Finite Group Databasebeta

← C11×#18892 #14596085

Subgroups — C11×#18892 #14596085

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic, complemented
2C11×#3205C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic, complemented
4C2×C11×#459C211yesmaximal, characteristic, complemented
5C11×#1625C214yesmaximal, complemented
6C11×#1619C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C22×C11×D8—21no—
12C11×#547—21no—
13C11×#547C2212yescomplemented
14C11×#546—22no—
15C11×#546—22no—
16D42×C11—21no—
17D42×C11C2212yescomplemented
18C11×#537—21no—
19C11×#534—22no—
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C2×C11×#127C2211yescharacteristic, complemented
23C2×C11×#121—22no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#493—21no—
26C11×#493C2212yescomplemented
27C11×#486—21no—
28C11×#486C2212yescomplemented
29C11×#459—22no—
30C11×#459—22no—
31C11×#459C2214yescomplemented
32C11×#459C2214yescomplemented
33C11×#447—22no—
34C11×#447—22no—
35C11×#431C2211yescharacteristic, complemented
36C11×#431C2211yescharacteristic, complemented
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×#102—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×D4⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C11×H(5,𝔽2)—44no—
44C11×H(5,𝔽2)—44no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×D4×C11—24no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11D411yescharacteristic
57C23×C4×C11—21no—
58C2×C11×D8—24no—
59C2×C11×D8—24no—
60C2×C11×D8—24no—
61C2×C11×D8—44no—
62C22×C8×C11—21no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127—21no—
66C11×#127—21no—
67C11×#127—21no—
68C11×#127D411yescharacteristic
69C11×#127C2312yes—
70C11×#127C2311yescharacteristic
71C11×#124—21no—
72C11×#124—21no—
73C11×#123—24no—
74C11×#123—24no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×#121—24no—
78C11×#121—24no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121D412yes—
86C11×#121D412yes—
87C11×#120—24no—
88C11×#120—24no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11D412yes—
94C4×D4×C11D412yes—
95C4×D4×C11C2312yes—
96C4×D4×C11C2312yes—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C22⋊C4—24no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C11×#102—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2312yes—
113#18892C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—21no—
115C24×C11—24no—
116C24×C11—41no—
117C11×#41—44no—
118C11×#41—48no—
119C11×#41—44no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—42no—
123C11×#41—42no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—44no—
141C2×D4×C11—48no—
142C2×D4×C11—416no—
143C2×D4×C11—44no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—82no—
150C2×D4×C11—84no—
151C2×D4×C11—82no—
152C2×D4×C11D814yescomplemented
153C2×D4×C11C2×D412yes—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D412yes—
156C22×C4×C11—24no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—82no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C11×D8—48no—
167C11×D8—84no—
168C11×D8—84no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—42no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2411yescharacteristic
192#3496C2×C1111yescharacteristic, complemented
193#3205C2×C1111yescharacteristic, complemented
194#3205C2×C1111yescharacteristic, complemented
195C2×#459C2×C1111yescharacteristic, complemented
196#1625C2×C1114yescomplemented
197#1619C2×C1114yescomplemented
198#1540C2×C1111yescharacteristic, complemented
199#1480C2×C1111yescharacteristic, complemented
200#1478C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—48no—
206C23×C11—42no—
207C23×C11—81no—
208C23×C11—81no—
209C23×C11—82no—
210C23×C11—82no—
211C23×C11—84no—
212C23×C11—84no—
213C23×C11—82no—
214C23×C11#12011yescharacteristic
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—42no—
218D4×C11—22no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—42no—
222D4×C11—44no—
223D4×C11—48no—
224D4×C11—48no—
225D4×C11—44no—
226D4×C11—44no—
227D4×C11—41no—
228D4×C11—42no—
229D4×C11—41no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—42no—
234D4×C11—81no—
235D4×C11—82no—
236D4×C11—82no—
237D4×C11—84no—
238D4×C11—82no—
239D4×C11C2×D814yes—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—82no—
251C2×C4×C11—81no—
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11C2×D812yes—
256C2×C4×C11AGL(1,ℤ/8)12yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C8×C11—42no—
261C8×C11—42no—
262C8×C11—42no—
263C2×H(5,𝔽2)—21no—
264C22×D8—21no—
265#547—21no—
266#547C22×C1112yescomplemented
267#546—22no—
268#546—22no—
269D42—21no—
270D42C22×C1112yescomplemented
271#537—21no—
272#534—22no—
273#532C22×C1111yescharacteristic
274#532C22×C1111yescharacteristic
275C2×#127C22×C1111yescharacteristic, complemented
276C2×#121—22no—
277C2×C4×D4C22×C1111yescharacteristic
278#493—21no—
279#493C22×C1112yescomplemented
280#486—21no—
281#486C22×C1112yescomplemented
282#459—22no—
283#459—22no—
284#459C22×C1114yescomplemented
285#459C22×C1114yescomplemented
286#447—22no—
287#447—22no—
288#431C22×C1111yescharacteristic, complemented
289#431C22×C1111yescharacteristic, complemented
290C2×C4⋊C8C22×C1111yescharacteristic, complemented
291C2×#102—21no—
292#332C22×C1112yescomplemented
293#331C22×C1112yescomplemented
294D4⋊C8C22×C1114yescomplemented
295D4⋊C8C22×C1114yescomplemented
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—24no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—84no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—164no—
312C22×C11—168no—
313C22×C11#44712yes—
314C22×C11C2×#12011yescharacteristic
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11#44712yes—
322C4×C11C22×D811yescharacteristic
323C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
324C4×C11#57612yes—
325H(5,𝔽2)—44no—
326H(5,𝔽2)—44no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—21no—
330C2×#41—21no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4D4×C1111yescharacteristic
339C23×C4—21no—
340C2×D8—24no—
341C2×D8—24no—
342C2×D8—24no—
343C2×D8—44no—
344C22×C8—21no—
345C4⋊Q8D4×C1111yescharacteristic
346C4⋊Q8C23×C1111yescharacteristic
347#127—21no—
348#127—21no—
349#127—21no—
350#127D4×C1111yescharacteristic
351#127C23×C1112yes—
352#127C23×C1111yescharacteristic
353#124—21no—
354#124—21no—
355#123—24no—
356#123—24no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359#121—24no—
360#121—24no—
361#121—22no—
362#121—22no—
363#121—21no—
364#121—21no—
365#121—22no—
366#121—22no—
367#121D4×C1112yes—
368#121D4×C1112yes—
369#120—24no—
370#120—24no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4D4×C1112yes—
376C4×D4D4×C1112yes—
377C4×D4C23×C1112yes—
378C4×D4C23×C1112yes—
379C2×C4⋊C4—22no—
380C2×C4⋊C4D4×C1111yescharacteristic
381C2×C22⋊C4—24no—
382C2×C22⋊C4—21no—
383C2×C42C23×C1111yescharacteristic
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8C23×C1112yes—
387C4⋊C8C23×C1112yes—
388#102—24no—
389#102—24no—
390#102—24no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C4×C8—21no—
394C4×C8C23×C1112yes—
395C2×C11—22no—
396C2×C11—44no—
397C2×C11—82no—
398C2×C11—82no—
399C2×C11—162no—
400C2×C11C2×#44711yescharacteristic
401C2×C11#300811yescharacteristic
402C2×C11#302111yescharacteristic
403C24—21no—
404C24—24no—
405C24—41no—
406#41—44no—
407#41—48no—
408#41—44no—
409#41—42no—
410#41—42no—
411#41—42no—
412#41—42no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—416no—
432C2×D4—44no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—82no—
439C2×D4—84no—
440C2×D4—82no—
441C2×D4C11×D814yescomplemented
442C2×D4C2×D4×C1112yes—
443C2×D4C2×D4×C1112yes—
444C2×D4C2×D4×C1112yes—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—82no—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455D8—48no—
456D8—84no—
457D8—84no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—42no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4C2×D4×C1112yes—
467C4⋊C4C2×D4×C1112yes—
468C4⋊C4C2×D4×C1112yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C42C2×D4×C1111yescharacteristic
478C42C2×D4×C1111yescharacteristic
479C42C2×D4×C1111yescharacteristic
480C42C24×C1111yescharacteristic
481C11#1889211yescharacteristic, direct product factor, Sylow
482C23—22no—
483C23—24no—
484C23—22no—
485C23—22no—
486C23—48no—
487C23—42no—
488C23—81no—
489C23—81no—
490C23—82no—
491C23—82no—
492C23—84no—
493C23—84no—
494C23—82no—
495C23C11×#12011yescharacteristic
496Q8—41no—
497Q8—41no—
498Q8—42no—
499D4—22no—
500D4—24no—
501D4—24no—
502D4—42no—
503D4—44no—
504D4—48no—
505D4—48no—
506D4—44no—
507D4—44no—
508D4—41no—
509D4—42no—
510D4—41no—
511D4—42no—
512D4—42no—
513D4—44no—
514D4—42no—
515D4—81no—
516D4—82no—
517D4—82no—
518D4—84no—
519D4—82no—
520D4C2×C11×D814yes—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—48no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—82no—
532C2×C4—81no—
533C2×C4C11×#12011yescharacteristic
534C2×C4C11×#12011yescharacteristic
535C2×C4C11×#12011yescharacteristic
536C2×C4C2×C11×D812yes—
537C2×C4C11×AGL(1,ℤ/8)12yes—
538C2×C4C22×D4×C1111yescharacteristic
539C2×C4C22×D4×C1111yescharacteristic
540C2×C4C22×D4×C1111yescharacteristic
541C8—42no—
542C8—42no—
543C8—42no—
544C22—21no—
545C22—21no—
546C22—24no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—84no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—164no—
560C22—168no—
561C22C11×#44712yes—
562C22C2×C11×#12011yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4C11×#44712yes—
570C4C22×C11×D811yescharacteristic
571C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
572C4C11×#57612yes—
573C2—22no—
574C2—44no—
575C2—82no—
576C2—82no—
577C2—162no—
578C2C2×C11×#44711yescharacteristic
579C2C11×#300811yescharacteristic
580C2C11×#302111yescharacteristic
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×#3496C2semidirect
2. C11×#3205C2semidirect
3. C11×#3205C2semidirect
4. C2×C11×#459C2semidirect
5. C11×#1625C2semidirect
6. C11×#1619C2semidirect
7. C11×#1540C2semidirect
8. C11×#1480C2semidirect
9. C11×#1478C2semidirect
13. C11×#547C22semidirect
17. D42×C11C22semidirect
22. C2×C11×#127C22semidirect
26. C11×#493C22semidirect
28. C11×#486C22semidirect
31. C11×#459C22semidirect
32. C11×#459C22semidirect
35. C11×#431C22semidirect
36. C11×#431C22semidirect
37. C2×C11×C4⋊C8C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×D4⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
113. #18892C11direct (N × H)
152. C2×D4×C11D8semidirect
192. #3496C2×C11semidirect
193. #3205C2×C11semidirect
194. #3205C2×C11semidirect
195. C2×#459C2×C11semidirect
196. #1625C2×C11semidirect
197. #1619C2×C11semidirect
198. #1540C2×C11semidirect
199. #1480C2×C11semidirect
200. #1478C2×C11semidirect
266. #547C22×C11semidirect
270. D42C22×C11semidirect
275. C2×#127C22×C11semidirect
279. #493C22×C11semidirect
281. #486C22×C11semidirect
284. #459C22×C11semidirect
285. #459C22×C11semidirect
288. #431C22×C11semidirect
289. #431C22×C11semidirect
290. C2×C4⋊C8C22×C11semidirect
292. #332C22×C11semidirect
293. #331C22×C11semidirect
294. D4⋊C8C22×C11semidirect
295. D4⋊C8C22×C11semidirect
441. C2×D4C11×D8semidirect
481. C11#18892direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#32052
C2×C11×#4592
C11×#16252
C11×#16192
C11×#15402
C11×#14802
C11×#14782
#1889211