Finite Group Databasebeta

← C11×#19166 #14596359

Subgroups — C11×#19166 #14596359

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3138C211yesmaximal, characteristic, complemented
2C11×#3101C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4D4×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1701C212yesmaximal, complemented
6C11×#1697C212yesmaximal, complemented
7C11×#1681C212yesmaximal, complemented
8C11×#1677C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1545C211yesmaximal, characteristic, complemented
12C22×C11×D8—21no—
13C22×C11×M16—21no—
14C11×#533C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#490—22no—
18C11×#486C2212yescomplemented
19C11×#486C2212yescomplemented
20C11×#483—21no—
21C11×#476C2211yescharacteristic, complemented
22C11×#476C2211yescharacteristic, complemented
23C11×#461C2211yescharacteristic, complemented
24C11×#461C2211yescharacteristic, complemented
25C11×#459—21no—
26C11×#459—21no—
27C11×#459C2212yes—
28C11×#459C2212yes—
29C11×#450—21no—
30C4×C11×SD16—21no—
31C4×C11×SD16—21no—
32C11×#436C2212yescomplemented
33C11×#435—22no—
34C8×D4×C11C2212yescomplemented
35C11×#431C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C11×#418—21no—
39C11×#418—21no—
40C2×C11×#102—21no—
41C11×#407—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#333C2212yescomplemented
46C11×#332C2212yescomplemented
47C11×#331C2212yescomplemented
48C11×#331C2212yescomplemented
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×D8—44no—
59C2×C11×M16—21no—
60C2×C11×M16—22no—
61C2×C11×M16—44no—
62C2×C11×M16D411yescharacteristic
63C2×C11×M16D411yescharacteristic
64C22×C8×C11—21no—
65C22×C8×C11—22no—
66C11×C4⋊Q8C2311yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×#127—21no—
69C11×#127—21no—
70C11×#127—21no—
71C11×#127C2312yes—
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11D411yescharacteristic
80C4×D4×C11D411yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C11×#106—21no—
88C11×#106—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×C4⋊C8C2311yescharacteristic
93C11×C4⋊C8C2311yescharacteristic
94C11×C4⋊C8C2312yes—
95C11×#103—21no—
96C11×#103—21no—
97C11×#102—21no—
98C11×#102—21no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—22no—
108C11×#97D412yes—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#19166C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C24×C11—41no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—41no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—82no—
130C2×D4×C11C2×D411yescharacteristic
131C2×D4×C11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C11×SD16—42no—
143C11×SD16—42no—
144C11×D8—44no—
145C11×D8—44no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—44no—
149C11×M16—42no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—42no—
155C2×C8×C11—44no—
156C2×C8×C11C2×D412yes—
157C2×C8×C11C2×D412yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4C2×D411yescharacteristic
166C11×C4⋊C4C2×D411yescharacteristic
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—41no—
172C42×C11—41no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11#4111yescharacteristic
176C42×C11C2411yescharacteristic
177#3138C2×C1111yescharacteristic, complemented
178#3101C2×C1111yescharacteristic, complemented
179C2×#459C2×C1111yescharacteristic
180D4×M16C2×C1111yescharacteristic, complemented
181#1701C2×C1112yescomplemented
182#1697C2×C1112yescomplemented
183#1681C2×C1112yescomplemented
184#1677C2×C1112yescomplemented
185#1565C2×C1111yescharacteristic, complemented
186#1550C2×C1111yescharacteristic, complemented
187#1545C2×C1111yescharacteristic, complemented
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—81no—
194C23×C11—82no—
195C23×C11—82no—
196C23×C11—82no—
197C23×C11#12111yescharacteristic
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—81no—
201D4×C11—21no—
202D4×C11—21no—
203D4×C11—21no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—82no—
210D4×C11—82no—
211D4×C11—82no—
212D4×C11—82no—
213D4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#13512yes—
232C2×C4×C11AGL(1,ℤ/8)12yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C8×C11—22no—
237C8×C11—22no—
238C8×C11—42no—
239C8×C11—42no—
240C8×C11—41no—
241C8×C11—41no—
242C22×D8—21no—
243C22×M16—21no—
244#533C22×C1111yescharacteristic
245C2×#127C22×C1111yescharacteristic
246C2×C4×D4C22×C1111yescharacteristic
247#490—22no—
248#486C22×C1112yescomplemented
249#486C22×C1112yescomplemented
250#483—21no—
251#476C22×C1111yescharacteristic, complemented
252#476C22×C1111yescharacteristic, complemented
253#461C22×C1111yescharacteristic, complemented
254#461C22×C1111yescharacteristic, complemented
255#459—21no—
256#459—21no—
257#459C22×C1112yes—
258#459C22×C1112yes—
259#450—21no—
260C4×SD16—21no—
261C4×SD16—21no—
262#436C22×C1112yescomplemented
263#435—22no—
264C8×D4C22×C1112yescomplemented
265#431C22×C1111yescharacteristic
266#423C22×C1111yescharacteristic
267C2×C4⋊C8C22×C1111yescharacteristic
268#418—21no—
269#418—21no—
270C2×#102—21no—
271#407—21no—
272C4×M16C22×C1111yescharacteristic
273#335C22×C1112yescomplemented
274#334C22×C1112yescomplemented
275#333C22×C1112yescomplemented
276#332C22×C1112yescomplemented
277#331C22×C1112yescomplemented
278#331C22×C1112yescomplemented
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—22no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—84no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—164no—
292C22×C11#46312yes—
293C22×C11C2×#12111yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11#46312yes—
302C4×C11C2×#13511yescharacteristic
303C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11#57511yescharacteristic
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4D4×C1111yescharacteristic
310C23×C4—21no—
311C2×SD16—21no—
312C2×SD16—21no—
313C2×D8—22no—
314C2×D8—22no—
315C2×D8—44no—
316C2×M16—21no—
317C2×M16—22no—
318C2×M16—44no—
319C2×M16D4×C1111yescharacteristic
320C2×M16D4×C1111yescharacteristic
321C22×C8—21no—
322C22×C8—22no—
323C4⋊Q8C23×C1111yescharacteristic
324C4⋊Q8C23×C1111yescharacteristic
325#127—21no—
326#127—21no—
327#127—21no—
328#127C23×C1112yes—
329#125—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4D4×C1111yescharacteristic
337C4×D4D4×C1111yescharacteristic
338C4×D4C23×C1111yescharacteristic
339C4×D4C23×C1111yescharacteristic
340#117—21no—
341C2×C4⋊C4D4×C1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C42C23×C1111yescharacteristic
344#106—21no—
345#106—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8C23×C1112yes—
349C4⋊C8C23×C1111yescharacteristic
350C4⋊C8C23×C1111yescharacteristic
351C4⋊C8C23×C1112yes—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—22no—
357#102—22no—
358#102—22no—
359#102—22no—
360#102—22no—
361#102—22no—
362C22⋊C8—21no—
363C22⋊C8—22no—
364C22⋊C8—22no—
365#97D4×C1112yes—
366C4×C8—21no—
367C4×C8C23×C1112yes—
368C2×C11—22no—
369C2×C11—42no—
370C2×C11—81no—
371C2×C11—162no—
372C2×C11C2×#46311yescharacteristic
373C2×C11#305511yescharacteristic
374C2×C11#306811yescharacteristic
375C24—21no—
376C24—41no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—82no—
393C2×D4C2×D4×C1111yescharacteristic
394C2×D4C2×D4×C1111yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C11×#4111yescharacteristic
405SD16—42no—
406SD16—42no—
407D8—44no—
408D8—44no—
409M16—22no—
410M16—22no—
411M16—44no—
412M16—42no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—44no—
418C2×C8—42no—
419C2×C8C2×D4×C1112yes—
420C2×C8C2×D4×C1112yes—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4C2×D4×C1111yescharacteristic
429C4⋊C4C2×D4×C1111yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—41no—
435C42—41no—
436C42C2×D4×C1111yescharacteristic
437C42C2×D4×C1111yescharacteristic
438C42C11×#4111yescharacteristic
439C42C24×C1111yescharacteristic
440C11#1916611yescharacteristic, direct product factor, Sylow
441C23—21no—
442C23—21no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—81no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23C11×#12111yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—81no—
454D4—21no—
455D4—21no—
456D4—21no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—82no—
463D4—82no—
464D4—82no—
465D4—82no—
466D4C11×AGL(1,ℤ/8)12yes—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4C11×#12111yescharacteristic
482C2×C4C11×#12111yescharacteristic
483C2×C4C11×#12111yescharacteristic
484C2×C4C11×#13512yes—
485C2×C4C11×AGL(1,ℤ/8)12yes—
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C22×D4×C1111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C8—22no—
490C8—22no—
491C8—42no—
492C8—42no—
493C8—41no—
494C8—41no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—84no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—164no—
508C22C11×#46312yes—
509C22C2×C11×#12111yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—81no—
517C4C11×#46312yes—
518C4C2×C11×#13511yescharacteristic
519C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
520C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
521C4C11×#57511yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—162no—
526C2C2×C11×#46311yescharacteristic
527C2C11×#305511yescharacteristic
528C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#459C2
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×#3138C2semidirect
2. C11×#3101C2semidirect
4. D4×C11×M16C2semidirect
5. C11×#1701C2semidirect
6. C11×#1697C2semidirect
7. C11×#1681C2semidirect
8. C11×#1677C2semidirect
9. C11×#1565C2semidirect
10. C11×#1550C2semidirect
11. C11×#1545C2semidirect
18. C11×#486C22semidirect
19. C11×#486C22semidirect
21. C11×#476C22semidirect
22. C11×#476C22semidirect
23. C11×#461C22semidirect
24. C11×#461C22semidirect
32. C11×#436C22semidirect
34. C8×D4×C11C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#332C22semidirect
47. C11×#331C22semidirect
48. C11×#331C22semidirect
111. #19166C11direct (N × H)
177. #3138C2×C11semidirect
178. #3101C2×C11semidirect
180. D4×M16C2×C11semidirect
181. #1701C2×C11semidirect
182. #1697C2×C11semidirect
183. #1681C2×C11semidirect
184. #1677C2×C11semidirect
185. #1565C2×C11semidirect
186. #1550C2×C11semidirect
187. #1545C2×C11semidirect
248. #486C22×C11semidirect
249. #486C22×C11semidirect
251. #476C22×C11semidirect
252. #476C22×C11semidirect
253. #461C22×C11semidirect
254. #461C22×C11semidirect
262. #436C22×C11semidirect
264. C8×D4C22×C11semidirect
273. #335C22×C11semidirect
274. #334C22×C11semidirect
275. #333C22×C11semidirect
276. #332C22×C11semidirect
277. #331C22×C11semidirect
278. #331C22×C11semidirect
440. C11#19166direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31382
C11×#31012
C2×C11×#4592
D4×C11×M162
C11×#17012
C11×#16972
C11×#16812
C11×#16772
C11×#15652
C11×#15502
C11×#15452
#1916611