no—
644#117—113no—
645#117—113no—
646#117—116no—
647#117—116no—
648#117—1112no—
649#117—1112no—
650#117—1112no—
651#117—1112no—
652#117—1112no—
653#117C22×D1116yes—
654C2×C42—116no—
655C2×C42—113no—
656C2×C42—1112no—
657C2×C42—116no—
658C2×C42—116no—
659C2×C42—116no—
660C2×C42—116no—
661C2×C42—116no—
662C2×C42—116no—
663C2×C42C22×D1113yes—
664C2×C11—43no—
665C2×C11—46no—
666C2×C11C2×#58512yes—
667C2×C11C2×#58511yescharacteristic
668D11—46no—
669C24—113no—
670C24C23×D1112yes—
671#41—46no—
672#41—42no—
673#41—4412no—
674#41—4424no—
675#41—4412no—
676#41—444no—
677C2×Q8—116no—
678C2×Q8—1112no—
679C2×Q8—116no—
680C2×Q8C23×D1111yescharacteristic
681C2×Q8C23×D1113yes—
682C2×Q8C23×D1112yes—
683C2×D4—1112no—
684C2×D4—1112no—
685C2×D4—1112no—
686C2×D4—1112no—
687C2×D4—116no—
688C2×D4—116no—
689C2×D4C23×D1113yes—
690C2×D4C23×D1116yes—
691C2×D4C23×D1113yes—
692C2×D4C23×D11112yes—
693C2×D4C23×D1116yes—
694C22×C4—44no—
695C22×C4—116no—
696C22×C4—1112no—
697C22×C4—113no—
698C22×C4—1112no—
699C22×C4—116no—
700C22×C4—116no—
701C22×C4—116no—
702C22×C4—116no—
703C22×C4—116no—
704C22×C4—116no—
705C22×C4—446no—
706C22×C4—4412no—
707C22×C4—448no—
708C22×C4C23×D1116yes—
709C22×C4C23×D1113yes—
710C22×C4C23×D1116yes—
711C22×C4C23×D1116yes—
712C4⋊C4—1112no—
713C4⋊C4—1112no—
714C4⋊C4—1112no—
715C4⋊C4—1112no—
716C4⋊C4—1112no—
717C4⋊C4—1112no—
718C4⋊C4—1112no—
719C4⋊C4—1112no—
720C4⋊C4—1112no—
721C4⋊C4—116no—
722C4⋊C4—116no—
723C4⋊C4—1112no—
724C4⋊C4—116no—
725C4⋊C4—116no—
726C4⋊C4C23×D1116yes—
727C4⋊C4C23×D1116yes—
728C4⋊C4C23×D11112yes—
729C4⋊C4C23×D11112yes—
730C22⋊C4—116no—
731C22⋊C4—116no—
732C22⋊C4—1112no—
733C22⋊C4—1112no—
734C22⋊C4—1112no—
735C22⋊C4—1112no—
736C22⋊C4—1112no—
737C22⋊C4—1112no—
738C22⋊C4—1112no—
739C22⋊C4—1112no—
740C22⋊C4—1112no—
741C22⋊C4—1112no—
742C22⋊C4C23×D11112yes—
743C22⋊C4C23×D11112yes—
744C22⋊C4C23×D11112yes—
745C22⋊C4C23×D1116yes—
746C22⋊C4C23×D1116yes—
747C42—1112no—
748C42—116no—
749C42—116no—
750C42—116no—
751C42—116no—
752C42—116no—
753C42—116no—
754C42—116no—
755C42—111no—
756C42—116no—
757C42—113no—
758C42C23×D1113yes—
759C42C23×D1113yes—
760C42C23×D1116yes—
761C11#6269411yescharacteristic, complemented, Sylow
762C23—42no—
763C23—44no—
764C23—116no—
765C23—446no—
766C23—443no—
767C23C24×D1113yes—
768C23C24×D1116yes—
769Q8—43no—
770Q8—41no—
771Q8—42no—
772Q8—4412no—
773Q8—446no—
774Q8—446no—
775D4—46no—
776D4—43no—
777D4—43no—
778D4—412no—
779D4—46no—
780D4—446no—
781D4—446no—
782D4—4412no—
783D4—4412no—
784D4—4412no—
785D4—4412no—
786C2×C4—212no—
787C2×C4—26no—
788C2×C4—46no—
789C2×C4—46no—
790C2×C4—112no—
791C2×C4—116no—
792C2×C4—1112no—
793C2×C4—116no—
794C2×C4—2212no—
795C2×C4—2212no—
796C2×C4—2212no—
797C2×C4—2224no—
798C2×C4—2212no—
799C2×C4—446no—
800C2×C4—446no—
801C2×C4—446no—
802C2×C4—4412no—
803C2×C4—443no—
804C2×C4C24×D1116yes—
805C2×C4C24×D1113yes—
806C2×C4C24×D1116yes—
807C2×C4C24×D1116yes—
808C2×C4C24×D1111yescharacteristic
809C22—26no—
810C22—212no—
811C22—26no—
812C22—23no—
813C22—48no—
814C22—226no—
815C22—226no—
816C22—226no—
817C22—4412no—
818C22C25×D1111yescharacteristic
819C4—26no—
820C4—26no—
821C4—26no—
822C4—23no—
823C4—114no—
824C4—226no—
825C4—2212no—
826C4—226no—
827C4#1062345512yes—
828C2—46no—
829C2—43no—
830C2—446no—
831C2D11×#58512yes—
832C2C2×#1062345511yescharacteristic
subgroupG/H
centerC2×C4C24×D11
commutator, socle, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC11×#3529C2
hypercenter#3529D11
hypocenterC11#62694
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #3529

Complements

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

NH ≅ G/Ntype
1. #13082762C2semidirect
2. #13082761C2semidirect
3. #13082760C2semidirect
4. #13082756C2semidirect
5. #13082754C2semidirect
6. #13082753C2semidirect
7. #13082752C2semidirect
8. #13082751C2semidirect
9. #13081911C2semidirect
10. #13081910C2semidirect
11. #13081908C2semidirect
12. C11×#3529C2semidirect
13. C11×#563C22semidirect
14. C11×#562C22semidirect
15. C11×H(3,𝔽4)C22semidirect
16. C11×#560C22semidirect
18. C11×#529C22semidirect
19. C11×#525C22semidirect
21. #10623359C22semidirect
22. #10623359C22semidirect
23. #41×Dic11C22semidirect
24. #41×Dic11C22semidirect
25. #10623322C22semidirect
26. C22×C4×Dic11C22semidirect
27. #10623266C22semidirect
28. #10623259C22semidirect
29. #10623251C22semidirect
31. #10623243C22semidirect
32. #10623243C22semidirect
33. #10623237C22semidirect
34. #10623237C22semidirect
35. #10623230C22semidirect
36. #10623222C22semidirect
37. #10623219C22semidirect
38. C11⋊#564C22semidirect
39. #10623215C22semidirect
40. #10623215C22semidirect
41. #10623214C22semidirect
42. #10623211C22semidirect
43. #10623211C22semidirect
44. #10623211C22semidirect
45. #10623203C22semidirect
46. #10623203C22semidirect
48. #10623198C22semidirect
49. #10623198C22semidirect
50. #10623197C22semidirect
51. #10623187C22semidirect
52. #10623182C22semidirect
53. #10623182C22semidirect
54. #10623180C22semidirect
55. #10623180C22semidirect
56. #10623180C22semidirect
57. #10623178C22semidirect
58. #10623177C22semidirect
59. #10623177C22semidirect
60. #10623158C22semidirect
61. #10623155C22semidirect
62. #10623153C22semidirect
63. #10623153C22semidirect
64. #10623152C22semidirect
65. #10623152C22semidirect
66. #10623152C22semidirect
67. #10623151C22semidirect
68. #10623151C22semidirect
69. #10623137C22semidirect
70. #10623137C22semidirect
71. #10623131C22semidirect
72. #10623131C22semidirect
75. #10623126C22semidirect
76. #10623126C22semidirect
77. #10623125C22semidirect
78. #10623117C22semidirect
79. #10623117C22semidirect
80. #10623109C22semidirect
81. C4×#4343C22semidirect
82. #10623088C22semidirect
84. #10623078C22semidirect
85. #10623069C22semidirect
86. #10623069C22semidirect
87. C4×#4341C22semidirect
88. C4×#4341C22semidirect
89. #10623059C22semidirect
90. #10623053C22semidirect
91. #10623048C22semidirect
92. #10623010C22semidirect
93. C2×C42×D11C22semidirect
94. #10623001C22semidirect
354. #3529D11semidirect
416. #563C2×D11semidirect
425. #562C2×D11semidirect
428. H(3,𝔽4)C2×D11semidirect
435. #560C2×D11semidirect
467. #529C2×D11semidirect
478. #525C2×D11semidirect
761. C11#62694semidirect

Maximal subgroups

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

subgroupindex
#130827622
#130827612
#130827602
#130827562
#130827542
#130827532
#130827522
#130827512
#130819112
#130819102
#130819082
C11×#35292
#6269411