Finite Group Databasebeta

← C11×#3493 #13066331

Subgroups — C11×#3493 #13066331

Order 1408.

1040 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#556C214yesmaximal, complemented
2C11×#555C214yesmaximal, complemented
3C11×#553C214yesmaximal, complemented
4C11×#552C214yesmaximal, complemented
5C11×#544C211yesmaximal, characteristic, complemented
6C11×#538C214yesmaximal, complemented
7C11×#537C211yesmaximal, characteristic, complemented
8C11×#529C214yesmaximal, complemented
9C11×#525C212yesmaximal, complemented
10C11×#520C212yesmaximal, complemented
11C2×C11×#117C211yesmaximal, characteristic, complemented
12C2×C11×#41C2212yes—
13C23×C4×C11C2211yescharacteristic
14C11×C4⋊Q8C2214yescomplemented
15C11×#126C2218yes—
16C11×#126C2218yescomplemented
17C11×#125C2214yescomplemented
18C11×#125C2214yescomplemented
19C11×#124C2218yes—
20C11×#124C2214yescomplemented
21C11×#123C2214yes—
22C11×#123C2218yes—
23C11×C22⋊Q8C2212yes—
24C11×C22⋊Q8C2212yes—
25C11×C22⋊Q8C2214yes—
26C11×C22⋊Q8C2214yescomplemented
27C11×#121C2212yes—
28C11×#121C2212yes—
29C11×#121C2214yes—
30C11×#121C2218yes—
31C11×#121C2214yescomplemented
32C11×#120C2214yes—
33C4×Q8×C11C2214yescomplemented
34C4×Q8×C11C2214yescomplemented
35C4×D4×C11C2218yes—
36C4×D4×C11C2214yes—
37C4×D4×C11C2214yes—
38C4×D4×C11C2214yescomplemented
39C4×D4×C11C2214yescomplemented
40C11×#117C2214yes—
41C11×#117C2214yes—
42C11×#117C2212yes—
43C11×#117C2214yescomplemented
44C11×#117C2218yescomplemented
45C2×C11×C4⋊C4C2211yescharacteristic
46C2×C11×C4⋊C4C2211yescharacteristic
47C2×C11×C4⋊C4C2214yescomplemented
48C2×C11×C22⋊C4C2212yes—
49C2×C42×C11C2212yes—
50C24×C11C2311yescharacteristic
51C11×#41—28no—
52C2×Q8×C11C2312yes—
53C2×Q8×C11C2314yes—
54C2×D4×C11C2314yes—
55C2×D4×C11C2312yes—
56C2×D4×C11C2314yes—
57C2×D4×C11C2314yes—
58C2×D4×C11C2314yes—
59C22×C4×C11—24no—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2314yes—
62C22×C4×C11C2312yes—
63C22×C4×C11C2312yes—
64C22×C4×C11C2312yes—
65C22×C4×C11C2312yes—
66C22×C4×C11C2318yes—
67C22×C4×C11C2311yescharacteristic
68C11×C4⋊C4C2314yes—
69C11×C4⋊C4C2314yes—
70C11×C4⋊C4C2312yes—
71C11×C4⋊C4C2318yes—
72C11×C4⋊C4C2312yes—
73C11×C4⋊C4C2314yes—
74C11×C4⋊C4C2318yes—
75C11×C4⋊C4C2314yes—
76C11×C4⋊C4C2314yes—
77C11×C4⋊C4C2314yes—
78C11×C22⋊C4C2318yes—
79C11×C22⋊C4C2314yes—
80C11×C22⋊C4C2314yes—
81C11×C22⋊C4C2318yes—
82C11×C22⋊C4C2318yes—
83C11×C22⋊C4C2314yes—
84C11×C22⋊C4C2314yes—
85C11×C22⋊C4C2314yes—
86C42×C11C2314yes—
87C42×C11C2314yes—
88C42×C11C2314yes—
89C42×C11C2318yes—
90#3493C1111yesmaximal, characteristic, direct product factor, Sylow
91C23×C11—22no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11C2412yes—
95C23×C11C2414yes—
96C23×C11C2411yescharacteristic
97Q8×C11—24no—
98Q8×C11—44no—
99D4×C11—28no—
100D4×C11—24no—
101D4×C11—44no—
102D4×C11—44no—
103D4×C11—44no—
104C2×C4×C11—22no—
105C2×C4×C11—24no—
106C2×C4×C11—24no—
107C2×C4×C11—28no—
108C2×C4×C11—42no—
109C2×C4×C11—48no—
110C2×C4×C11—42no—
111C2×C4×C11#4114yes—
112C2×C4×C11C2411yescharacteristic
113C2×C4×C11C2411yescharacteristic
114C2×C4×C11C2414yes—
115C2×C4×C11C2414yes—
116C2×C4×C11C2414yes—
117C2×C4×C11C2414yes—
118C2×C4×C11C2414yes—
119C2×C4×C11C2412yes—
120#556C2×C1114yescomplemented
121#555C2×C1114yescomplemented
122#553C2×C1114yescomplemented
123#552C2×C1114yescomplemented
124#544C2×C1111yescharacteristic, complemented
125#538C2×C1114yescomplemented
126#537C2×C1111yescharacteristic, complemented
127#529C2×C1114yescomplemented
128#525C2×C1112yescomplemented
129#520C2×C1112yescomplemented
130C2×#117C2×C1111yescharacteristic, complemented
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—22no—
134C22×C11—24no—
135C22×C11—24no—
136C22×C11—24no—
137C22×C11—22no—
138C22×C11—22no—
139C22×C11—44no—
140C22×C11C2×#4112yes—
141C22×C11C2511yescharacteristic
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—24no—
145C4×C11—24no—
146C4×C11—24no—
147C4×C11—24no—
148C4×C11—24no—
149C4×C11C2×#4114yes—
150C2×#41C22×C1112yes—
151C23×C4C22×C1111yescharacteristic
152C4⋊Q8C22×C1114yescomplemented
153#126C22×C1118yes—
154#126C22×C1118yescomplemented
155#125C22×C1114yescomplemented
156#125C22×C1114yescomplemented
157#124C22×C1118yes—
158#124C22×C1114yescomplemented
159#123C22×C1114yes—
160#123C22×C1118yes—
161C22⋊Q8C22×C1112yes—
162C22⋊Q8C22×C1112yes—
163C22⋊Q8C22×C1114yes—
164C22⋊Q8C22×C1114yescomplemented
165#121C22×C1112yes—
166#121C22×C1112yes—
167#121C22×C1114yes—
168#121C22×C1118yes—
169#121C22×C1114yescomplemented
170#120C22×C1114yes—
171C4×Q8C22×C1114yescomplemented
172C4×Q8C22×C1114yescomplemented
173C4×D4C22×C1118yes—
174C4×D4C22×C1114yes—
175C4×D4C22×C1114yes—
176C4×D4C22×C1114yescomplemented
177C4×D4C22×C1114yescomplemented
178#117C22×C1114yes—
179#117C22×C1114yes—
180#117C22×C1112yes—
181#117C22×C1114yescomplemented
182#117C22×C1118yescomplemented
183C2×C4⋊C4C22×C1111yescharacteristic
184C2×C4⋊C4C22×C1111yescharacteristic
185C2×C4⋊C4C22×C1114yescomplemented
186C2×C22⋊C4C22×C1112yes—
187C2×C42C22×C1112yes—
188C2×C11—22no—
189C2×C11—44no—
190C2×C11—42no—
191C2×C11C22×#4111yescharacteristic
192C2×C11#58511yescharacteristic
193C2×C11#58511yescharacteristic
194C24C23×C1111yescharacteristic
195#41—28no—
196C2×Q8C23×C1112yes—
197C2×Q8C23×C1114yes—
198C2×D4C23×C1114yes—
199C2×D4C23×C1112yes—
200C2×D4C23×C1114yes—
201C2×D4C23×C1114yes—
202C2×D4C23×C1114yes—
203C22×C4—24no—
204C22×C4C23×C1111yescharacteristic
205C22×C4C23×C1114yes—
206C22×C4C23×C1112yes—
207C22×C4C23×C1112yes—
208C22×C4C23×C1112yes—
209C22×C4C23×C1112yes—
210C22×C4C23×C1118yes—
211C22×C4C23×C1111yescharacteristic
212C4⋊C4C23×C1114yes—
213C4⋊C4C23×C1114yes—
214C4⋊C4C23×C1112yes—
215C4⋊C4C23×C1118yes—
216C4⋊C4C23×C1112yes—
217C4⋊C4C23×C1114yes—
218C4⋊C4C23×C1118yes—
219C4⋊C4C23×C1114yes—
220C4⋊C4C23×C1114yes—
221C4⋊C4C23×C1114yes—
222C22⋊C4C23×C1118yes—
223C22⋊C4C23×C1114yes—
224C22⋊C4C23×C1114yes—
225C22⋊C4C23×C1118yes—
226C22⋊C4C23×C1118yes—
227C22⋊C4C23×C1114yes—
228C22⋊C4C23×C1114yes—
229C22⋊C4C23×C1114yes—
230C42C23×C1114yes—
231C42C23×C1114yes—
232C42C23×C1114yes—
233C42C23×C1118yes—
234C11#349311yescharacteristic, direct product factor, Sylow
235C23—22no—
236C23—41no—
237C23—41no—
238C23C24×C1112yes—
239C23C24×C1114yes—
240C23C24×C1111yescharacteristic
241Q8—24no—
242Q8—44no—
243D4—28no—
244D4—24no—
245D4—44no—
246D4—44no—
247D4—44no—
248C2×C4—22no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—28no—
252C2×C4—42no—
253C2×C4—48no—
254C2×C4—42no—
255C2×C4C11×#4114yes—
256C2×C4C24×C1111yescharacteristic
257C2×C4C24×C1111yescharacteristic
258C2×C4C24×C1114yes—
259C2×C4C24×C1114yes—
260C2×C4C24×C1114yes—
261C2×C4C24×C1114yes—
262C2×C4C24×C1114yes—
263C2×C4C24×C1112yes—
264C22—21no—
265C22—21no—
266C22—22no—
267C22—24no—
268C22—24no—
269C22—24no—
270C22—22no—
271C22—22no—
272C22—44no—
273C22C2×C11×#4112yes—
274C22C25×C1111yescharacteristic
275C4—21no—
276C4—21no—
277C4—24no—
278C4—24no—
279C4—24no—
280C4—24no—
281C4—24no—
282C4C2×C11×#4114yes—
283C2—22no—
284C2—42no—
285C2—44no—
286C2C22×C11×#4111yescharacteristic
287C2C11×#58511yescharacteristic
288C2C11×#58511yescharacteristic
subgroupG/H
center, socleC22×C11C25
commutator, Frattini, cosocleC22C25×C11
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
2. C11×#555C2semidirect
3. C11×#553C2semidirect
4. C11×#552C2semidirect
5. C11×#544C2semidirect
6. C11×#538C2semidirect
7. C11×#537C2semidirect
8. C11×#529C2semidirect
9. C11×#525C2semidirect
10. C11×#520C2semidirect
11. C2×C11×#117C2semidirect
14. C11×C4⋊Q8C22semidirect
16. C11×#126C22semidirect
17. C11×#125C22semidirect
18. C11×#125C22semidirect
20. C11×#124C22semidirect
26. C11×C22⋊Q8C22semidirect
31. C11×#121C22semidirect
33. C4×Q8×C11C22semidirect
34. C4×Q8×C11C22semidirect
38. C4×D4×C11C22semidirect
39. C4×D4×C11C22semidirect
43. C11×#117C22semidirect
44. C11×#117C22semidirect
47. C2×C11×C4⋊C4C22semidirect
90. #3493C11direct (N × H)
120. #556C2×C11semidirect
121. #555C2×C11semidirect
122. #553C2×C11semidirect
123. #552C2×C11semidirect
124. #544C2×C11semidirect
125. #538C2×C11semidirect
126. #537C2×C11semidirect
127. #529C2×C11semidirect
128. #525C2×C11semidirect
129. #520C2×C11semidirect
130. C2×#117C2×C11semidirect
152. C4⋊Q8C22×C11semidirect
154. #126C22×C11semidirect
155. #125C22×C11semidirect
156. #125C22×C11semidirect
158. #124C22×C11semidirect
164. C22⋊Q8C22×C11semidirect
169. #121C22×C11semidirect
171. C4×Q8C22×C11semidirect
172. C4×Q8C22×C11semidirect
176. C4×D4C22×C11semidirect
177. C4×D4C22×C11semidirect
181. #117C22×C11semidirect
182. #117C22×C11semidirect
185. C2×C4⋊C4C22×C11semidirect
234. C11#3493direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5562
C11×#5552
C11×#5532
C11×#5522
C11×#5442
C11×#5382
C11×#5372
C11×#5292
C11×#5252
C11×#5202
C2×C11×#1172
#349311