Finite Group Databasebeta

← C11×#18934 #14596127

Subgroups — C11×#18934 #14596127

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3549C211yesmaximal, characteristic, complemented
2C11×#3245C211yesmaximal, characteristic, complemented
3C11×#3214C211yesmaximal, characteristic, complemented
4C11×#3207C211yesmaximal, characteristic, complemented
5C11×#1646C212yesmaximal, complemented
6C11×#1639C212yesmaximal, complemented
7C11×#1624C212yesmaximal, complemented
8C11×#1619C212yesmaximal, complemented
9C11×#1551C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1480C211yesmaximal, characteristic, complemented
12C11×H(3,𝔽4)—22no—
13C11×#555—21no—
14C11×#555—21no—
15C11×#555C2212yes—
16D42×C11—21no—
17D42×C11—21no—
18D42×C11C2212yes—
19C11×#535—22no—
20C11×#535—22no—
21C11×#535—22no—
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic, complemented
26C11×#496—21no—
27C11×#493C2211yescharacteristic
28C11×#492C2211yescharacteristic, complemented
29C11×#489—21no—
30C11×#487C2211yescharacteristic, complemented
31C11×#486C2211yescharacteristic
32C11×#474—21no—
33C11×#474C2212yescomplemented
34C11×#466—22no—
35C11×#463—22no—
36C11×#461C2212yescomplemented
37C11×#459—21no—
38C11×#459C2212yescomplemented
39C11×#459C2212yescomplemented
40C11×#449—22no—
41C11×#449—22no—
42C11×#432C2211yescharacteristic, complemented
43C11×#431C2211yescharacteristic, complemented
44C2×C11×C4⋊C8C2211yescharacteristic, complemented
45C11×#333C2212yescomplemented
46C11×#331C2212yes—
47C11×D4⋊C8C2212yescomplemented
48C11×D4⋊C8C2212yescomplemented
49C11×D4⋊C8C2212yescomplemented
50C11×D4⋊C8C2212yescomplemented
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41D412yes—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×D8—22no—
61C2×C11×D8—22no—
62C2×C11×D8—22no—
63C22×C8×C11—21no—
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×#127—24no—
69C11×#127D411yescharacteristic
70C11×#127D411yescharacteristic
71C11×#127C2311yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#124—24no—
74C11×#124—24no—
75C11×#124—24no—
76C11×#124—21no—
77C11×#124—21no—
78C11×#124—21no—
79C11×#124D412yes—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121D412yes—
93C11×#121D412yes—
94C11×#120—24no—
95C11×#120—24no—
96C11×#120—24no—
97C11×#120—24no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11C2312yes—
105C4×D4×C11C2312yes—
106C11×#117—22no—
107C11×#117—22no—
108C11×#117—22no—
109C2×C42×C11C2311yescharacteristic
110C11×#107—22no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×#103—22no—
116C11×#103—22no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18934C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11—24no—
128C11×#41—81no—
129C11×#41—82no—
130C11×#41—81no—
131C11×#41—82no—
132C11×#41—82no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11—82no—
154C2×D4×C11—82no—
155C2×D4×C11—82no—
156C2×D4×C11—82no—
157C2×D4×C11—84no—
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×D412yes—
160C2×D4×C11C2×D412yes—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—41no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C11×SD16—82no—
169C11×SD16—82no—
170C11×D8—82no—
171C11×D8—82no—
172C11×D8—82no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—81no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C42×C11—24no—
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2411yescharacteristic
202#3549C2×C1111yescharacteristic, complemented
203#3245C2×C1111yescharacteristic, complemented
204#3214C2×C1111yescharacteristic, complemented
205#3207C2×C1111yescharacteristic, complemented
206#1646C2×C1112yescomplemented
207#1639C2×C1112yescomplemented
208#1624C2×C1112yescomplemented
209#1619C2×C1112yescomplemented
210#1551C2×C1111yescharacteristic, complemented
211#1496C2×C1111yescharacteristic, complemented
212#1480C2×C1111yescharacteristic, complemented
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—84no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11#12011yescharacteristic
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11—81no—
224Q8×C11—81no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—42no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—81no—
240D4×C11—81no—
241D4×C11—82no—
242D4×C11—82no—
243D4×C11—82no—
244D4×C11—84no—
245D4×C11—84no—
246D4×C11—84no—
247D4×C11—82no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—44no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—82no—
262C2×C4×C11#12011yescharacteristic
263C2×C4×C11#12011yescharacteristic
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—42no—
271C8×C11—42no—
272H(3,𝔽4)—22no—
273#555—21no—
274#555—21no—
275#555C22×C1112yes—
276D42—21no—
277D42—21no—
278D42C22×C1112yes—
279#535—22no—
280#535—22no—
281#535—22no—
282#532C22×C1111yescharacteristic
283#532C22×C1111yescharacteristic
284#532C22×C1111yescharacteristic
285#532C22×C1111yescharacteristic, complemented
286#496—21no—
287#493C22×C1111yescharacteristic
288#492C22×C1111yescharacteristic, complemented
289#489—21no—
290#487C22×C1111yescharacteristic, complemented
291#486C22×C1111yescharacteristic
292#474—21no—
293#474C22×C1112yescomplemented
294#466—22no—
295#463—22no—
296#461C22×C1112yescomplemented
297#459—21no—
298#459C22×C1112yescomplemented
299#459C22×C1112yescomplemented
300#449—22no—
301#449—22no—
302#432C22×C1111yescharacteristic, complemented
303#431C22×C1111yescharacteristic, complemented
304C2×C4⋊C8C22×C1111yescharacteristic, complemented
305#333C22×C1112yescomplemented
306#331C22×C1112yes—
307D4⋊C8C22×C1112yescomplemented
308D4⋊C8C22×C1112yescomplemented
309D4⋊C8C22×C1112yescomplemented
310D4⋊C8C22×C1112yescomplemented
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—168no—
327C22×C11C2×#12011yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11#57612yes—
337C4×C11#57611yescharacteristic
338C4×C11#57711yescharacteristic
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41D4×C1112yes—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—22no—
351C22×C8—21no—
352C4⋊Q8D4×C1111yescharacteristic
353C4⋊Q8D4×C1111yescharacteristic
354C4⋊Q8C23×C1111yescharacteristic
355C4⋊Q8C23×C1111yescharacteristic
356#127—24no—
357#127D4×C1111yescharacteristic
358#127D4×C1111yescharacteristic
359#127C23×C1111yescharacteristic
360#127C23×C1111yescharacteristic
361#124—24no—
362#124—24no—
363#124—24no—
364#124—21no—
365#124—21no—
366#124—21no—
367#124D4×C1112yes—
368#121—22no—
369#121—22no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—22no—
377#121—22no—
378#121—21no—
379#121—21no—
380#121D4×C1112yes—
381#121D4×C1112yes—
382#120—24no—
383#120—24no—
384#120—24no—
385#120—24no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C1112yes—
393C4×D4C23×C1112yes—
394#117—22no—
395#117—22no—
396#117—22no—
397C2×C42C23×C1111yescharacteristic
398#107—22no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C1112yes—
402C4⋊C8C23×C1112yes—
403#103—22no—
404#103—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#102—22no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411#97—21no—
412C4×C8C23×C1111yescharacteristic
413C4×C8C23×C1111yescharacteristic
414C2×C11—41no—
415C2×C11—82no—
416C2×C11—82no—
417C2×C11—82no—
418C2×C11—161no—
419C2×C11#300811yescharacteristic
420C2×C11#301211yescharacteristic
421C2×C11#301911yescharacteristic
422C24—24no—
423#41—81no—
424#41—82no—
425#41—81no—
426#41—82no—
427#41—82no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C1112yes—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—82no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4—82no—
452C2×D4—84no—
453C2×D4C2×D4×C1112yes—
454C2×D4C2×D4×C1112yes—
455C2×D4C2×D4×C1112yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—41no—
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463SD16—82no—
464SD16—82no—
465D8—82no—
466D8—82no—
467D8—82no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—81no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C2×D4×C1112yes—
480C4⋊C4C2×D4×C1112yes—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—24no—
493C42C2×D4×C1111yescharacteristic
494C42C2×D4×C1111yescharacteristic
495C42C2×D4×C1111yescharacteristic
496C42C24×C1111yescharacteristic
497C11#1893411yescharacteristic, direct product factor, Sylow
498C23—22no—
499C23—22no—
500C23—22no—
501C23—41no—
502C23—84no—
503C23—84no—
504C23—84no—
505C23C11×#12011yescharacteristic
506Q8—42no—
507Q8—42no—
508Q8—81no—
509Q8—81no—
510D4—22no—
511D4—22no—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—41no—
520D4—41no—
521D4—42no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—84no—
530D4—84no—
531D4—84no—
532D4—82no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4C11×#12011yescharacteristic
548C2×C4C11×#12011yescharacteristic
549C2×C4C11×#12011yescharacteristic
550C2×C4C22×D4×C1111yescharacteristic
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C8—41no—
554C8—41no—
555C8—42no—
556C8—42no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—168no—
573C22C2×C11×#12011yescharacteristic
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—81no—
582C4C11×#57612yes—
583C4C11×#57611yescharacteristic
584C4C11×#57711yescharacteristic
585C2—41no—
586C2—82no—
587C2—82no—
588C2—82no—
589C2—161no—
590C2C11×#300811yescharacteristic
591C2C11×#301211yescharacteristic
592C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3549C2semidirect
2. C11×#3245C2semidirect
3. C11×#3214C2semidirect
4. C11×#3207C2semidirect
5. C11×#1646C2semidirect
6. C11×#1639C2semidirect
7. C11×#1624C2semidirect
8. C11×#1619C2semidirect
9. C11×#1551C2semidirect
10. C11×#1496C2semidirect
11. C11×#1480C2semidirect
25. C11×#532C22semidirect
28. C11×#492C22semidirect
30. C11×#487C22semidirect
33. C11×#474C22semidirect
36. C11×#461C22semidirect
38. C11×#459C22semidirect
39. C11×#459C22semidirect
42. C11×#432C22semidirect
43. C11×#431C22semidirect
44. C2×C11×C4⋊C8C22semidirect
45. C11×#333C22semidirect
47. C11×D4⋊C8C22semidirect
48. C11×D4⋊C8C22semidirect
49. C11×D4⋊C8C22semidirect
50. C11×D4⋊C8C22semidirect
126. #18934C11direct (N × H)
202. #3549C2×C11semidirect
203. #3245C2×C11semidirect
204. #3214C2×C11semidirect
205. #3207C2×C11semidirect
206. #1646C2×C11semidirect
207. #1639C2×C11semidirect
208. #1624C2×C11semidirect
209. #1619C2×C11semidirect
210. #1551C2×C11semidirect
211. #1496C2×C11semidirect
212. #1480C2×C11semidirect
285. #532C22×C11semidirect
288. #492C22×C11semidirect
290. #487C22×C11semidirect
293. #474C22×C11semidirect
296. #461C22×C11semidirect
298. #459C22×C11semidirect
299. #459C22×C11semidirect
302. #432C22×C11semidirect
303. #431C22×C11semidirect
304. C2×C4⋊C8C22×C11semidirect
305. #333C22×C11semidirect
307. D4⋊C8C22×C11semidirect
308. D4⋊C8C22×C11semidirect
309. D4⋊C8C22×C11semidirect
310. D4⋊C8C22×C11semidirect
497. C11#18934direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35492
C11×#32452
C11×#32142
C11×#32072
C11×#16462
C11×#16392
C11×#16242
C11×#16192
C11×#15512
C11×#14962
C11×#14802
#1893411