Finite Group Databasebeta

← C2×C11×#3444 #14639861

Subgroups — C2×C11×#3444 #14639861

Order 2816.

8518 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3444C2132yesmaximal, direct product factor
2C2×C11×#533C213yesmaximal, complemented
3C2×C11×#532C213yesmaximal, complemented
4C2×C11×#529C2112yesmaximal, complemented
5C2×C11×#525C216yesmaximal, complemented
6C2×C4×C11×#41C216yesmaximal, complemented
7C23×C42×C11C211yesmaximal, characteristic, complemented
8C22×C11×#41C2216yes—
9C24×C4×C11C2213yes—
10C11×#533C22148yescomplemented
11C11×#532C22148yescomplemented
12C2×C11×C4⋊Q8C2213yescomplemented
13C2×C11×#127C2211yescharacteristic, complemented
14C11×#529C221192yescomplemented
15C2×C11×#126C2218yescomplemented
16C2×C11×#125C2216yescomplemented
17C2×C11×#124C2216yescomplemented
18C11×#525C22196yescomplemented
19C2×C11×#123C22112yes—
20C2×C11×C22⋊Q8C22112yes—
21C2×C11×#121C22112yes—
22C2×C11×#120C2214yes—
23C4×C11×#41C22196yescomplemented
24C2×C4×Q8×C11C22112yescomplemented
25C2×C4×D4×C11C22124yes—
26C2×C4×D4×C11C22112yescomplemented
27C2×C11×#117C2216yes—
28C2×C11×#117C22112yescomplemented
29C22×C42×C11C2216yes—
30C22×C42×C11C2213yes—
31C22×C42×C11C2213yes—
32C22×C42×C11C22116yescomplemented
33C22×C42×C11C2214yescomplemented
34C25×C11C2311yescharacteristic
35C2×C11×#41—248no—
36C2×C11×#41C23148yes—
37C22×Q8×C11C2316yes—
38C22×D4×C11C23112yes—
39C22×D4×C11C2316yes—
40C23×C4×C11—224no—
41C23×C4×C11C2316yes—
42C23×C4×C11C2316yes—
43C23×C4×C11C2313yes—
44C23×C4×C11C23124yes—
45C23×C4×C11C23112yes—
46C23×C4×C11C2313yes—
47C11×C4⋊Q8C23124yescomplemented
48C11×#127C2318yescomplemented
49C11×#126C23164yescomplemented
50C11×#125C23148yescomplemented
51C11×#124C23148yescomplemented
52C11×#123C23196yes—
53C11×C22⋊Q8C23196yes—
54C11×#121C23196yes—
55C11×#120C23132yes—
56C4×Q8×C11C23196yescomplemented
57C4×D4×C11C231192yes—
58C4×D4×C11C23196yescomplemented
59C11×#117C23148yes—
60C11×#117C23196yescomplemented
61C2×C11×C4⋊C4C23112yes—
62C2×C11×C4⋊C4C23124yes—
63C2×C11×C22⋊C4C23112yes—
64C2×C11×C22⋊C4C23124yes—
65C2×C42×C11C2313yes—
66C2×C42×C11C2316yes—
67C2×C42×C11C2313yes—
68C2×C42×C11C2312yes—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C23124yes—
71C2×C42×C11C23148yes—
72C2×C42×C11C23124yes—
73C2×C42×C11C23112yes—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C23132yescomplemented
76C2×#3444C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—212no—
78C24×C11C2414yes—
79C24×C11C2414yes—
80C24×C11C2413yes—
81C11×#41—2192no—
82C2×Q8×C11—224no—
83C2×Q8×C11C24124yes—
84C2×D4×C11—248no—
85C2×D4×C11—224no—
86C2×D4×C11C24148yes—
87C2×D4×C11C24124yes—
88C22×C4×C11—212no—
89C22×C4×C11—224no—
90C22×C4×C11—224no—
91C22×C4×C11—248no—
92C22×C4×C11—296no—
93C22×C4×C11#41124yescomplemented
94C22×C4×C11C2416yes—
95C22×C4×C11C24124yes—
96C22×C4×C11C24124yes—
97C22×C4×C11C24112yes—
98C22×C4×C11C24112yes—
99C22×C4×C11C24148yes—
100C22×C4×C11C2413yes—
101C22×C4×C11C2413yes—
102C22×C4×C11C24112yes—
103C11×C4⋊C4C24148yes—
104C11×C4⋊C4C24196yes—
105C11×C22⋊C4C24148yes—
106C11×C22⋊C4C24196yes—
107C42×C11C24112yes—
108C42×C11C24124yes—
109C42×C11C24112yes—
110C42×C11C2418yes—
111C42×C11C2414yes—
112C42×C11C2414yes—
113C42×C11C24148yes—
114#3444C2×C11132yesdirect product factor
115C2×#533C2×C1113yescomplemented
116C2×#532C2×C1113yescomplemented
117C2×#529C2×C11112yescomplemented
118C2×#525C2×C1116yescomplemented
119C2×C4×#41C2×C1116yescomplemented
120C23×C42C2×C1111yescharacteristic, complemented
121C23×C11—232no—
122C23×C11—224no—
123C23×C11—212no—
124C23×C11—224no—
125C23×C11C2×#41112yes—
126C23×C11C2518yes—
127C23×C11C2516yes—
128C23×C11C2511yescharacteristic
129Q8×C11—248no—
130D4×C11—296no—
131D4×C11—248no—
132C2×C4×C11—224no—
133C2×C4×C11—212no—
134C2×C4×C11—224no—
135C2×C4×C11—248no—
136C2×C4×C11—248no—
137C2×C4×C11—296no—
138C2×C4×C11C2×#41112yes—
139C2×C4×C11C2×#41112yes—
140C2×C4×C11C2×#41148yescomplemented
141C2×C4×C11C25112yes—
142C2×C4×C11C25124yes—
143C2×C4×C11C2516yes—
144C2×C4×C11C2516yes—
145C22×#41C22×C1116yes—
146C24×C4C22×C1113yes—
147#533C22×C11148yescomplemented
148#532C22×C11148yescomplemented
149C2×C4⋊Q8C22×C1113yescomplemented
150C2×#127C22×C1111yescharacteristic, complemented
151#529C22×C111192yescomplemented
152C2×#126C22×C1118yescomplemented
153C2×#125C22×C1116yescomplemented
154C2×#124C22×C1116yescomplemented
155#525C22×C11196yescomplemented
156C2×#123C22×C11112yes—
157C2×C22⋊Q8C22×C11112yes—
158C2×#121C22×C11112yes—
159C2×#120C22×C1114yes—
160C4×#41C22×C11196yescomplemented
161C2×C4×Q8C22×C11112yescomplemented
162C2×C4×D4C22×C11124yes—
163C2×C4×D4C22×C11112yescomplemented
164C2×#117C22×C1116yes—
165C2×#117C22×C11112yescomplemented
166C22×C42C22×C1113yes—
167C22×C42C22×C1116yes—
168C22×C42C22×C1113yes—
169C22×C42C22×C11116yescomplemented
170C22×C42C22×C1114yescomplemented
171C22×C11—232no—
172C22×C11—212no—
173C22×C11—224no—
174C22×C11—224no—
175C22×C11—416no—
176C22×C11C22×#41112yes—
177C22×C11C22×#4116yes—
178C22×C11C2611yescharacteristic
179C4×C11—212no—
180C4×C11—224no—
181C4×C11C22×#41112yes—
182C4×C11C22×#41112yes—
183C25C23×C1111yescharacteristic
184C2×#41—248no—
185C2×#41C23×C11148yes—
186C22×Q8C23×C1116yes—
187C22×D4C23×C11112yes—
188C22×D4C23×C1116yes—
189C23×C4—224no—
190C23×C4C23×C11112yes—
191C23×C4C23×C1116yes—
192C23×C4C23×C1116yes—
193C23×C4C23×C1113yes—
194C23×C4C23×C11124yes—
195C23×C4C23×C1113yes—
196C4⋊Q8C23×C11124yescomplemented
197#127C23×C1118yescomplemented
198#126C23×C11164yescomplemented
199#125C23×C11148yescomplemented
200#124C23×C11148yescomplemented
201#123C23×C11196yes—
202C22⋊Q8C23×C11196yes—
203#121C23×C11196yes—
204#120C23×C11132yes—
205C4×Q8C23×C11196yescomplemented
206C4×D4C23×C111192yes—
207C4×D4C23×C11196yescomplemented
208#117C23×C11148yes—
209#117C23×C11196yescomplemented
210C2×C4⋊C4C23×C11112yes—
211C2×C4⋊C4C23×C11124yes—
212C2×C22⋊C4C23×C11112yes—
213C2×C22⋊C4C23×C11124yes—
214C2×C42C23×C11112yes—
215C2×C42C23×C1113yes—
216C2×C42C23×C1116yes—
217C2×C42C23×C11124yes—
218C2×C42C23×C1113yes—
219C2×C42C23×C1112yes—
220C2×C42C23×C11148yes—
221C2×C42C23×C1111yescharacteristic
222C2×C42C23×C11124yes—
223C2×C42C23×C1111yescharacteristic
224C2×C42C23×C11132yescomplemented
225C2×C11—212no—
226C2×C11—48no—
227C2×C11#344414yesdirect product factor
228C2×C11C23×#4113yes—
229C24—212no—
230C24C24×C1114yes—
231C24C24×C1114yes—
232C24C24×C1113yes—
233#41—2192no—
234C2×Q8—224no—
235C2×Q8C24×C11124yes—
236C2×D4—248no—
237C2×D4—224no—
238C2×D4C24×C11148yes—
239C2×D4C24×C11124yes—
240C22×C4—212no—
241C22×C4—224no—
242C22×C4—224no—
243C22×C4—248no—
244C22×C4—296no—
245C22×C4C11×#41124yescomplemented
246C22×C4C24×C1116yes—
247C22×C4C24×C11124yes—
248C22×C4C24×C11124yes—
249C22×C4C24×C11112yes—
250C22×C4C24×C11112yes—
251C22×C4C24×C11148yes—
252C22×C4C24×C1113yes—
253C22×C4C24×C1113yes—
254C22×C4C24×C11112yes—
255C4⋊C4C24×C11148yes—
256C4⋊C4C24×C11196yes—
257C22⋊C4C24×C11148yes—
258C22⋊C4C24×C11196yes—
259C42C24×C1114yes—
260C42C24×C11112yes—
261C42C24×C11124yes—
262C42C24×C11112yes—
263C42C24×C1118yes—
264C42C24×C1114yes—
265C42C24×C11148yes—
266C11C2×#344411yescharacteristic, direct product factor, Sylow
267C23—232no—
268C23—224no—
269C23—212no—
270C23—224no—
271C23C2×C11×#41112yes—
272C23C25×C1118yes—
273C23C25×C1116yes—
274C23C25×C1111yescharacteristic
275Q8—248no—
276D4—296no—
277D4—248no—
278C2×C4—224no—
279C2×C4—212no—
280C2×C4—224no—
281C2×C4—248no—
282C2×C4—248no—
283C2×C4—296no—
284C2×C4C2×C11×#41112yes—
285C2×C4C2×C11×#41112yes—
286C2×C4C2×C11×#41148yescomplemented
287C2×C4C25×C11112yes—
288C2×C4C25×C11124yes—
289C2×C4C25×C1116yes—
290C2×C4C25×C1116yes—
291C22—232no—
292C22—224no—
293C22—212no—
294C22—224no—
295C22—416no—
296C22C22×C11×#41112yes—
297C22C22×C11×#4116yes—
298C22C26×C1111yescharacteristic
299C4—212no—
300C4—224no—
301C4C22×C11×#41112yes—
302C4C22×C11×#41112yes—
303C2—212no—
304C2—48no—
305C2C11×#344414yesdirect product factor
306C2C23×C11×#4113yes—
subgroupG/H
centerC2×C42×C11C23
commutator, Frattini, cosocleC22C26×C11
socleC23×C11C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3444C2direct (N × H)
2. C2×C11×#533C2semidirect
3. C2×C11×#532C2semidirect
4. C2×C11×#529C2semidirect
5. C2×C11×#525C2semidirect
6. C2×C4×C11×#41C2semidirect
7. C23×C42×C11C2semidirect
10. C11×#533C22semidirect
11. C11×#532C22semidirect
12. C2×C11×C4⋊Q8C22semidirect
13. C2×C11×#127C22semidirect
14. C11×#529C22semidirect
15. C2×C11×#126C22semidirect
16. C2×C11×#125C22semidirect
17. C2×C11×#124C22semidirect
18. C11×#525C22semidirect
23. C4×C11×#41C22semidirect
24. C2×C4×Q8×C11C22semidirect
26. C2×C4×D4×C11C22semidirect
28. C2×C11×#117C22semidirect
32. C22×C42×C11C22semidirect
33. C22×C42×C11C22semidirect
47. C11×C4⋊Q8C23semidirect
48. C11×#127C23semidirect
49. C11×#126C23semidirect
50. C11×#125C23semidirect
51. C11×#124C23semidirect
56. C4×Q8×C11C23semidirect
58. C4×D4×C11C23semidirect
60. C11×#117C23semidirect
75. C2×C42×C11C23semidirect
76. C2×#3444C11direct (N × H)
93. C22×C4×C11#41semidirect
114. #3444C2×C11direct (N × H)
115. C2×#533C2×C11semidirect
116. C2×#532C2×C11semidirect
117. C2×#529C2×C11semidirect
118. C2×#525C2×C11semidirect
119. C2×C4×#41C2×C11semidirect
120. C23×C42C2×C11semidirect
140. C2×C4×C11C2×#41semidirect
147. #533C22×C11semidirect
148. #532C22×C11semidirect
149. C2×C4⋊Q8C22×C11semidirect
150. C2×#127C22×C11semidirect
151. #529C22×C11semidirect
152. C2×#126C22×C11semidirect
153. C2×#125C22×C11semidirect
154. C2×#124C22×C11semidirect
155. #525C22×C11semidirect
160. C4×#41C22×C11semidirect
161. C2×C4×Q8C22×C11semidirect
163. C2×C4×D4C22×C11semidirect
165. C2×#117C22×C11semidirect
169. C22×C42C22×C11semidirect
170. C22×C42C22×C11semidirect
196. C4⋊Q8C23×C11semidirect
197. #127C23×C11semidirect
198. #126C23×C11semidirect
199. #125C23×C11semidirect
200. #124C23×C11semidirect
205. C4×Q8C23×C11semidirect
207. C4×D4C23×C11semidirect
209. #117C23×C11semidirect
224. C2×C42C23×C11semidirect
227. C2×C11#3444direct (N × H)
245. C22×C4C11×#41semidirect
266. C11C2×#3444direct (N × H)
286. C2×C4C2×C11×#41semidirect
305. C2C11×#3444direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34442
C2×C11×#5332
C2×C11×#5322
C2×C11×#5292
C2×C11×#5252
C2×C4×C11×#412
C23×C42×C112
C2×#344411