Finite Group Databasebeta

← C11×#23587 #14600780

Subgroups — C11×#23587 #14600780

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3460C211yesmaximal, characteristic, complemented
2C4×C11×AGL(1,ℤ/8)C212yesmaximal, complemented
3C4×C11×#127C211yesmaximal, characteristic, complemented
4C11×#2060C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#2027C211yesmaximal, characteristic, complemented
8C11×#2006C211yesmaximal, characteristic, complemented
9C11×#2002C212yesmaximal, complemented
10C4×C11×#104C212yesmaximal, complemented
11C4×C11×#100C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C11×#544C2211yescharacteristic
14C11×#542—22no—
15C11×#540—22no—
16C11×#538—22no—
17C11×#537C2211yescharacteristic
18C11×#535C2212yes—
19C11×#532—22no—
20C2×C11×#127C2211yescharacteristic
21C11×#529—22no—
22C11×#525—22no—
23C4×C11×#41C2212yes—
24C2×C4×D4×C11—22no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C11×#442—22no—
28C11×#440—22no—
29C4×C11×SD16—22no—
30C4×C11×D8—22no—
31C11×#428C2212yes—
32C2×C11×#104C2212yes—
33C2×C11×#104C2212yes—
34C11×#418C2212yes—
35C11×#417C2212yes—
36C2×C11×#100C2212yes—
37C4×C11×M16C2212yes—
38C11×#390—22no—
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#384C2211yescharacteristic
42C43×C11C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41C2312yes—
49C22×D4×C11—22no—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D412yes—
54C11×AGL(1,ℤ/8)—24no—
55C11×AGL(1,ℤ/8)—24no—
56C2×C11×SD16—22no—
57C2×C11×D8—22no—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C11×C4⋊Q8—22no—
61C11×#127—22no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#126—24no—
65C11×#125—22no—
66C11×#124—24no—
67C11×#124—22no—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×#121—22no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#120—24no—
80C4×Q8×C11D412yescomplemented
81C4×Q8×C11D412yescomplemented
82C4×D4×C11—24no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—48no—
90C4×D4×C11D412yescomplemented
91C4×D4×C11D412yescomplemented
92C11×#117—22no—
93C11×#117—22no—
94C11×#117C2312yes—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D412yes—
102C2×C42×C11—21no—
103C2×C42×C11—22no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C11×#107—22no—
109C11×#106—22no—
110C11×#104—24no—
111C11×#104—24no—
112C11×#103—22no—
113C11×#102—22no—
114C11×#102—22no—
115C11×#102—22no—
116C11×#100—24no—
117C11×#97—22no—
118C4×C8×C11—22no—
119#23587C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11C2×D412yes—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—84no—
127C2×Q8×C11—22no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—28no—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11C2×D412yes—
144C2×D4×C11#4112yescomplemented
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C11×SD16—28no—
162C11×D8—28no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16#4114yescomplemented
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—44no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—42no—
189C42×C11—24no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—21no—
194C42×C11—22no—
195C42×C11—42no—
196C42×C11C2×D412yes—
197C42×C11C2×D412yes—
198C42×C11#4112yescomplemented
199#3460C2×C1111yescharacteristic, complemented
200C4×AGL(1,ℤ/8)C2×C1112yescomplemented
201C4×#127C2×C1111yescharacteristic, complemented
202#2060C2×C1111yescharacteristic, complemented
203#2039C2×C1111yescharacteristic, complemented
204#2037C2×C1112yescomplemented
205#2027C2×C1111yescharacteristic, complemented
206#2006C2×C1111yescharacteristic, complemented
207#2002C2×C1112yescomplemented
208C4×#104C2×C1112yescomplemented
209C4×#100C2×C1111yescharacteristic, complemented
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11C22×D411yescharacteristic
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—82no—
225D4×C11—22no—
226D4×C11—24no—
227D4×C11—22no—
228D4×C11—416no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—84no—
235D4×C11—82no—
236D4×C11—84no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—82no—
257C2×C4×C11—82no—
258C2×C4×C11—82no—
259C2×C4×C11—82no—
260C2×C4×C11#12012yes—
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11#12011yescharacteristic
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2×#4111yescharacteristic
267C8×C11—24no—
268C8×C11—42no—
269C2×AGL(1,ℤ/8)C22×C1112yes—
270#544C22×C1111yescharacteristic
271#542—22no—
272#540—22no—
273#538—22no—
274#537C22×C1111yescharacteristic
275#535C22×C1112yes—
276#532—22no—
277C2×#127C22×C1111yescharacteristic
278#529—22no—
279#525—22no—
280C4×#41C22×C1112yes—
281C2×C4×D4—22no—
282C2×C4×D4C22×C1111yescharacteristic
283C2×C4×D4C22×C1111yescharacteristic
284#442—22no—
285#440—22no—
286C4×SD16—22no—
287C4×D8—22no—
288#428C22×C1112yes—
289C2×#104C22×C1112yes—
290C2×#104C22×C1112yes—
291#418C22×C1112yes—
292#417C22×C1112yes—
293C2×#100C22×C1112yes—
294C4×M16C22×C1112yes—
295#390—22no—
296#390C22×C1111yescharacteristic
297#390C22×C1111yescharacteristic
298#384C22×C1111yescharacteristic
299C43C22×C1111yescharacteristic
300#343C22×C1111yescharacteristic
301#343C22×C1111yescharacteristic
302#339C22×C1112yes—
303#339C22×C1112yes—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11C2×#12011yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11#53211yescharacteristic
322C4×C11—24no—
323C4×C11—21no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11#45312yes—
332C4×C11#52512yes—
333C4×C11#53212yes—
334C2×#41—22no—
335C2×#41C23×C1112yes—
336C22×D4—22no—
337C22×D4C23×C1111yescharacteristic
338C22×D4C23×C1111yescharacteristic
339C23×C4—21no—
340C23×C4D4×C1112yes—
341AGL(1,ℤ/8)—24no—
342AGL(1,ℤ/8)—24no—
343C2×SD16—22no—
344C2×D8—22no—
345C2×M16C23×C1112yes—
346C2×M16C23×C1112yes—
347C4⋊Q8—22no—
348#127—22no—
349#127—22no—
350#127—22no—
351#126—24no—
352#125—22no—
353#124—24no—
354#124—22no—
355#123—24no—
356#123—24no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360#121—22no—
361#121—24no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366#120—24no—
367C4×Q8D4×C1112yescomplemented
368C4×Q8D4×C1112yescomplemented
369C4×D4—24no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—48no—
377C4×D4D4×C1112yescomplemented
378C4×D4D4×C1112yescomplemented
379#117—22no—
380#117—22no—
381#117C23×C1112yes—
382C2×C4⋊C4—22no—
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4D4×C1112yes—
389C2×C42—21no—
390C2×C42—22no—
391C2×C42—21no—
392C2×C42C23×C1111yescharacteristic
393C2×C42C23×C1111yescharacteristic
394C2×C42C23×C1111yescharacteristic
395#107—22no—
396#106—22no—
397#104—24no—
398#104—24no—
399#103—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403#100—24no—
404#97—22no—
405C4×C8—22no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—82no—
409C2×C11—82no—
410C2×C11—82no—
411C2×C11#238811yescharacteristic
412C2×C11C2×#45311yescharacteristic
413C2×C11#301811yescharacteristic
414C24—21no—
415C24C2×D4×C1112yes—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—84no—
421C2×Q8—22no—
422C2×Q8C2×D4×C1112yes—
423C2×D4—28no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4C2×D4×C1112yes—
438C2×D4C11×#4112yescomplemented
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1112yes—
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C24×C1111yescharacteristic
455SD16—28no—
456D8—28no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16C11×#4114yescomplemented
461C2×C8—22no—
462C2×C8—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—44no—
471C4⋊C4C2×D4×C1112yes—
472C4⋊C4C2×D4×C1112yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—44no—
481C22⋊C4—44no—
482C22⋊C4—42no—
483C42—24no—
484C42—22no—
485C42—22no—
486C42—22no—
487C42—21no—
488C42—22no—
489C42—42no—
490C42C2×D4×C1112yes—
491C42C2×D4×C1112yes—
492C42C11×#4112yescomplemented
493C11#2358711yescharacteristic, direct product factor, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23C22×D4×C1111yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—82no—
509D4—22no—
510D4—24no—
511D4—22no—
512D4—416no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—84no—
519D4—82no—
520D4—84no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4C11×#12012yes—
545C2×C4C11×#12011yescharacteristic
546C2×C4C11×#12011yescharacteristic
547C2×C4C22×D4×C1112yes—
548C2×C4C2×C11×#4111yescharacteristic
549C2×C4C2×C11×#4112yes—
550C2×C4C2×C11×#4111yescharacteristic
551C8—24no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—44no—
556C22—44no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—82no—
565C22—82no—
566C22—81no—
567C22—81no—
568C22C2×C11×#12011yescharacteristic
569C22C11×#52511yescharacteristic
570C22C11×#53211yescharacteristic
571C4—24no—
572C4—21no—
573C4—22no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—81no—
580C4C11×#45312yes—
581C4C11×#52512yes—
582C4C11×#53212yes—
583C2—21no—
584C2—21no—
585C2—82no—
586C2—82no—
587C2—82no—
588C2C11×#238811yescharacteristic
589C2C2×C11×#45311yescharacteristic
590C2C11×#301811yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×#120
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3460C2semidirect
2. C4×C11×AGL(1,ℤ/8)C2semidirect
3. C4×C11×#127C2semidirect
4. C11×#2060C2semidirect
5. C11×#2039C2semidirect
6. C11×#2037C2semidirect
7. C11×#2027C2semidirect
8. C11×#2006C2semidirect
9. C11×#2002C2semidirect
10. C4×C11×#104C2semidirect
11. C4×C11×#100C2semidirect
80. C4×Q8×C11D4semidirect
81. C4×Q8×C11D4semidirect
90. C4×D4×C11D4semidirect
91. C4×D4×C11D4semidirect
119. #23587C11direct (N × H)
144. C2×D4×C11#41semidirect
166. C11×M16#41semidirect
198. C42×C11#41semidirect
199. #3460C2×C11semidirect
200. C4×AGL(1,ℤ/8)C2×C11semidirect
201. C4×#127C2×C11semidirect
202. #2060C2×C11semidirect
203. #2039C2×C11semidirect
204. #2037C2×C11semidirect
205. #2027C2×C11semidirect
206. #2006C2×C11semidirect
207. #2002C2×C11semidirect
208. C4×#104C2×C11semidirect
209. C4×#100C2×C11semidirect
367. C4×Q8D4×C11semidirect
368. C4×Q8D4×C11semidirect
377. C4×D4D4×C11semidirect
378. C4×D4D4×C11semidirect
438. C2×D4C11×#41semidirect
460. M16C11×#41semidirect
492. C42C11×#41semidirect
493. C11#23587direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34602
C4×C11×AGL(1,ℤ/8)2
C4×C11×#1272
C11×#20602
C11×#20392
C11×#20372
C11×#20272
C11×#20062
C11×#20022
C4×C11×#1042
C4×C11×#1002
#2358711