Finite Group Databasebeta

← C11×#18916 #14596109

Subgroups — C11×#18916 #14596109

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic, complemented
4C2×C11×#459C211yesmaximal, characteristic, complemented
5C11×#1628C214yesmaximal, complemented
6C11×#1621C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C22×C11×D8—21no—
11C11×#559—22no—
12C11×#556C2212yescomplemented
13C11×#555—21no—
14C11×#553—22no—
15C11×#550C2212yescomplemented
16C11×#547—21no—
17C11×#538—22no—
18C11×#535—21no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C11×#525—22no—
23C11×#520—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#493C2212yescomplemented
26C11×#492—21no—
27C11×#486—21no—
28C11×#486C2212yescomplemented
29C11×#460C2214yescomplemented
30C11×#459—22no—
31C11×#459—22no—
32C11×#459C2214yes—
33C11×#450—22no—
34C11×#447—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C2×C11×SD16—24no—
51C2×C11×D8—24no—
52C2×C11×D8—24no—
53C2×C11×D8—44no—
54C22×C8×C11—21no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127—22no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127C2312yes—
63C11×#127C2311yescharacteristic
64C11×#126—24no—
65C11×#125—21no—
66C11×#124—24no—
67C11×#124—22no—
68C11×#124—21no—
69C11×#123—24no—
70C11×#123—24no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8D412yes—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—24no—
77C11×#121—21no—
78C11×#121—22no—
79C11×#121D412yes—
80C11×#120—24no—
81C4×Q8×C11—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2312yes—
84C4×D4×C11—24no—
85C4×D4×C11—24no—
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11D412yes—
91C4×D4×C11D412yes—
92C4×D4×C11C2312yes—
93C11×#117—22no—
94C11×#117—21no—
95C11×#117—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18916C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C24×C11—41no—
114C11×#41—42no—
115C11×#41—42no—
116C11×#41—84no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—22no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—82no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C11×SD16—84no—
150C11×D8—48no—
151C11×D8—84no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—42no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C42×C11—24no—
176C42×C11—22no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2411yescharacteristic
181#3506C2×C1111yescharacteristic, complemented
182#3208C2×C1111yescharacteristic, complemented
183#3205C2×C1111yescharacteristic, complemented
184C2×#459C2×C1111yescharacteristic, complemented
185#1628C2×C1114yescomplemented
186#1621C2×C1114yescomplemented
187#1540C2×C1111yescharacteristic, complemented
188#1481C2×C1111yescharacteristic, complemented
189#1478C2×C1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—81no—
195C23×C11—81no—
196C23×C11—82no—
197C23×C11—82no—
198C23×C11—82no—
199C23×C11#12011yescharacteristic
200Q8×C11—24no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—81no—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—42no—
207D4×C11—44no—
208D4×C11—44no—
209D4×C11—41no—
210D4×C11—42no—
211D4×C11—41no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—44no—
215D4×C11—42no—
216D4×C11—82no—
217D4×C11—82no—
218D4×C11—84no—
219D4×C11—84no—
220D4×C11—82no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—82no—
230C2×C4×C11—81no—
231C2×C4×C11—84no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#13512yes—
236C2×C4×C11AGL(1,ℤ/8)12yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C8×C11—42no—
241C8×C11—42no—
242C8×C11—42no—
243C22×D8—21no—
244#559—22no—
245#556C22×C1112yescomplemented
246#555—21no—
247#553—22no—
248#550C22×C1112yescomplemented
249#547—21no—
250#538—22no—
251#535—21no—
252#533C22×C1111yescharacteristic
253#532C22×C1111yescharacteristic
254C2×#127C22×C1111yescharacteristic
255#525—22no—
256#520—21no—
257C2×C4×D4C22×C1111yescharacteristic
258#493C22×C1112yescomplemented
259#492—21no—
260#486—21no—
261#486C22×C1112yescomplemented
262#460C22×C1114yescomplemented
263#459—22no—
264#459—22no—
265#459C22×C1114yes—
266#450—22no—
267#447—22no—
268#431C22×C1111yescharacteristic
269#431C22×C1111yescharacteristic
270C2×C4⋊C8C22×C1111yescharacteristic
271C2×#102—21no—
272#332C22×C1112yescomplemented
273#331C22×C1112yescomplemented
274Q8⋊C8C22×C1114yescomplemented
275D4⋊C8C22×C1114yescomplemented
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—84no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—164no—
289C22×C11#44912yes—
290C22×C11C2×#12011yescharacteristic
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11#44912yes—
299C4×C11C2×#13511yescharacteristic
300C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C11#57612yes—
302C2×#41—22no—
303C2×#41—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4D4×C1111yescharacteristic
308C23×C4—21no—
309C2×SD16—24no—
310C2×D8—24no—
311C2×D8—24no—
312C2×D8—44no—
313C22×C8—21no—
314C4⋊Q8D4×C1111yescharacteristic
315C4⋊Q8D4×C1111yescharacteristic
316C4⋊Q8C23×C1111yescharacteristic
317#127—22no—
318#127—21no—
319#127—21no—
320#127—21no—
321#127C23×C1112yes—
322#127C23×C1111yescharacteristic
323#126—24no—
324#125—21no—
325#124—24no—
326#124—22no—
327#124—21no—
328#123—24no—
329#123—24no—
330C22⋊Q8—22no—
331C22⋊Q8—21no—
332C22⋊Q8D4×C1112yes—
333#121—22no—
334#121—22no—
335#121—24no—
336#121—21no—
337#121—22no—
338#121D4×C1112yes—
339#120—24no—
340C4×Q8—22no—
341C4×Q8—21no—
342C4×Q8C23×C1112yes—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—22no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4D4×C1112yes—
350C4×D4D4×C1112yes—
351C4×D4C23×C1112yes—
352#117—22no—
353#117—21no—
354#117—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C1111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C42C23×C1111yescharacteristic
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8C23×C1112yes—
362C4⋊C8C23×C1112yes—
363#102—24no—
364#102—24no—
365#102—24no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C4×C8—21no—
369C4×C8C23×C1112yes—
370C2×C11—22no—
371C2×C11—82no—
372C2×C11—82no—
373C2×C11—162no—
374C2×C11C2×#44911yescharacteristic
375C2×C11#300811yescharacteristic
376C2×C11#302111yescharacteristic
377C24—21no—
378C24—41no—
379#41—42no—
380#41—42no—
381#41—84no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8C2×D4×C1112yes—
385C2×D4—22no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—82no—
402C2×D4—82no—
403C2×D4C2×D4×C1112yes—
404C2×D4C2×D4×C1112yes—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—82no—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414SD16—84no—
415D8—48no—
416D8—84no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—42no—
421C4⋊C4—24no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4C2×D4×C1112yes—
430C4⋊C4C2×D4×C1112yes—
431C4⋊C4C2×D4×C1112yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C42—24no—
441C42—22no—
442C42C2×D4×C1111yescharacteristic
443C42C2×D4×C1111yescharacteristic
444C42C2×D4×C1111yescharacteristic
445C42C24×C1111yescharacteristic
446C11#1891611yescharacteristic, direct product factor, Sylow
447C23—22no—
448C23—22no—
449C23—42no—
450C23—42no—
451C23—81no—
452C23—81no—
453C23—82no—
454C23—82no—
455C23—82no—
456C23C11×#12011yescharacteristic
457Q8—24no—
458Q8—41no—
459Q8—41no—
460Q8—81no—
461D4—22no—
462D4—22no—
463D4—42no—
464D4—44no—
465D4—44no—
466D4—41no—
467D4—42no—
468D4—41no—
469D4—42no—
470D4—42no—
471D4—44no—
472D4—42no—
473D4—82no—
474D4—82no—
475D4—84no—
476D4—84no—
477D4—82no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—41no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—82no—
487C2×C4—81no—
488C2×C4—84no—
489C2×C4C11×#12011yescharacteristic
490C2×C4C11×#12011yescharacteristic
491C2×C4C11×#12011yescharacteristic
492C2×C4C11×#13512yes—
493C2×C4C11×AGL(1,ℤ/8)12yes—
494C2×C4C22×D4×C1111yescharacteristic
495C2×C4C22×D4×C1111yescharacteristic
496C2×C4C22×D4×C1111yescharacteristic
497C8—42no—
498C8—42no—
499C8—42no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—84no—
509C22—82no—
510C22—82no—
511C22—82no—
512C22—164no—
513C22C11×#44912yes—
514C22C2×C11×#12011yescharacteristic
515C4—21no—
516C4—21no—
517C4—21no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4C11×#44912yes—
523C4C2×C11×#13511yescharacteristic
524C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
525C4C11×#57612yes—
526C2—22no—
527C2—82no—
528C2—82no—
529C2—162no—
530C2C2×C11×#44911yescharacteristic
531C2C11×#300811yescharacteristic
532C2C11×#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×#3506C2semidirect
2. C11×#3208C2semidirect
3. C11×#3205C2semidirect
4. C2×C11×#459C2semidirect
5. C11×#1628C2semidirect
6. C11×#1621C2semidirect
7. C11×#1540C2semidirect
8. C11×#1481C2semidirect
9. C11×#1478C2semidirect
12. C11×#556C22semidirect
15. C11×#550C22semidirect
25. C11×#493C22semidirect
28. C11×#486C22semidirect
29. C11×#460C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
111. #18916C11direct (N × H)
181. #3506C2×C11semidirect
182. #3208C2×C11semidirect
183. #3205C2×C11semidirect
184. C2×#459C2×C11semidirect
185. #1628C2×C11semidirect
186. #1621C2×C11semidirect
187. #1540C2×C11semidirect
188. #1481C2×C11semidirect
189. #1478C2×C11semidirect
245. #556C22×C11semidirect
248. #550C22×C11semidirect
258. #493C22×C11semidirect
261. #486C22×C11semidirect
262. #460C22×C11semidirect
272. #332C22×C11semidirect
273. #331C22×C11semidirect
274. Q8⋊C8C22×C11semidirect
275. D4⋊C8C22×C11semidirect
446. C11#18916direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#32082
C11×#32052
C2×C11×#4592
C11×#16282
C11×#16212
C11×#15402
C11×#14812
C11×#14782
#1891611