Finite Group Databasebeta

← C11×#61105 #14638298

Subgroups — C11×#61105 #14638298

Order 2816.

2620 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3584C214yesmaximal, complemented
2C11×#3293C212yesmaximal, complemented
3C11×#3292C212yesmaximal, complemented
4C11×#3291C214yesmaximal, complemented
5C11×#3290C218yesmaximal, complemented
6C11×#3147C211yesmaximal, characteristic, complemented
7C11×#3067C214yesmaximal, complemented
8C11×#3018C214yesmaximal, complemented
9C2×C11×#443C212yesmaximal, complemented
10C11×#585C2214yescomplemented
11C11×#578—24no—
12C11×#578C2218yescomplemented
13C11×#577—28no—
14C11×#577C22116yescomplemented
15C11×#576—24no—
16C11×#576C2218yescomplemented
17C11×#575—28no—
18C11×#575C2218yescomplemented
19C2×C11×#135—28no—
20C2×C11×#135C2212yes—
21C2×C11×#135C2214yescomplemented
22C2×C11×#131C2214yescomplemented
23C11×#532C2212yescomplemented
24C11×#495C2214yescomplemented
25C11×#494C2211yescharacteristic, complemented
26C11×#493C2211yescharacteristic, complemented
27C11×#492C2212yescomplemented
28C11×#473C2218yescomplemented
29C11×#472C2218yescomplemented
30C11×#471C22116yescomplemented
31C11×#456C2218yescomplemented
32C11×#455C2218yescomplemented
33C11×#454C2218yescomplemented
34C11×#453C2218yescomplemented
35C11×#443C2214yescomplemented
36C11×#443C2214yescomplemented
37C11×#443C2214yescomplemented
38C11×#443C2214yescomplemented
39C2×C11×#108C2212yescomplemented
40C2×C11×#104C2214yescomplemented
41C11×#413C2214yescomplemented
42C2×C4×C8×C11C2211yescharacteristic, complemented
43C11×2−1+4—28no—
44C11×2−1+4C2318yes—
45C11×H(5,𝔽2)—28no—
46C11×H(5,𝔽2)—44no—
47C11×H(5,𝔽2)C2318yes—
48C2×C11×#41—216no—
49C2×C11×#41—44no—
50C2×C11×#41C2314yes—
51C2×C11×#41C2314yes—
52C11×#137—28no—
53C11×#137—216no—
54C11×#137—216no—
55C11×#137C23116yes—
56C11×AGL(1,ℤ/8)—28no—
57C11×AGL(1,ℤ/8)—216no—
58C11×AGL(1,ℤ/8)—216no—
59C11×AGL(1,ℤ/8)C23116yes—
60C11×#135—216no—
61C11×#135—28no—
62C11×#135—216no—
63C11×#135—28no—
64C11×#135—24no—
65C11×#135—24no—
66C11×#135—24no—
67C11×#135—24no—
68C11×#135D414yescomplemented
69C11×#135D414yescomplemented
70C11×#135C2314yes—
71C11×#135C2314yes—
72C2×C11×Q16—28no—
73C2×C11×Q16D412yescomplemented
74C2×C11×Q16C2314yes—
75C2×C11×SD16—216no—
76C2×C11×SD16D414yescomplemented
77C2×C11×SD16C2318yes—
78C2×C11×D8—28no—
79C2×C11×D8D412yescomplemented
80C2×C11×D8C2314yes—
81C11×#131—24no—
82C11×#131—24no—
83C11×#131C2318yes—
84C11×#131C2318yes—
85C2×C11×M16—24no—
86C2×C11×M16C2314yes—
87C22×C8×C11—24no—
88C22×C8×C11C2312yes—
89C11×C4⋊Q8C2312yes—
90C11×#127C2312yes—
91C11×#124C2314yes—
92C11×#121—42no—
93C4×D4×C11—42no—
94C2×C42×C11C2311yescharacteristic
95C11×#108C2314yes—
96C11×#108C2314yes—
97C11×#104C2318yes—
98C11×#104C2318yes—
99C11×#101C2318yes—
100C11×#100C2318yes—
101C4×C8×C11C2311yescharacteristic
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2312yes—
104#61105C1111yesmaximal, characteristic, direct product factor, Sylow
105C11×#41—24no—
106C11×#41—24no—
107C11×#41—216no—
108C11×#41—216no—
109C11×#41—28no—
110C11×#41—28no—
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—416no—
114C11×#41—48no—
115C11×#41C2×D418yes—
116C11×#41C2418yes—
117C2×Q8×C11—216no—
118C2×Q8×C11—44no—
119C2×Q8×C11C2×D414yes—
120C2×Q8×C11C2414yes—
121C2×D4×C11—24no—
122C2×D4×C11—216no—
123C2×D4×C11—24no—
124C2×D4×C11—42no—
125C2×D4×C11—48no—
126C2×D4×C11—44no—
127C2×D4×C11—416no—
128C2×D4×C11C2×D414yes—
129C2×D4×C11C2414yes—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—24no—
133C22×C4×C11—48no—
134C22×C4×C11C2411yescharacteristic
135C11×Q16—24no—
136C11×Q16—24no—
137C11×Q16—216no—
138C11×Q16C2×D414yes—
139C11×Q16C2×D414yes—
140C11×SD16—28no—
141C11×SD16—28no—
142C11×SD16—216no—
143C11×SD16—216no—
144C11×SD16C2×D418yes—
145C11×SD16C2×D418yes—
146C11×D8—24no—
147C11×D8—24no—
148C11×D8—216no—
149C11×D8C2×D414yes—
150C11×D8C2×D414yes—
151C11×M16—28no—
152C11×M16—28no—
153C11×M16—24no—
154C11×M16C2418yes—
155C2×C8×C11—28no—
156C2×C8×C11—28no—
157C2×C8×C11—24no—
158C2×C8×C11C2×D412yes—
159C2×C8×C11C2×D412yes—
160C2×C8×C11C2×D412yes—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2412yes—
163C2×C8×C11C2412yes—
164C11×C4⋊C4—42no—
165C11×C22⋊C4—44no—
166C42×C11—21no—
167C42×C11C2411yescharacteristic
168C42×C11C2411yescharacteristic
169#3584C2×C1114yescomplemented
170#3293C2×C1112yescomplemented
171#3292C2×C1112yescomplemented
172#3291C2×C1114yescomplemented
173#3290C2×C1118yescomplemented
174#3147C2×C1111yescharacteristic, complemented
175#3067C2×C1114yescomplemented
176#3018C2×C1114yescomplemented
177C2×#443C2×C1112yescomplemented
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—48no—
181C23×C11H(5,𝔽2)11yescharacteristic
182Q8×C11—24no—
183Q8×C11—28no—
184Q8×C11—48no—
185Q8×C11C22×D418yes—
186D4×C11—28no—
187D4×C11—28no—
188D4×C11—24no—
189D4×C11—28no—
190D4×C11—416no—
191D4×C11—48no—
192D4×C11—48no—
193D4×C11—84no—
194D4×C11C22×D418yes—
195C2×C4×C11—24no—
196C2×C4×C11—21no—
197C2×C4×C11—28no—
198C2×C4×C11—28no—
199C2×C4×C11—21no—
200C2×C4×C11—24no—
201C2×C4×C11—48no—
202C2×C4×C11—416no—
203C2×C4×C11—42no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11C22×D412yes—
207C2×C4×C11C22×D412yes—
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C11C2511yescharacteristic
210C8×C11—28no—
211C8×C11C22×D412yes—
212C8×C11C22×D412yes—
213C8×C11C22×D412yes—
214C8×C11C22×D412yes—
215#585C22×C1114yescomplemented
216#578—24no—
217#578C22×C1118yescomplemented
218#577—28no—
219#577C22×C11116yescomplemented
220#576—24no—
221#576C22×C1118yescomplemented
222#575—28no—
223#575C22×C1118yescomplemented
224C2×#135—28no—
225C2×#135C22×C1112yes—
226C2×#135C22×C1114yescomplemented
227C2×#131C22×C1114yescomplemented
228#532C22×C1112yescomplemented
229#495C22×C1114yescomplemented
230#494C22×C1111yescharacteristic, complemented
231#493C22×C1111yescharacteristic, complemented
232#492C22×C1112yescomplemented
233#473C22×C1118yescomplemented
234#472C22×C1118yescomplemented
235#471C22×C11116yescomplemented
236#456C22×C1118yescomplemented
237#455C22×C1118yescomplemented
238#454C22×C1118yescomplemented
239#453C22×C1118yescomplemented
240#443C22×C1114yescomplemented
241#443C22×C1114yescomplemented
242#443C22×C1114yescomplemented
243#443C22×C1114yescomplemented
244C2×#108C22×C1112yescomplemented
245C2×#104C22×C1114yescomplemented
246#413C22×C1114yescomplemented
247C2×C4×C8C22×C1111yescharacteristic, complemented
248C22×C11—28no—
249C22×C11—41no—
250C22×C11—44no—
251C22×C11—84no—
252C22×C11—84no—
253C22×C11—168no—
254C22×C11D4212yes—
255C22×C11C2×H(5,𝔽2)11yescharacteristic
256C4×C11—22no—
257C4×C11—28no—
258C4×C11—41no—
259C4×C11—44no—
260C4×C11D4211yescharacteristic
261C4×C11D4211yescharacteristic
262C4×C11C23×D412yes—
2632−1+4—28no—
2642−1+4C23×C1118yes—
265H(5,𝔽2)—28no—
266H(5,𝔽2)—44no—
267H(5,𝔽2)C23×C1118yes—
268C2×#41—216no—
269C2×#41—44no—
270C2×#41C23×C1114yes—
271C2×#41C23×C1114yes—
272#137—28no—
273#137—216no—
274#137—216no—
275#137C23×C11116yes—
276AGL(1,ℤ/8)—28no—
277AGL(1,ℤ/8)—216no—
278AGL(1,ℤ/8)—216no—
279AGL(1,ℤ/8)C23×C11116yes—
280#135—216no—
281#135—28no—
282#135—216no—
283#135—28no—
284#135—24no—
285#135—24no—
286#135—24no—
287#135—24no—
288#135D4×C1114yescomplemented
289#135D4×C1114yescomplemented
290#135C23×C1114yes—
291#135C23×C1114yes—
292C2×Q16—28no—
293C2×Q16D4×C1112yescomplemented
294C2×Q16C23×C1114yes—
295C2×SD16—216no—
296C2×SD16D4×C1114yescomplemented
297C2×SD16C23×C1118yes—
298C2×D8—28no—
299C2×D8D4×C1112yescomplemented
300C2×D8C23×C1114yes—
301#131—24no—
302#131—24no—
303#131C23×C1118yes—
304#131C23×C1118yes—
305C2×M16—24no—
306C2×M16C23×C1114yes—
307C22×C8—24no—
308C22×C8C23×C1112yes—
309C4⋊Q8C23×C1112yes—
310#127C23×C1112yes—
311#124C23×C1114yes—
312#121—42no—
313C4×D4—42no—
314C2×C42C23×C1111yescharacteristic
315#108C23×C1114yes—
316#108C23×C1114yes—
317#104C23×C1118yes—
318#104C23×C1118yes—
319#101C23×C1118yes—
320#100C23×C1118yes—
321C4×C8C23×C1111yescharacteristic
322C4×C8C23×C1111yescharacteristic
323C4×C8C23×C1112yes—
324C2×C11—21no—
325C2×C11—22no—
326C2×C11—48no—
327C2×C11—84no—
328C2×C11C2×D4211yescharacteristic
329#41—24no—
330#41—24no—
331#41—216no—
332#41—216no—
333#41—28no—
334#41—28no—
335#41—48no—
336#41—48no—
337#41—416no—
338#41—48no—
339#41C2×D4×C1118yes—
340#41C24×C1118yes—
341C2×Q8—216no—
342C2×Q8—44no—
343C2×Q8C2×D4×C1114yes—
344C2×Q8C24×C1114yes—
345C2×D4—24no—
346C2×D4—216no—
347C2×D4—24no—
348C2×D4—42no—
349C2×D4—48no—
350C2×D4—44no—
351C2×D4—416no—
352C2×D4C2×D4×C1114yes—
353C2×D4C24×C1114yes—
354C22×C4—24no—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—48no—
358C22×C4C24×C1111yescharacteristic
359Q16—216no—
360Q16—24no—
361Q16—24no—
362Q16C2×D4×C1114yes—
363Q16C2×D4×C1114yes—
364SD16—216no—
365SD16—216no—
366SD16—28no—
367SD16—28no—
368SD16C2×D4×C1118yes—
369SD16C2×D4×C1118yes—
370D8—216no—
371D8—24no—
372D8—24no—
373D8C2×D4×C1114yes—
374D8C2×D4×C1114yes—
375M16—24no—
376M16—28no—
377M16—28no—
378M16C24×C1118yes—
379C2×C8—24no—
380C2×C8—28no—
381C2×C8—28no—
382C2×C8C2×D4×C1112yes—
383C2×C8C2×D4×C1112yes—
384C2×C8C2×D4×C1112yes—
385C2×C8C2×D4×C1112yes—
386C2×C8C24×C1112yes—
387C2×C8C24×C1112yes—
388C4⋊C4—42no—
389C22⋊C4—44no—
390C42—21no—
391C42C24×C1111yescharacteristic
392C42C24×C1111yescharacteristic
393C11#6110511yescharacteristic, direct product factor, Sylow
394C23—24no—
395C23—24no—
396C23—48no—
397C23C11×H(5,𝔽2)11yescharacteristic
398Q8—24no—
399Q8—28no—
400Q8—48no—
401Q8C22×D4×C1118yes—
402D4—28no—
403D4—28no—
404D4—24no—
405D4—28no—
406D4—416no—
407D4—48no—
408D4—48no—
409D4—84no—
410D4C22×D4×C1118yes—
411C2×C4—24no—
412C2×C4—21no—
413C2×C4—28no—
414C2×C4—28no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—48no—
418C2×C4—416no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4C22×D4×C1112yes—
423C2×C4C22×D4×C1112yes—
424C2×C4C11×H(5,𝔽2)11yescharacteristic
425C2×C4C25×C1111yescharacteristic
426C8—28no—
427C8C22×D4×C1112yes—
428C8C22×D4×C1112yes—
429C8C22×D4×C1112yes—
430C8C22×D4×C1112yes—
431C22—28no—
432C22—41no—
433C22—44no—
434C22—84no—
435C22—84no—
436C22—168no—
437C22D42×C1112yes—
438C22C2×C11×H(5,𝔽2)11yescharacteristic
439C4—22no—
440C4—28no—
441C4—41no—
442C4—44no—
443C4D42×C1111yescharacteristic
444C4D42×C1111yescharacteristic
445C4C23×D4×C1112yes—
446C2—21no—
447C2—22no—
448C2—48no—
449C2—84no—
450C2C2×D42×C1111yescharacteristic
subgroupG/H
centerC4×C11D42
commutator, Frattini, cosocleC2×C4C25×C11
socleC2×C11C2×D42
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3584C2semidirect
2. C11×#3293C2semidirect
3. C11×#3292C2semidirect
4. C11×#3291C2semidirect
5. C11×#3290C2semidirect
6. C11×#3147C2semidirect
7. C11×#3067C2semidirect
8. C11×#3018C2semidirect
9. C2×C11×#443C2semidirect
10. C11×#585C22semidirect
12. C11×#578C22semidirect
14. C11×#577C22semidirect
16. C11×#576C22semidirect
18. C11×#575C22semidirect
21. C2×C11×#135C22semidirect
22. C2×C11×#131C22semidirect
23. C11×#532C22semidirect
24. C11×#495C22semidirect
25. C11×#494C22semidirect
26. C11×#493C22semidirect
27. C11×#492C22semidirect
28. C11×#473C22semidirect
29. C11×#472C22semidirect
30. C11×#471C22semidirect
31. C11×#456C22semidirect
32. C11×#455C22semidirect
33. C11×#454C22semidirect
34. C11×#453C22semidirect
35. C11×#443C22semidirect
36. C11×#443C22semidirect
37. C11×#443C22semidirect
38. C11×#443C22semidirect
39. C2×C11×#108C22semidirect
40. C2×C11×#104C22semidirect
41. C11×#413C22semidirect
42. C2×C4×C8×C11C22semidirect
68. C11×#135D4semidirect
69. C11×#135D4semidirect
73. C2×C11×Q16D4semidirect
76. C2×C11×SD16D4semidirect
79. C2×C11×D8D4semidirect
104. #61105C11direct (N × H)
169. #3584C2×C11semidirect
170. #3293C2×C11semidirect
171. #3292C2×C11semidirect
172. #3291C2×C11semidirect
173. #3290C2×C11semidirect
174. #3147C2×C11semidirect
175. #3067C2×C11semidirect
176. #3018C2×C11semidirect
177. C2×#443C2×C11semidirect
215. #585C22×C11semidirect
217. #578C22×C11semidirect
219. #577C22×C11semidirect
221. #576C22×C11semidirect
223. #575C22×C11semidirect
226. C2×#135C22×C11semidirect
227. C2×#131C22×C11semidirect
228. #532C22×C11semidirect
229. #495C22×C11semidirect
230. #494C22×C11semidirect
231. #493C22×C11semidirect
232. #492C22×C11semidirect
233. #473C22×C11semidirect
234. #472C22×C11semidirect
235. #471C22×C11semidirect
236. #456C22×C11semidirect
237. #455C22×C11semidirect
238. #454C22×C11semidirect
239. #453C22×C11semidirect
240. #443C22×C11semidirect
241. #443C22×C11semidirect
242. #443C22×C11semidirect
243. #443C22×C11semidirect
244. C2×#108C22×C11semidirect
245. C2×#104C22×C11semidirect
246. #413C22×C11semidirect
247. C2×C4×C8C22×C11semidirect
288. #135D4×C11semidirect
289. #135D4×C11semidirect
293. C2×Q16D4×C11semidirect
296. C2×SD16D4×C11semidirect
299. C2×D8D4×C11semidirect
393. C11#61105direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35842
C11×#32932
C11×#32922
C11×#32912
C11×#32902
C11×#31472
C11×#30672
C11×#30182
C2×C11×#4432
#6110511