Finite Group Databasebeta

← C11×#62686 #14639879

Subgroups — C11×#62686 #14639879

Order 2816.

7226 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3461C2112yesmaximal, complemented
2C11×#3460C2112yesmaximal, complemented
3C11×#3459C218yesmaximal, complemented
4C11×#3458C211yesmaximal, characteristic, complemented
5C11×#3455C2112yesmaximal, complemented
6C11×#3449C213yesmaximal, complemented
7C11×#3444C2112yesmaximal, complemented
8C2×C4×C11×#41C213yesmaximal, complemented
9C22×C11×#41C2213yes—
10C11×#544C22112yescomplemented
11C11×#543C2214yes—
12C11×#542C22148yescomplemented
13C11×#541C22124yescomplemented
14C11×#540C22124yescomplemented
15C11×#539C22148yescomplemented
16C11×#538C22148yescomplemented
17C11×#537C22112yes—
18C11×#536C22112yescomplemented
19C11×#535C22112yescomplemented
20C11×#534C22112yes—
21C11×#533C22112yescomplemented
22C11×#533C22124yescomplemented
23C11×#532C22112yes—
24C11×#532C22124yescomplemented
25C11×#529C22148yescomplemented
26C11×#529C22148yescomplemented
27C11×#529C22148yescomplemented
28C11×#525C22124yescomplemented
29C11×#525C22148yescomplemented
30C4×C11×#41C22112yescomplemented
31C4×C11×#41C22112yescomplemented
32C4×C11×#41C22124yescomplemented
33C4×C11×#41C22116yescomplemented
34C2×C4×Q8×C11C2216yescomplemented
35C2×C4×D4×C11C22112yes—
36C2×C4×D4×C11C2216yescomplemented
37C2×C11×#117C2213yes—
38C2×C11×#117C2216yescomplemented
39C22×C42×C11C2211yescharacteristic
40C22×C42×C11C2216yescomplemented
41C2×C11×#41—224no—
42C2×C11×#41C23112yes—
43C2×C11×#41C23112yes—
44C2×C11×#41C23116yes—
45C22×Q8×C11C2313yes—
46C22×D4×C11C2316yes—
47C22×D4×C11C2313yes—
48C23×C4×C11C2316yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C23112yes—
51C23×C4×C11C2311yescharacteristic
52C11×C4⋊Q8C23112yes—
53C11×C4⋊Q8C23124yes—
54C11×#127C23112yes—
55C11×#126C23196yes—
56C11×#125C23148yes—
57C11×#125C23124yes—
58C11×#124C23124yes—
59C11×#124C23148yes—
60C11×#123C23148yes—
61C11×#123C23196yes—
62C11×C22⋊Q8C23148yes—
63C11×C22⋊Q8C23148yes—
64C11×C22⋊Q8C23148yes—
65C11×#121C23148yes—
66C11×#121C23148yes—
67C11×#121C23148yes—
68C11×#120C23148yes—
69C4×Q8×C11C23124yes—
70C4×Q8×C11C23124yes—
71C4×Q8×C11C23116yes—
72C4×Q8×C11C23116yes—
73C4×D4×C11C23148yes—
74C4×D4×C11C23148yes—
75C4×D4×C11C23124yes—
76C4×D4×C11C23124yes—
77C4×D4×C11C23148yes—
78C4×D4×C11C23148yes—
79C11×#117C23112yes—
80C11×#117C23112yes—
81C11×#117C23124yes—
82C11×#117C23124yes—
83C11×#117C23148yes—
84C2×C11×C4⋊C4C2316yes—
85C2×C11×C4⋊C4C23112yes—
86C2×C11×C22⋊C4C2316yes—
87C2×C11×C22⋊C4C23112yes—
88C2×C42×C11C2313yes—
89C2×C42×C11C2316yes—
90C2×C42×C11C2316yes—
91C2×C42×C11C23112yes—
92C2×C42×C11C23112yes—
93C2×C42×C11C23124yes—
94C2×C42×C11C2313yes—
95C2×C42×C11C23112yes—
96#62686C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C2416yes—
98C24×C11C2411yescharacteristic
99C11×#41—248no—
100C11×#41—248no—
101C11×#41—432no—
102C2×Q8×C11—212no—
103C2×Q8×C11C24112yes—
104C2×Q8×C11C24116yes—
105C2×D4×C11—224no—
106C2×D4×C11—212no—
107C2×D4×C11C24124yes—
108C2×D4×C11C24112yes—
109C2×D4×C11C24148yes—
110C22×C4×C11—224no—
111C22×C4×C11—44no—
112C22×C4×C11—424no—
113C22×C4×C11#4118yescomplemented
114C22×C4×C11C2416yes—
115C22×C4×C11C2416yes—
116C22×C4×C11C24112yes—
117C22×C4×C11C24124yes—
118C22×C4×C11C24112yes—
119C22×C4×C11C2416yes—
120C22×C4×C11C24112yes—
121C22×C4×C11C24124yes—
122C22×C4×C11C2413yes—
123C22×C4×C11C2413yes—
124C11×C4⋊C4C24124yes—
125C11×C4⋊C4C24148yes—
126C11×C4⋊C4C24148yes—
127C11×C4⋊C4C24148yes—
128C11×C22⋊C4C24124yes—
129C11×C22⋊C4C24148yes—
130C11×C22⋊C4C24196yes—
131C42×C11C2413yes—
132C42×C11C2416yes—
133C42×C11C2416yes—
134C42×C11C24112yes—
135C42×C11C24124yes—
136C42×C11C24112yes—
137C42×C11C24124yes—
138C42×C11C2411yescharacteristic
139#3461C2×C11112yescomplemented
140#3460C2×C11112yescomplemented
141#3459C2×C1118yescomplemented
142#3458C2×C1111yescharacteristic, complemented
143#3455C2×C11112yescomplemented
144#3449C2×C1113yescomplemented
145#3444C2×C11112yescomplemented
146C2×C4×#41C2×C1113yescomplemented
147C23×C11—212no—
148C23×C11—42no—
149C23×C11—412no—
150C23×C11C2×#4114yes—
151C23×C11C25112yes—
152C23×C11C2513yes—
153Q8×C11—224no—
154Q8×C11—416no—
155D4×C11—248no—
156D4×C11—224no—
157D4×C11—448no—
158C2×C4×C11—212no—
159C2×C4×C11—224no—
160C2×C4×C11—224no—
161C2×C4×C11—212no—
162C2×C4×C11—248no—
163C2×C4×C11—46no—
164C2×C4×C11—424no—
165C2×C4×C11—412no—
166C2×C4×C11C2×#41112yes—
167C2×C4×C11C2×#41112yes—
168C2×C4×C11C2516yes—
169C2×C4×C11C25112yes—
170C2×C4×C11C25124yes—
171C2×C4×C11C2511yescharacteristic
172C2×C4×C11C2513yes—
173C2×C4×C11C2512yes—
174C22×#41C22×C1113yes—
175#544C22×C11112yescomplemented
176#543C22×C1114yes—
177#542C22×C11148yescomplemented
178#541C22×C11124yescomplemented
179#540C22×C11124yescomplemented
180#539C22×C11148yescomplemented
181#538C22×C11148yescomplemented
182#537C22×C11112yes—
183#536C22×C11112yescomplemented
184#535C22×C11112yescomplemented
185#534C22×C11112yes—
186#533C22×C11112yescomplemented
187#533C22×C11124yescomplemented
188#532C22×C11112yes—
189#532C22×C11124yescomplemented
190#529C22×C11148yescomplemented
191#529C22×C11148yescomplemented
192#529C22×C11148yescomplemented
193#525C22×C11124yescomplemented
194#525C22×C11148yescomplemented
195C4×#41C22×C11112yescomplemented
196C4×#41C22×C11112yescomplemented
197C4×#41C22×C11124yescomplemented
198C4×#41C22×C11116yescomplemented
199C2×C4×Q8C22×C1116yescomplemented
200C2×C4×D4C22×C11112yes—
201C2×C4×D4C22×C1116yescomplemented
202C2×#117C22×C1113yes—
203C2×#117C22×C1116yescomplemented
204C22×C42C22×C1111yescharacteristic
205C22×C42C22×C1116yescomplemented
206C22×C11—26no—
207C22×C11—212no—
208C22×C11—224no—
209C22×C11—44no—
210C22×C11—424no—
211C22×C11C22×#4116yes—
212C22×C11C2611yescharacteristic
213C4×C11—212no—
214C4×C11—26no—
215C4×C11—224no—
216C4×C11C22×#4112yes—
217C4×C11C22×#4116yes—
218C4×C11#58514yes—
219C2×#41—224no—
220C2×#41C23×C11112yes—
221C2×#41C23×C11112yes—
222C2×#41C23×C11116yes—
223C22×Q8C23×C1113yes—
224C22×D4C23×C1116yes—
225C22×D4C23×C1113yes—
226C23×C4C23×C1116yes—
227C23×C4C23×C1112yes—
228C23×C4C23×C11112yes—
229C23×C4C23×C1111yescharacteristic
230C4⋊Q8C23×C11112yes—
231C4⋊Q8C23×C11124yes—
232#127C23×C11112yes—
233#126C23×C11196yes—
234#125C23×C11148yes—
235#125C23×C11124yes—
236#124C23×C11124yes—
237#124C23×C11148yes—
238#123C23×C11148yes—
239#123C23×C11196yes—
240C22⋊Q8C23×C11148yes—
241C22⋊Q8C23×C11148yes—
242C22⋊Q8C23×C11148yes—
243#121C23×C11148yes—
244#121C23×C11148yes—
245#121C23×C11148yes—
246#120C23×C11148yes—
247C4×Q8C23×C11124yes—
248C4×Q8C23×C11124yes—
249C4×Q8C23×C11116yes—
250C4×Q8C23×C11116yes—
251C4×D4C23×C11148yes—
252C4×D4C23×C11148yes—
253C4×D4C23×C11124yes—
254C4×D4C23×C11124yes—
255C4×D4C23×C11148yes—
256C4×D4C23×C11148yes—
257#117C23×C11112yes—
258#117C23×C11112yes—
259#117C23×C11124yes—
260#117C23×C11124yes—
261#117C23×C11148yes—
262C2×C4⋊C4C23×C1116yes—
263C2×C4⋊C4C23×C11112yes—
264C2×C22⋊C4C23×C1116yes—
265C2×C22⋊C4C23×C11112yes—
266C2×C42C23×C1116yes—
267C2×C42C23×C1113yes—
268C2×C42C23×C11112yes—
269C2×C42C23×C1116yes—
270C2×C42C23×C11112yes—
271C2×C42C23×C1113yes—
272C2×C42C23×C11112yes—
273C2×C42C23×C11124yes—
274C2×C11—26no—
275C2×C11—412no—
276C2×C11C23×#4111yescharacteristic
277C2×C11C2×#58512yes—
278C24C24×C1116yes—
279C24C24×C1111yescharacteristic
280#41—248no—
281#41—248no—
282#41—432no—
283C2×Q8—212no—
284C2×Q8C24×C11112yes—
285C2×Q8C24×C11116yes—
286C2×D4—224no—
287C2×D4—212no—
288C2×D4C24×C11124yes—
289C2×D4C24×C11112yes—
290C2×D4C24×C11148yes—
291C22×C4—224no—
292C22×C4—44no—
293C22×C4—424no—
294C22×C4C11×#4118yescomplemented
295C22×C4C24×C1116yes—
296C22×C4C24×C1116yes—
297C22×C4C24×C11112yes—
298C22×C4C24×C11124yes—
299C22×C4C24×C11112yes—
300C22×C4C24×C1116yes—
301C22×C4C24×C11112yes—
302C22×C4C24×C11124yes—
303C22×C4C24×C1113yes—
304C22×C4C24×C1113yes—
305C4⋊C4C24×C11124yes—
306C4⋊C4C24×C11148yes—
307C4⋊C4C24×C11148yes—
308C4⋊C4C24×C11148yes—
309C22⋊C4C24×C11124yes—
310C22⋊C4C24×C11148yes—
311C22⋊C4C24×C11196yes—
312C42C24×C1111yescharacteristic
313C42C24×C1113yes—
314C42C24×C1116yes—
315C42C24×C1116yes—
316C42C24×C11112yes—
317C42C24×C11124yes—
318C42C24×C11112yes—
319C42C24×C11124yes—
320C11#6268611yescharacteristic, direct product factor, Sylow
321C23—212no—
322C23—42no—
323C23—412no—
324C23C2×C11×#4114yes—
325C23C25×C11112yes—
326C23C25×C1113yes—
327Q8—224no—
328Q8—416no—
329D4—248no—
330D4—224no—
331D4—448no—
332C2×C4—212no—
333C2×C4—224no—
334C2×C4—224no—
335C2×C4—212no—
336C2×C4—248no—
337C2×C4—46no—
338C2×C4—424no—
339C2×C4—412no—
340C2×C4C2×C11×#41112yes—
341C2×C4C2×C11×#41112yes—
342C2×C4C25×C1116yes—
343C2×C4C25×C11112yes—
344C2×C4C25×C11124yes—
345C2×C4C25×C1111yescharacteristic
346C2×C4C25×C1113yes—
347C2×C4C25×C1112yes—
348C22—26no—
349C22—212no—
350C22—224no—
351C22—44no—
352C22—424no—
353C22C22×C11×#4116yes—
354C22C26×C1111yescharacteristic
355C4—212no—
356C4—26no—
357C4—224no—
358C4C22×C11×#4112yes—
359C4C22×C11×#4116yes—
360C4C11×#58514yes—
361C2—26no—
362C2—412no—
363C2C23×C11×#4111yescharacteristic
364C2C2×C11×#58512yes—
subgroupG/H
centerC42×C11C24
commutator, Frattini, cosocleC22C26×C11
socleC22×C11C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3461C2semidirect
2. C11×#3460C2semidirect
3. C11×#3459C2semidirect
4. C11×#3458C2semidirect
5. C11×#3455C2semidirect
6. C11×#3449C2semidirect
7. C11×#3444C2semidirect
8. C2×C4×C11×#41C2semidirect
10. C11×#544C22semidirect
12. C11×#542C22semidirect
13. C11×#541C22semidirect
14. C11×#540C22semidirect
15. C11×#539C22semidirect
16. C11×#538C22semidirect
18. C11×#536C22semidirect
19. C11×#535C22semidirect
21. C11×#533C22semidirect
22. C11×#533C22semidirect
24. C11×#532C22semidirect
25. C11×#529C22semidirect
26. C11×#529C22semidirect
27. C11×#529C22semidirect
28. C11×#525C22semidirect
29. C11×#525C22semidirect
30. C4×C11×#41C22semidirect
31. C4×C11×#41C22semidirect
32. C4×C11×#41C22semidirect
33. C4×C11×#41C22semidirect
34. C2×C4×Q8×C11C22semidirect
36. C2×C4×D4×C11C22semidirect
38. C2×C11×#117C22semidirect
40. C22×C42×C11C22semidirect
96. #62686C11direct (N × H)
113. C22×C4×C11#41semidirect
139. #3461C2×C11semidirect
140. #3460C2×C11semidirect
141. #3459C2×C11semidirect
142. #3458C2×C11semidirect
143. #3455C2×C11semidirect
144. #3449C2×C11semidirect
145. #3444C2×C11semidirect
146. C2×C4×#41C2×C11semidirect
175. #544C22×C11semidirect
177. #542C22×C11semidirect
178. #541C22×C11semidirect
179. #540C22×C11semidirect
180. #539C22×C11semidirect
181. #538C22×C11semidirect
183. #536C22×C11semidirect
184. #535C22×C11semidirect
186. #533C22×C11semidirect
187. #533C22×C11semidirect
189. #532C22×C11semidirect
190. #529C22×C11semidirect
191. #529C22×C11semidirect
192. #529C22×C11semidirect
193. #525C22×C11semidirect
194. #525C22×C11semidirect
195. C4×#41C22×C11semidirect
196. C4×#41C22×C11semidirect
197. C4×#41C22×C11semidirect
198. C4×#41C22×C11semidirect
199. C2×C4×Q8C22×C11semidirect
201. C2×C4×D4C22×C11semidirect
203. C2×#117C22×C11semidirect
205. C22×C42C22×C11semidirect
294. C22×C4C11×#41semidirect
320. C11#62686direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34612
C11×#34602
C11×#34592
C11×#34582
C11×#34552
C11×#34492
C11×#34442
C2×C4×C11×#412
#6268611