Finite Group Databasebeta

← D11×#3529 #15660660

Subgroups — D11×#3529 #15660660

Order 2816.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082757C213yesmaximal, complemented
2#13082756C211yesmaximal, characteristic, complemented
3#13082755C216yesmaximal, complemented
4#13082754C216yesmaximal, complemented
5#13082753C216yesmaximal, complemented
6#13082752C213yesmaximal, complemented
7#13082751C216yesmaximal, complemented
8D11×#563C213yesmaximal, complemented
9D11×#562C216yesmaximal, complemented
10D11×H(3,𝔽4)C211yesmaximal, characteristic, complemented
11D11×#560C216yesmaximal, complemented
12D11×#532C213yesmaximal, complemented
13D11×#529C216yesmaximal, complemented
14D11×#525C216yesmaximal, complemented
15C11×#3529C211yesmaximal, characteristic, complemented
16C2×#41×D11C2213yes—
17C2×#41×D11C2211yescharacteristic, complemented
18C23×C4×D11C2212yescomplemented
19C11×#563C2213yescomplemented
20C11×#562C2216yescomplemented
21C11×H(3,𝔽4)C2211yescharacteristic, complemented
22C11×#560C2216yescomplemented
23C11×#532C2213yescomplemented
24C11×#529C2216yescomplemented
25C11×#525C2216yescomplemented
26#10623363C2213yescomplemented
27#10623363C2213yescomplemented
28#10623359C2216yescomplemented
29#10623322C2216yescomplemented
30#10623266C2216yescomplemented
31#10623256C2213yescomplemented
32D11×C4⋊Q8C2213yescomplemented
33#10623251C2216yescomplemented
34#10623247C2213yescomplemented
35D11×#127C2213yes—
36#10623243C22112yescomplemented
37#10623242C22112yescomplemented
38#10623237C22112yescomplemented
39D11×#126C22112yescomplemented
40#10623231C2216yescomplemented
41#10623230C2216yescomplemented
42#10623222C2216yescomplemented
43D11×#125C2216yescomplemented
44#10623215C2216yescomplemented
45#10623215C2216yescomplemented
46#10623214C2213yescomplemented
47#10623214C2216yescomplemented
48#10623211C2216yescomplemented
49D11×#124C2216yes—
50D11×#124C2213yes—
51D11×#124C2213yescomplemented
52#10623203C2213yescomplemented
53#10623199C2213yescomplemented
54#10623199C2213yescomplemented
55#10623198C22112yescomplemented
56#10623198C22112yescomplemented
57#10623197C22112yescomplemented
58#10623197C2216yescomplemented
59#10623187C2216yescomplemented
60#10623187C2216yescomplemented
61D11×#123C2216yes—
62D11×#123C22112yescomplemented
63D11×#123C2216yescomplemented
64#10623182C2216yescomplemented
65#10623180C22112yescomplemented
66#10623178C22112yescomplemented
67#10623178C22112yescomplemented
68#10623177C22112yescomplemented
69#10623158C22112yescomplemented
70D11×C22⋊Q8C2216yescomplemented
71D11×C22⋊Q8C22112yescomplemented
72#10623155C2216yescomplemented
73#10623152C22112yescomplemented
74#10623152C22112yescomplemented
75#10623151C22112yescomplemented
76#10623151C22112yescomplemented
77#10623151C22112yescomplemented
78#10623137C22112yescomplemented
79D11×#121C2216yes—
80D11×#121C22112yes—
81D11×#121C22112yescomplemented
82#10623131C2216yescomplemented
83#10623127C22112yescomplemented
84#10623126C22112yescomplemented
85#10623126C2216yescomplemented
86#10623125C2216yescomplemented
87D11×#120C2216yes—
88D11×#120C2216yescomplemented
89#10623117C2216yescomplemented
90#10623117C2216yescomplemented
91#10623111C2216yescomplemented
92C4×Q8×D11C2212yescomplemented
93#10623088C2216yescomplemented
94#10623079C22112yescomplemented
95#10623078C22112yescomplemented
96#10623078C22112yescomplemented
97C4×D4×D11C2216yes—
98C4×D4×D11C22112yescomplemented
99#10623069C22112yescomplemented
100#10623059C22112yescomplemented
101#10623055C2216yescomplemented
102D11×#117C2216yescomplemented
103#10623010C2216yescomplemented
104#10623008C2213yescomplemented
105C2×C42×D11C2213yescomplemented
106C24×D11C2312yes—
107C2×C11×#41C2313yes—
108C2×C11×#41C2311yescharacteristic, complemented
109C23×C4×C11C2312yescomplemented
110C23×Dic11C2312yescomplemented
111#41×D11—412no—
112#41×D11—44no—
113C2×#4343C2313yes—
114C2×#4343C2311yescharacteristic, complemented
115C2×Q8×D11C2311yescharacteristic
116C2×Q8×D11C2313yes—
117C2×Q8×D11C2312yes—
118C2×#4341C2313yes—
119C2×#4341C2316yes—
120C2×#4341C2313yescomplemented
121C2×D4×D11C23112yes—
122C2×D4×D11C2313yes—
123C2×D4×D11C2313yes—
124C2×D4×D11C2316yes—
125C2×D4×D11C2316yes—
126C2×#4339C2313yes—
127C2×#4339C2316yes—
128C2×#4339C2313yescomplemented
129C22×C4×D11—48no—
130C22×C4×D11C2313yes—
131C22×C4×D11C2316yes—
132C22×C4×D11C2316yes—
133C22×C4×D11C2316yes—
134C22×C4×D11C2316yescomplemented
135C22×C4×D11C2316yescomplemented
136C11×C4⋊Q8C2313yescomplemented
137C11×#127C2313yes—
138C11×#126C23112yescomplemented
139C11×#125C2316yescomplemented
140C11×#124C2316yes—
141C11×#124C2313yes—
142C11×#124C2313yescomplemented
143C11×#123C2316yes—
144C11×#123C2316yescomplemented
145C11×#123C23112yescomplemented
146C11×C22⋊Q8C23112yescomplemented
147C11×C22⋊Q8C2316yescomplemented
148C11×#121C23112yes—
149C11×#121C2316yes—
150C11×#121C23112yescomplemented
151C11×#120C2316yes—
152C11×#120C2316yescomplemented
153C4×Q8×C11C2312yescomplemented
154C4×D4×C11C2316yes—
155C4×D4×C11C23112yescomplemented
156C11×#117C2316yescomplemented
157C2×C42×C11C2313yescomplemented
158#67006C2316yes—
159#67006C2316yescomplemented
160#67000C2313yes—
161#67000C2316yes—
162#67000C2313yescomplemented
163#66999C23112yescomplemented
164#66999C2316yescomplemented
165Q8×Dic11C2312yescomplemented
166#66997C2313yescomplemented
167#66997C2313yescomplemented
168#66993C23112yes—
169#66993C2313yes—
170#66993C2313yes—
171#66992C23112yes—
172#66992C23112yes—
173#66992C23112yes—
174#66992C23112yescomplemented
175#66992C23112yescomplemented
176#66991C2316yes—
177#66991C23112yes—
178#66991C23112yescomplemented
179#66990C2316yes—
180#66990C23112yes—
181#66990C23112yescomplemented
182#66990C2316yescomplemented
183#66989C2313yes—
184#66989C2316yes—
185#66989C2313yescomplemented
186#66988C2316yes—
187#66988C23112yescomplemented
188#66988C2316yescomplemented
189D4×Dic11C2316yes—
190D4×Dic11C23112yescomplemented
191#66983C2316yes—
192#66983C23112yes—
193#66983C23112yescomplemented
194#66982C2316yes—
195#66982C23112yescomplemented
196#66982C2316yescomplemented
197C4×C22⋊D11C23112yes—
198C4×C22⋊D11C23112yescomplemented
199C4×C22⋊D11C23112yescomplemented
200#66979C2316yescomplemented
201#66977C2316yescomplemented
202#66977C23112yescomplemented
203C2×C4×Dic11C2313yescomplemented
204C2×C4×Dic11C2316yescomplemented
205#66951C23112yescomplemented
206#66951C23112yescomplemented
207#66951C23112yescomplemented
208#66950C23112yescomplemented
209#66950C2316yescomplemented
210#66949C23112yescomplemented
211#66949C23112yescomplemented
212#66949C23112yescomplemented
213#66948C2316yes—
214#66948C23112yes—
215#66948C23112yescomplemented
216#66947C23112yes—
217#66947C23112yescomplemented
218#66947C23112yescomplemented
219#66947C23112yescomplemented
220#66946C2316yes—
221#66946C23112yescomplemented
222#66945C23112yescomplemented
223C4⋊C4×D11C2316yes—
224C4⋊C4×D11C23112yes—
225C4⋊C4×D11C23112yes—
226C4⋊C4×D11C2316yes—
227#66943C2316yescomplemented
228#66943C2316yescomplemented
229#66942C23112yescomplemented
230#66942C23112yescomplemented
231#66941C23112yescomplemented
232#66940C2316yescomplemented
233#66939C2316yes—
234#66939C2316yescomplemented
235#66939C23112yescomplemented
236#66938C23112yes—
237#66938C23112yes—
238#66938C23112yes—
239#66938C23112yescomplemented
240#66937C23112yes—
241#66937C23112yes—
242#66937C23112yes—
243#66937C23112yescomplemented
244#66937C23112yescomplemented
245#66936C23112yes—
246#66936C23112yescomplemented
247#66936C23112yescomplemented
248#66936C23112yescomplemented
249#66935C23112yes—
250#66935C2316yes—
251#66935C2316yescomplemented
252#66935C23112yescomplemented
253(C22⋊D11)⋊C4C23112yes—
254(C22⋊D11)⋊C4C23112yescomplemented
255(C22⋊D11)⋊C4C23112yescomplemented
256C22⋊C4×D11C2316yes—
257C22⋊C4×D11C23112yes—
258C22⋊C4×D11C23112yes—
259C22⋊C4×D11C2316yes—
260C22⋊C4×D11C23112yes—
261#66932C23112yescomplemented
262#66932C23112yescomplemented
263#66932C23112yescomplemented
264#66931C23112yescomplemented
265#66931C23112yescomplemented
266#66931C23112yescomplemented
267#66930C2316yescomplemented
268#66930C2316yescomplemented
269#66929C23112yescomplemented
270#66928C2313yes—
271#66928C2316yes—
272#66928C2313yescomplemented
273#66927C2313yes—
274C4×D44C2316yes—
275C4×D44C23112yescomplemented
276#66925C23112yescomplemented
277C42×D11C2313yes—
278C42×D11C2316yes—
279C42×D11C2313yes—
280C42×D11C2313yescomplemented
281C42×D11C2316yescomplemented
282C42×D11C2313yescomplemented
283#66923C2316yescomplemented
284#66922C2313yescomplemented
285C4×Dic22C2316yescomplemented
286C2×#3529—111nomaximal, Sylow
287C24×C11C2412yes—
288C23×D11—44no—
289C23×D11—48no—
290C23×D11C2416yes—
291C23×D11C2413yes—
292C23×D11C2416yes—
293C11×#41—46no—
294C11×#41—42no—
295C2×Q8×C11C2411yescharacteristic
296C2×Q8×C11C2413yes—
297C2×Q8×C11C2412yes—
298C2×D4×C11C2416yes—
299C2×D4×C11C24112yes—
300C2×D4×C11C2413yes—
301C2×D4×C11C2416yes—
302C2×D4×C11C2413yes—
303C22×C4×C11—44no—
304C22×C4×C11C2413yes—
305C22×C4×C11C2416yes—
306C22×C4×C11C2416yes—
307C22×C4×C11C2416yes—
308C2×C22⋊D11C24112yes—
309C2×C22⋊D11C24112yes—
310C2×C22⋊D11C24112yes—
311C2×C22⋊D11C2416yes—
312C2×C22⋊D11C2416yes—
313C2×C22⋊D11C2416yes—
314C2×C22⋊D11C2416yes—
315C22×Dic11—44no—
316C22×Dic11C2416yes—
317C22×Dic11C2413yes—
318C22×Dic11C2416yes—
319C22×Dic11C2416yes—
320#4343—46no—
321#4343—42no—
322Q8×D11—44no—
323Q8×D11—46no—
324Q8×D11—42no—
325#4341—412no—
326#4341—46no—
327#4341—46no—
328D4×D11—424no—
329D4×D11—412no—
330D4×D11—46no—
331D4×D11—412no—
332D4×D11—46no—
333#4339—412no—
334#4339—46no—
335#4339—46no—
336C2×D44C2416yes—
337C2×D44C24112yes—
338C2×D44C2413yes—
339C2×D44C2413yes—
340C2×D44C2416yes—
341C2×C4×D11—224no—
342C2×C4×D11—212no—
343C2×C4×D11—412no—
344C2×C4×D11—412no—
345C2×C4×D11—412no—
346C2×C4×D11—412no—
347C2×C4×D11C2416yes—
348C2×C4×D11C2416yes—
349C2×C4×D11C2413yes—
350C2×C4×D11C2413yes—
351C2×C4×D11C2413yes—
352C2×C4×D11C2416yes—
353C2×C4×D11C2416yes—
354C2×C4×D11C2416yes—
355C2×C4×D11C2416yes—
356C2×C4×D11C2416yes—
357C2×C4×D11C24112yes—
358C2×C4×D11C2411yescharacteristic
359C2×Dic22C2416yes—
360C2×Dic22C2413yes—
361C2×Dic22C2413yes—
362C2×Dic22C2416yes—
363C11×C4⋊C4C2416yes—
364C11×C4⋊C4C24112yes—
365C11×C4⋊C4C24112yes—
366C11×C4⋊C4C2416yes—
367C11×C22⋊C4C2416yes—
368C11×C22⋊C4C2416yes—
369C11×C22⋊C4C24112yes—
370C11×C22⋊C4C24112yes—
371C11×C22⋊C4C24112yes—
372C42×C11C2416yes—
373C42×C11C2413yes—
374C42×C11C2413yes—
375C22⋊Dic11C2416yes—
376C22⋊Dic11C2416yes—
377C22⋊Dic11C24112yes—
378C22⋊Dic11C24112yes—
379C22⋊Dic11C24112yes—
380(C2×D11)⋊C4C24112yes—
381(C2×D11)⋊C4C24112yes—
382(C2×D11)⋊C4C24112yes—
383(C2×D11)⋊C4C24112yes—
384(C2×D11)⋊C4C24112yes—
385(C2×D11)⋊C4C24112yes—
386(C2×D11)⋊C4C24112yes—
387(C2×D11)⋊C4C24112yes—
388C4⋊Dic11C2416yes—
389C4⋊Dic11C24112yes—
390C4⋊Dic11C2416yes—
391C4⋊Dic11C24112yes—
392Dic11⋊C4C24112yes—
393Dic11⋊C4C24112yes—
394Dic11⋊C4C24112yes—
395Dic11⋊C4C24112yes—
396Dic11⋊C4C24112yes—
397Dic11⋊C4C24112yes—
398C4×Dic11C2416yes—
399C4×Dic11C2416yes—
400C4×Dic11C2416yes—
401C4×Dic11C2416yes—
402C4×Dic11C2413yes—
403C4×Dic11C2416yes—
404C4×Dic11C2413yes—
405#3529—113no—
406#3529—116no—
407#3529—111no—
408#3529—116no—
409#3529—113no—
410#3529—116no—
411#3529—116no—
412#3529D1111yescharacteristic, direct product factor
413C2×#563—113no—
414C2×#562—116no—
415C2×H(3,𝔽4)—111no—
416C2×#560—116no—
417C2×#532—113no—
418C2×#529—116no—
419C2×#525—116no—
420C23×C11—42no—
421C23×C11—44no—
422C23×C11C2516yes—
423C23×C11C2513yes—
424C22×D11—212no—
425C22×D11—26no—
426C22×D11—212no—
427C22×D11—224no—
428C22×D11—46no—
429C22×D11—412no—
430C22×D11—432no—
431C22×D11C2516yes—
432C22×D11C2513yes—
433C22×D11C2511yescharacteristic
434Q8×C11—43no—
435Q8×C11—41no—
436Q8×C11—42no—
437D4×C11—46no—
438D4×C11—43no—
439D4×C11—43no—
440D4×C11—412no—
441D4×C11—46no—
442C2×C4×C11—212no—
443C2×C4×C11—26no—
444C2×C4×C11—46no—
445C2×C4×C11—46no—
446C2×C4×C11C2516yes—
447C2×C4×C11C2513yes—
448C2×C4×C11C2516yes—
449C2×C4×C11C2516yes—
450C2×C4×C11C2511yescharacteristic
451C22⋊D11—46no—
452C22⋊D11—46no—
453C22⋊D11—46no—
454C22⋊D11—46no—
455C22⋊D11—412no—
456C22⋊D11—412no—
457C22⋊D11—412no—
458C2×Dic11—212no—
459C2×Dic11—26no—
460C2×Dic11—46no—
461C2×Dic11—46no—
462C2×Dic11C2516yes—
463C2×Dic11C2516yes—
464C2×Dic11C2513yes—
465C2×Dic11C2516yes—
466C2×Dic11C2511yescharacteristic
467D44—46no—
468D44—43no—
469D44—43no—
470D44—412no—
471D44—46no—
472C4×D11—212no—
473C4×D11—26no—
474C4×D11—212no—
475C4×D11—212no—
476C4×D11—212no—
477C4×D11—26no—
478C4×D11—212no—
479C4×D11—26no—
480C4×D11—412no—
481C4×D11—46no—
482C4×D11—46no—
483C4×D11H(5,𝔽2)14yes—
484Dic22—43no—
485Dic22—46no—
486Dic22—43no—
487Dic22—46no—
488C22×#41—113no—
489C22×#41—111no—
490C24×C4—112no—
491#563—116no—
492#563—1112no—
493#563—116no—
494#563—113no—
495#563—116no—
496#563—1112no—
497#563C2×D1113yescomplemented
498#562—116no—
499#562—116no—
500#562—116no—
501#562—1112no—
502#562—1112no—
503#562—1112no—
504#562—1112no—
505#562—1112no—
506#562—1112no—
507#562C2×D1116yescomplemented
508H(3,𝔽4)—116no—
509H(3,𝔽4)—113no—
510H(3,𝔽4)—116no—
511H(3,𝔽4)C2×D1111yescharacteristic, complemented
512#560—116no—
513#560—1112no—
514#560—116no—
515#560—1112no—
516#560—1112no—
517#560—1112no—
518#560—1112no—
519#560—116no—
520#560—1112no—
521#560C2×D1116yescomplemented
522#532—113no—
523#532—113no—
524#532—113no—
525#532—113no—
526#532—113no—
527#532—113no—
528#532—1112no—
529#532—1112no—
530#532—113no—
531#532C2×D1113yescomplemented
532C2×C4⋊Q8—113no—
533C2×#127—113no—
534#529—1112no—
535#529—116no—
536#529—116no—
537#529—1112no—
538#529—116no—
539#529—116no—
540#529—116no—
541#529—116no—
542#529—1112no—
543#529—1112no—
544#529—116no—
545#529C2×D1116yescomplemented
546C2×#126—1112no—
547C2×#125—116no—
548C2×#124—116no—
549C2×#124—113no—
550C2×#124—113no—
551#525—116no—
552#525—116no—
553#525—116no—
554#525—116no—
555#525—1112no—
556#525—1112no—
557#525—116no—
558#525—116no—
559#525—1112no—
560#525—1112no—
561#525—116no—
562#525C2×D1116yescomplemented
563C2×#123—116no—
564C2×#123—116no—
565C2×#123—1112no—
566C2×C22⋊Q8—1112no—
567C2×C22⋊Q8—116no—
568C2×#121—1112no—
569C2×#121—116no—
570C2×#121—1112no—
571C2×#120—116no—
572C2×#120—116no—
573C2×C4×Q8—112no—
574C2×C4×D4—116no—
575C2×C4×D4—1112no—
576C2×#117—116no—
577C22×C42—113no—
578C22×C11—26no—
579C22×C11—23no—
580C22×C11—26no—
581C22×C11—212no—
582C22×C11—48no—
583C22×C11C2611yescharacteristic
584C2×D11—26no—
585C2×D11—23no—
586C2×D11—212no—
587C2×D11—26no—
588C2×D11—424no—
589C2×D11—412no—
590C2×D11—424no—
591C2×D11C2×H(5,𝔽2)12yes—
592C2×D11#58514yes—
593C4×C11—26no—
594C4×C11—23no—
595C4×C11—26no—
596C4×C11—26no—
597C4×C11C2×H(5,𝔽2)12yes—
598Dic11—23no—
599Dic11—26no—
600Dic11—26no—
601Dic11—26no—
602Dic11C2×H(5,𝔽2)12yes—
603C25—112no—
604C2×#41—113no—
605C2×#41—111no—
606C2×#41—116no—
607C2×#41—113no—
608C2×#41—113no—
609C2×#41—116no—
610C2×#41—113no—
611C2×#41—113no—
612C2×#41—4412no—
613C2×#41—444no—
614C2×#41C22×D1113yes—
615C2×#41C22×D1111yescharacteristic, complemented
616C22×Q8—112no—
617C22×Q8—113no—
618C22×Q8—111no—
619C22×D4—116no—
620C22×D4—1112no—
621C22×D4—113no—
622C22×D4—116no—
623C22×D4—113no—
624C23×C4—112no—
625C23×C4—116no—
626C23×C4—113no—
627C23×C4—116no—
628C23×C4—116no—
629C23×C4—116no—
630C23×C4—116no—
631C23×C4—448no—
632C23×C4C22×D1112yescomplemented
633C4⋊Q8—113no—
634C4⋊Q8—113no—
635C4⋊Q8—1112no—
636C4⋊Q8—113no—
637C4⋊Q8C22×D1113yescomplemented
638#127—113no—
639#127—113no—
640#127—1112no—
641#127—113no—
642#127C22×D1113yes—
643#126—1112no—
644#126—1112no—
645#126—1112no—
646#126—1112no—
647#126—1112no—
648#126—1112no—
649#126—1112no—
650#126C22×D11112yescomplemented
651#125—1112no—
652#125—1112no—
653#125—116no—
654#125—116no—
655#125—116no—
656#125C22×D1116yescomplemented
657#124—116no—
658#124—113no—
659#124—113no—
660#124—116no—
661#124—113no—
662#124—113no—
663#124—1112no—
664#124—1112no—
665#124—1112no—
666#124—1112no—
667#124—116no—
668#124—113no—
669#124—113no—
670#124C22×D1116yes—
671#124C22×D1113yes—
672#124C22×D1113yescomplemented
673#123—116no—
674#123—116no—
675#123—1112no—
676#123—116no—
677#123—116no—
678#123—1112no—
679#123—1112no—
680#123—1112no—
681#123—1112no—
682#123—1112no—
683#123—1112no—
684#123—116no—
685#123—1112no—
686#123—116no—
687#123—1112no—
688#123—1112no—
689#123—1112no—
690#123C22×D1116yes—
691#123C22×D1116yescomplemented
692#123C22×D11112yescomplemented
693C22⋊Q8—1112no—
694C22⋊Q8—116no—
695C22⋊Q8—1112no—
696C22⋊Q8—116no—
697C22⋊Q8—1112no—
698C22⋊Q8—1112no—
699C22⋊Q8—1112no—
700C22⋊Q8—1112no—
701C22⋊Q8—116no—
702C22⋊Q8—1112no—
703C22⋊Q8—1112no—
704C22⋊Q8—1112no—
705C22⋊Q8C22×D11112yescomplemented
706C22⋊Q8C22×D1116yescomplemented
707#121—1112no—
708#121—1112no—
709#121—1112no—
710#121—116no—
711#121—1112no—
712#121—1112no—
713#121—1112no—
714#121—1112no—
715#121—1112no—
716#121—116no—
717#121—1112no—
718#121—1112no—
719#121—116no—
720#121—1112no—
721#121—1112no—
722#121—1112no—
723#121—1112no—
724#121—1112no—
725#121—1112no—
726#121C22×D11112yes—
727#121C22×D1116yes—
728#121C22×D11112yescomplemented
729#120—116no—
730#120—116no—
731#120—116no—
732#120—1112no—
733#120—116no—
734#120—1112no—
735#120—1112no—
736#120—116no—
737#120—1112no—
738#120—116no—
739#120C22×D1116yes—
740#120C22×D1116yescomplemented
741C4×Q8—112no—
742C4×Q8—116no—
743C4×Q8—116no—
744C4×Q8C22×D1112yescomplemented
745C4×D4—116no—
746C4×D4—1112no—
747C4×D4—1112no—
748C4×D4—1112no—
749C4×D4—1112no—
750C4×D4—116no—
751C4×D4—1112no—
752C4×D4—1112no—
753C4×D4—1112no—
754C4×D4—1112no—
755C4×D4—116no—
756C4×D4—1112no—
757C4×D4C22×D1116yes—
758C4×D4C22×D11112yescomplemented
759#117—116no—
760#117—1112no—
761#117—116no—
762#117—116no—
763#117—1112no—
764#117C22×D1116yescomplemented
765C2×C4⋊C4—1112no—
766C2×C4⋊C4—1112no—
767C2×C4⋊C4—116no—
768C2×C4⋊C4—116no—
769C2×C22⋊C4—116no—
770C2×C22⋊C4—116no—
771C2×C22⋊C4—1112no—
772C2×C22⋊C4—1112no—
773C2×C22⋊C4—1112no—
774C2×C42—116no—
775C2×C42—113no—
776C2×C42—116no—
777C2×C42—113no—
778C2×C42—113no—
779C2×C42—113no—
780C2×C42—113no—
781C2×C42—116no—
782C2×C42C22×D1113yescomplemented
783C2×C11—46no—
784C2×C11—43no—
785C2×C11C22×H(5,𝔽2)11yescharacteristic
786C2×C11C2×#58512yes—
787D11—43no—
788D11—46no—
789D11#352914yesdirect product factor
790C24—116no—
791C24—113no—
792C24—116no—
793C24—444no—
794C24—448no—
795C24C23×D1112yes—
796#41—46no—
797#41—42no—
798#41—4412no—
799#41—446no—
800#41—446no—
801#41—4412no—
802#41—446no—
803#41—446no—
804#41—446no—
805#41—442no—
806C2×Q8—116no—
807C2×Q8—116no—
808C2×Q8—113no—
809C2×Q8—113no—
810C2×Q8—446no—
811C2×Q8—442no—
812C2×Q8—444no—
813C2×Q8C23×D1112yes—
814C2×Q8C23×D1113yes—
815C2×Q8C23×D1111yescharacteristic
816C2×D4—1112no—
817C2×D4—1112no—
818C2×D4—1112no—
819C2×D4—116no—
820C2×D4—116no—
821C2×D4—116no—
822C2×D4—116no—
823C2×D4—116no—
824C2×D4—1112no—
825C2×D4—113no—
826C2×D4—116no—
827C2×D4—113no—
828C2×D4—4412no—
829C2×D4—446no—
830C2×D4—446no—
831C2×D4—4424no—
832C2×D4—4412no—
833C2×D4C23×D1116yes—
834C2×D4C23×D11112yes—
835C2×D4C23×D1113yes—
836C2×D4C23×D1116yes—
837C2×D4C23×D1113yes—
838C22×C4—44no—
839C22×C4—111no—
840C22×C4—113no—
841C22×C4—116no—
842C22×C4—116no—
843C22×C4—116no—
844C22×C4—116no—
845C22×C4—116no—
846C22×C4—113no—
847C22×C4—113no—
848C22×C4—116no—
849C22×C4—116no—
850C22×C4—113no—
851C22×C4—116no—
852C22×C4—116no—
853C22×C4—116no—
854C22×C4—1112no—
855C22×C4—2224no—
856C22×C4—2212no—
857C22×C4—4412no—
858C22×C4—4412no—
859C22×C4—4412no—
860C22×C4—4412no—
861C22×C4—444no—
862C22×C4C23×D1113yes—
863C22×C4C23×D1116yes—
864C22×C4C23×D1116yes—
865C22×C4C23×D1116yes—
866C4⋊C4—1112no—
867C4⋊C4—1112no—
868C4⋊C4—1112no—
869C4⋊C4—1112no—
870C4⋊C4—1112no—
871C4⋊C4—1112no—
872C4⋊C4—1112no—
873C4⋊C4—116no—
874C4⋊C4—1112no—
875C4⋊C4—116no—
876C4⋊C4C23×D11112yes—
877C4⋊C4C23×D1116yes—
878C4⋊C4C23×D11112yes—
879C4⋊C4C23×D1116yes—
880C22⋊C4—116no—
881C22⋊C4—116no—
882C22⋊C4—1112no—
883C22⋊C4—1112no—
884C22⋊C4—1112no—
885C22⋊C4—1112no—
886C22⋊C4—1112no—
887C22⋊C4—1112no—
888C22⋊C4—1112no—
889C22⋊C4—1112no—
890C22⋊C4—1112no—
891C22⋊C4—1112no—
892C22⋊C4—1112no—
893C22⋊C4C23×D1116yes—
894C22⋊C4C23×D1116yes—
895C22⋊C4C23×D11112yes—
896C22⋊C4C23×D11112yes—
897C22⋊C4C23×D11112yes—
898C42—116no—
899C42—116no—
900C42—113no—
901C42—116no—
902C42—113no—
903C42—116no—
904C42—116no—
905C42C23×D1113yes—
906C42C23×D1113yes—
907C42C23×D1116yes—
908C11C2×#352911yescharacteristic, complemented, Sylow
909C23—42no—
910C23—44no—
911C23—111no—
912C23—116no—
913C23—113no—
914C23—2212no—
915C23—226no—
916C23—2212no—
917C23—2224no—
918C23—446no—
919C23—4412no—
920C23—4432no—
921C23C24×D1116yes—
922C23C24×D1113yes—
923Q8—42no—
924Q8—43no—
925Q8—41no—
926Q8—446no—
927Q8—443no—
928Q8—443no—
929Q8—446no—
930D4—412no—
931D4—46no—
932D4—46no—
933D4—43no—
934D4—43no—
935D4—446no—
936D4—443no—
937D4—443no—
938D4—4412no—
939D4—446no—
940D4—446no—
941D4—446no—
942D4—446no—
943D4—446no—
944D4—4412no—
945D4—4412no—
946D4—4412no—
947C2×C4—212no—
948C2×C4—26no—
949C2×C4—46no—
950C2×C4—46no—
951C2×C4—111no—
952C2×C4—114no—
953C2×C4—116no—
954C2×C4—116no—
955C2×C4—113no—
956C2×C4—116no—
957C2×C4—2212no—
958C2×C4—226no—
959C2×C4—2212no—
960C2×C4—226no—
961C2×C4—2212no—
962C2×C4—2212no—
963C2×C4—2212no—
964C2×C4—226no—
965C2×C4—2212no—
966C2×C4—226no—
967C2×C4—4412no—
968C2×C4—446no—
969C2×C4—446no—
970C2×C4—446no—
971C2×C4—446no—
972C2×C4C24×D1116yes—
973C2×C4C24×D1116yes—
974C2×C4C24×D1113yes—
975C2×C4C24×D1116yes—
976C2×C4C24×D1111yescharacteristic
977C22—26no—
978C22—23no—
979C22—26no—
980C22—212no—
981C22—48no—
982C22—112no—
983C22—114no—
984C22—226no—
985C22—223no—
986C22—226no—
987C22—2212no—
988C22—4424no—
989C22—4412no—
990C22—4424no—
991C22C25×D1111yescharacteristic
992C4—26no—
993C4—23no—
994C4—26no—
995C4—26no—
996C4—112no—
997C4—226no—
998C4—223no—
999C4—226no—
1000C4—226no—
1001C4D11×H(5,𝔽2)12yes—
1002C2—46no—
1003C2—43no—
1004C2—114no—
1005C2—446no—
1006C2—443no—
1007C2C2×D11×H(5,𝔽2)11yescharacteristic
1008C2D11×#58512yes—
subgroupG/H
centerC2×C4C24×D11
commutator, socle, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC11×#3529C2
hypercenter#3529D11
hypocenterC11C2×#3529
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #3529

Complements

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

NH ≅ G/Ntype
1. #13082757C2semidirect
2. #13082756C2semidirect
3. #13082755C2semidirect
4. #13082754C2semidirect
5. #13082753C2semidirect
6. #13082752C2semidirect
7. #13082751C2semidirect
8. D11×#563C2semidirect
9. D11×#562C2semidirect
10. D11×H(3,𝔽4)C2semidirect
11. D11×#560C2semidirect
12. D11×#532C2semidirect
13. D11×#529C2semidirect
14. D11×#525C2semidirect
15. C11×#3529C2semidirect
17. C2×#41×D11C22semidirect
18. C23×C4×D11C22semidirect
19. C11×#563C22semidirect
20. C11×#562C22semidirect
21. C11×H(3,𝔽4)C22semidirect
22. C11×#560C22semidirect
23. C11×#532C22semidirect
24. C11×#529C22semidirect
25. C11×#525C22semidirect
26. #10623363C22semidirect
27. #10623363C22semidirect
28. #10623359C22semidirect
29. #10623322C22semidirect
30. #10623266C22semidirect
31. #10623256C22semidirect
32. D11×C4⋊Q8C22semidirect
33. #10623251C22semidirect
34. #10623247C22semidirect
36. #10623243C22semidirect
37. #10623242C22semidirect
38. #10623237C22semidirect
39. D11×#126C22semidirect
40. #10623231C22semidirect
41. #10623230C22semidirect
42. #10623222C22semidirect
43. D11×#125C22semidirect
44. #10623215C22semidirect
45. #10623215C22semidirect
46. #10623214C22semidirect
47. #10623214C22semidirect
48. #10623211C22semidirect
51. D11×#124C22semidirect
52. #10623203C22semidirect
53. #10623199C22semidirect
54. #10623199C22semidirect
55. #10623198C22semidirect
56. #10623198C22semidirect
57. #10623197C22semidirect
58. #10623197C22semidirect
59. #10623187C22semidirect
60. #10623187C22semidirect
62. D11×#123C22semidirect
63. D11×#123C22semidirect
64. #10623182C22semidirect
65. #10623180C22semidirect
66. #10623178C22semidirect
67. #10623178C22semidirect
68. #10623177C22semidirect
69. #10623158C22semidirect
70. D11×C22⋊Q8C22semidirect
71. D11×C22⋊Q8C22semidirect
72. #10623155C22semidirect
73. #10623152C22semidirect
74. #10623152C22semidirect
75. #10623151C22semidirect
76. #10623151C22semidirect
77. #10623151C22semidirect
78. #10623137C22semidirect
81. D11×#121C22semidirect
82. #10623131C22semidirect
83. #10623127C22semidirect
84. #10623126C22semidirect
85. #10623126C22semidirect
86. #10623125C22semidirect
88. D11×#120C22semidirect
89. #10623117C22semidirect
90. #10623117C22semidirect
91. #10623111C22semidirect
92. C4×Q8×D11C22semidirect
93. #10623088C22semidirect
94. #10623079C22semidirect
95. #10623078C22semidirect
96. #10623078C22semidirect
98. C4×D4×D11C22semidirect
99. #10623069C22semidirect
100. #10623059C22semidirect
101. #10623055C22semidirect
102. D11×#117C22semidirect
103. #10623010C22semidirect
104. #10623008C22semidirect
105. C2×C42×D11C22semidirect
108. C2×C11×#41C23semidirect
109. C23×C4×C11C23semidirect
110. C23×Dic11C23semidirect
114. C2×#4343C23semidirect
120. C2×#4341C23semidirect
128. C2×#4339C23semidirect
134. C22×C4×D11C23semidirect
135. C22×C4×D11C23semidirect
136. C11×C4⋊Q8C23semidirect
138. C11×#126C23semidirect
139. C11×#125C23semidirect
142. C11×#124C23semidirect
144. C11×#123C23semidirect
145. C11×#123C23semidirect
146. C11×C22⋊Q8C23semidirect
147. C11×C22⋊Q8C23semidirect
150. C11×#121C23semidirect
152. C11×#120C23semidirect
153. C4×Q8×C11C23semidirect
155. C4×D4×C11C23semidirect
156. C11×#117C23semidirect
157. C2×C42×C11C23semidirect
159. #67006C23semidirect
162. #67000C23semidirect
163. #66999C23semidirect
164. #66999C23semidirect
165. Q8×Dic11C23semidirect
166. #66997C23semidirect
167. #66997C23semidirect
174. #66992C23semidirect
175. #66992C23semidirect
178. #66991C23semidirect
181. #66990C23semidirect
182. #66990C23semidirect
185. #66989C23semidirect
187. #66988C23semidirect
188. #66988C23semidirect
190. D4×Dic11C23semidirect
193. #66983C23semidirect
195. #66982C23semidirect
196. #66982C23semidirect
198. C4×C22⋊D11C23semidirect
199. C4×C22⋊D11C23semidirect
200. #66979C23semidirect
201. #66977C23semidirect
202. #66977C23semidirect
203. C2×C4×Dic11C23semidirect
204. C2×C4×Dic11C23semidirect
205. #66951C23semidirect
206. #66951C23semidirect
207. #66951C23semidirect
208. #66950C23semidirect
209. #66950C23semidirect
210. #66949C23semidirect
211. #66949C23semidirect
212. #66949C23semidirect
215. #66948C23semidirect
217. #66947C23semidirect
218. #66947C23semidirect
219. #66947C23semidirect
221. #66946C23semidirect
222. #66945C23semidirect
227. #66943C23semidirect
228. #66943C23semidirect
229. #66942C23semidirect
230. #66942C23semidirect
231. #66941C23semidirect
232. #66940C23semidirect
234. #66939C23semidirect
235. #66939C23semidirect
239. #66938C23semidirect
243. #66937C23semidirect
244. #66937C23semidirect
246. #66936C23semidirect
247. #66936C23semidirect
248. #66936C23semidirect
251. #66935C23semidirect
252. #66935C23semidirect
254. (C22⋊D11)⋊C4C23semidirect
255. (C22⋊D11)⋊C4C23semidirect
261. #66932C23semidirect
262. #66932C23semidirect
263. #66932C23semidirect
264. #66931C23semidirect
265. #66931C23semidirect
266. #66931C23semidirect
267. #66930C23semidirect
268. #66930C23semidirect
269. #66929C23semidirect
272. #66928C23semidirect
275. C4×D44C23semidirect
276. #66925C23semidirect
280. C42×D11C23semidirect
281. C42×D11C23semidirect
282. C42×D11C23semidirect
283. #66923C23semidirect
284. #66922C23semidirect
285. C4×Dic22C23semidirect
412. #3529D11direct (N × H)
497. #563C2×D11semidirect
507. #562C2×D11semidirect
511. H(3,𝔽4)C2×D11semidirect
521. #560C2×D11semidirect
531. #532C2×D11semidirect
545. #529C2×D11semidirect
562. #525C2×D11semidirect
615. C2×#41C22×D11semidirect
632. C23×C4C22×D11semidirect
637. C4⋊Q8C22×D11semidirect
650. #126C22×D11semidirect
656. #125C22×D11semidirect
672. #124C22×D11semidirect
691. #123C22×D11semidirect
692. #123C22×D11semidirect
705. C22⋊Q8C22×D11semidirect
706. C22⋊Q8C22×D11semidirect
728. #121C22×D11semidirect
740. #120C22×D11semidirect
744. C4×Q8C22×D11semidirect
758. C4×D4C22×D11semidirect
764. #117C22×D11semidirect
782. C2×C42C22×D11semidirect
789. D11#3529direct (N × H)
908. C11C2×#3529semidirect

Maximal subgroups

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

subgroupindex
#130827572
#130827562
#130827552
#130827542
#130827532
#130827522
#130827512
D11×#5632
D11×#5622
D11×H(3,𝔽4)2
D11×#5602
D11×#5322
D11×#5292
D11×#5252
C11×#35292
C2×#352911