Finite Group Databasebeta

← C2×C11×#3414 #14639824

Subgroups — C2×C11×#3414 #14639824

Order 2816.

2098 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C212yesmaximal, complemented
2C11×#3414C2116yesmaximal, direct product factor
3C2×C11×#510C214yesmaximal, complemented
4C2×C11×#509C214yesmaximal, complemented
5C2×C11×#508C214yesmaximal, complemented
6C22×C11×M32C211yesmaximal, characteristic, complemented
7C22×C11×#41—22no—
8C2×C11×#135—22no—
9C2×C11×#135—22no—
10C2×C11×#135—28no—
11C2×C11×#135C2214yes—
12C2×C11×#135C2214yescomplemented
13C2×C11×#135C22116yescomplemented
14C22×C11×Q16C2212yescomplemented
15C22×C11×SD16—22no—
16C22×C11×D8C2212yescomplemented
17C23×C8×C11C2211yescharacteristic
18C11×#510C22132yescomplemented
19C11×#509C22132yescomplemented
20C11×#508C22132yescomplemented
21C2×C11×Q32C2214yescomplemented
22C2×C11×SD32C2218yescomplemented
23C2×C11×D16C2214yescomplemented
24C2×C11×M32C2214yescomplemented
25C2×C11×M32C2218yescomplemented
26C22×C11×C16C2212yescomplemented
27C2×C11×#41—24no—
28C2×C11×#41—216no—
29C2×C11×#41—24no—
30C2×C11×#41—42no—
31C2×C11×#41—48no—
32C2×C11×#41—42no—
33C22×Q8×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—42no—
36C23×C4×C11—42no—
37C23×C4×C11D411yescharacteristic
38C11×#135—28no—
39C11×#135—216no—
40C11×#135—28no—
41C11×#135—216no—
42C11×#135C23116yes—
43C11×#135C23116yescomplemented
44C2×C11×Q16—22no—
45C2×C11×Q16—24no—
46C2×C11×Q16C2314yes—
47C2×C11×Q16C2318yescomplemented
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—216no—
51C2×C11×D8—22no—
52C2×C11×D8—24no—
53C2×C11×D8C2314yes—
54C2×C11×D8C2318yescomplemented
55C22×C8×C11D412yes—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D414yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2314yes—
61C11×Q32C23116yescomplemented
62C11×SD32C23132yescomplemented
63C11×D16C23116yescomplemented
64C11×M32C23116yescomplemented
65C2×C11×C16C2314yes—
66C2×C11×C16C2318yescomplemented
67C2×#3414C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—42no—
69C24×C11D811yescharacteristic
70C11×#41—216no—
71C11×#41—216no—
72C11×#41—416no—
73C11×#41—48no—
74C11×#41—48no—
75C11×#41—416no—
76C2×Q8×C11—24no—
77C2×Q8×C11—28no—
78C2×Q8×C11—42no—
79C2×Q8×C11—44no—
80C2×D4×C11—24no—
81C2×D4×C11—28no—
82C2×D4×C11—44no—
83C2×D4×C11—44no—
84C2×D4×C11—416no—
85C2×D4×C11—42no—
86C2×D4×C11—44no—
87C22×C4×C11—42no—
88C22×C4×C11—44no—
89C22×C4×C11—416no—
90C22×C4×C11—44no—
91C22×C4×C11D811yescharacteristic
92C22×C4×C11D814yes—
93C22×C4×C11D812yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D414yes—
96C22×C4×C11C2×D411yescharacteristic
97C11×Q16—24no—
98C11×Q16—28no—
99C11×Q16C2418yes—
100C11×SD16—216no—
101C11×SD16—216no—
102C11×D8—24no—
103C11×D8—28no—
104C11×D8C2418yes—
105C2×C8×C11C2×D412yes—
106C2×C8×C11C2×D414yes—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D418yes—
109C2×C8×C11C2×D412yes—
110C2×C8×C11C2×D414yes—
111C2×C8×C11C2411yescharacteristic
112C2×C8×C11C2412yes—
113C2×C8×C11C2414yes—
114C11×C16C2418yes—
115C22×#135C2×C1112yescomplemented
116#3414C2×C11116yesdirect product factor
117C2×#510C2×C1114yescomplemented
118C2×#509C2×C1114yescomplemented
119C2×#508C2×C1114yescomplemented
120C22×M32C2×C1111yescharacteristic, complemented
121C23×C11—42no—
122C23×C11—48no—
123C23×C11—44no—
124C23×C11—88no—
125C23×C11C2×D812yes—
126C23×C11C2×D811yescharacteristic
127C23×C11C2×D814yes—
128Q8×C11—28no—
129Q8×C11—48no—
130Q8×C11—44no—
131D4×C11—28no—
132D4×C11—416no—
133D4×C11—416no—
134D4×C11—48no—
135D4×C11—44no—
136C2×C4×C11—48no—
137C2×C4×C11—44no—
138C2×C4×C11—416no—
139C2×C4×C11—416no—
140C2×C4×C11C2×D812yes—
141C2×C4×C11C2×D818yes—
142C2×C4×C11C2×D814yes—
143C2×C4×C11C2×D812yes—
144C2×C4×C11C2×D814yes—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×D414yes—
148C2×C4×C11C22×D412yes—
149C8×C11C22×D411yescharacteristic
150C8×C11C22×D414yes—
151C8×C11C22×D412yes—
152C8×C11C2511yescharacteristic
153C22×#41—22no—
154C2×#135—22no—
155C2×#135—22no—
156C2×#135—28no—
157C2×#135C22×C1114yes—
158C2×#135C22×C1114yescomplemented
159C2×#135C22×C11116yescomplemented
160C22×Q16C22×C1112yescomplemented
161C22×SD16—22no—
162C22×D8C22×C1112yescomplemented
163C23×C8C22×C1111yescharacteristic
164#510C22×C11132yescomplemented
165#509C22×C11132yescomplemented
166#508C22×C11132yescomplemented
167C2×Q32C22×C1114yescomplemented
168C2×SD32C22×C1118yescomplemented
169C2×D16C22×C1114yescomplemented
170C2×M32C22×C1114yescomplemented
171C2×M32C22×C1118yescomplemented
172C22×C16C22×C1112yescomplemented
173C22×C11—24no—
174C22×C11—22no—
175C22×C11—44no—
176C22×C11—48no—
177C22×C11—816no—
178C22×C11—88no—
179C22×C11C22×D814yes—
180C22×C11C22×D812yes—
181C22×C11C22×D811yescharacteristic
182C4×C11—48no—
183C4×C11C22×D812yes—
184C4×C11C22×D814yes—
185C4×C11C22×D811yescharacteristic
186C4×C11C23×D411yescharacteristic
187C2×#41—24no—
188C2×#41—24no—
189C2×#41—216no—
190C2×#41—42no—
191C2×#41—42no—
192C2×#41—48no—
193C22×Q8—22no—
194C22×D4—22no—
195C22×D4—42no—
196C23×C4—42no—
197C23×C4D4×C1111yescharacteristic
198#135—28no—
199#135—216no—
200#135—28no—
201#135—216no—
202#135C23×C11116yes—
203#135C23×C11116yescomplemented
204C2×Q16—22no—
205C2×Q16—24no—
206C2×Q16C23×C1114yes—
207C2×Q16C23×C1118yescomplemented
208C2×SD16—24no—
209C2×SD16—24no—
210C2×SD16—216no—
211C2×D8—22no—
212C2×D8—24no—
213C2×D8C23×C1114yes—
214C2×D8C23×C1118yescomplemented
215C22×C8D4×C1112yes—
216C22×C8D4×C1111yescharacteristic
217C22×C8D4×C1114yes—
218C22×C8C23×C1112yes—
219C22×C8C23×C1111yescharacteristic
220C22×C8C23×C1114yes—
221Q32C23×C11116yescomplemented
222SD32C23×C11132yescomplemented
223D16C23×C11116yescomplemented
224M32C23×C11116yescomplemented
225C2×C16C23×C1114yes—
226C2×C16C23×C1118yescomplemented
227C2×C11—24no—
228C2×C11—22no—
229C2×C11—88no—
230C2×C11#341412yesdirect product factor
231C2×C11C23×D811yescharacteristic
232C24—42no—
233C24C11×D811yescharacteristic
234#41—216no—
235#41—216no—
236#41—416no—
237#41—48no—
238#41—48no—
239#41—416no—
240C2×Q8—24no—
241C2×Q8—28no—
242C2×Q8—42no—
243C2×Q8—44no—
244C2×D4—24no—
245C2×D4—28no—
246C2×D4—44no—
247C2×D4—44no—
248C2×D4—416no—
249C2×D4—42no—
250C2×D4—44no—
251C22×C4—42no—
252C22×C4—44no—
253C22×C4—416no—
254C22×C4—44no—
255C22×C4C11×D812yes—
256C22×C4C11×D811yescharacteristic
257C22×C4C11×D814yes—
258C22×C4C2×D4×C1112yes—
259C22×C4C2×D4×C1114yes—
260C22×C4C2×D4×C1111yescharacteristic
261Q16—24no—
262Q16—28no—
263Q16C24×C1118yes—
264SD16—216no—
265SD16—216no—
266D8—24no—
267D8—28no—
268D8C24×C1118yes—
269C2×C8C2×D4×C1112yes—
270C2×C8C2×D4×C1114yes—
271C2×C8C2×D4×C1111yescharacteristic
272C2×C8C2×D4×C1118yes—
273C2×C8C2×D4×C1112yes—
274C2×C8C2×D4×C1114yes—
275C2×C8C24×C1111yescharacteristic
276C2×C8C24×C1112yes—
277C2×C8C24×C1114yes—
278C16C24×C1118yes—
279C11C2×#341411yescharacteristic, direct product factor, Sylow
280C23—42no—
281C23—48no—
282C23—44no—
283C23—88no—
284C23C2×C11×D812yes—
285C23C2×C11×D811yescharacteristic
286C23C2×C11×D814yes—
287Q8—28no—
288Q8—48no—
289Q8—44no—
290D4—28no—
291D4—416no—
292D4—416no—
293D4—48no—
294D4—44no—
295C2×C4—48no—
296C2×C4—44no—
297C2×C4—416no—
298C2×C4—416no—
299C2×C4C2×C11×D812yes—
300C2×C4C2×C11×D818yes—
301C2×C4C2×C11×D814yes—
302C2×C4C2×C11×D812yes—
303C2×C4C2×C11×D814yes—
304C2×C4C2×C11×D811yescharacteristic
305C2×C4C22×D4×C1111yescharacteristic
306C2×C4C22×D4×C1114yes—
307C2×C4C22×D4×C1112yes—
308C8C22×D4×C1111yescharacteristic
309C8C22×D4×C1114yes—
310C8C22×D4×C1112yes—
311C8C25×C1111yescharacteristic
312C22—24no—
313C22—22no—
314C22—44no—
315C22—48no—
316C22—816no—
317C22—88no—
318C22C22×C11×D814yes—
319C22C22×C11×D812yes—
320C22C22×C11×D811yescharacteristic
321C4—48no—
322C4C22×C11×D812yes—
323C4C22×C11×D814yes—
324C4C22×C11×D811yescharacteristic
325C4C23×D4×C1111yescharacteristic
326C2—24no—
327C2—22no—
328C2—88no—
329C2C11×#341412yesdirect product factor
330C2C23×C11×D811yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D8
commutator, Frattini, cosocleC8C25×C11
socleC22×C11C22×D8
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#135C2semidirect
2. C11×#3414C2direct (N × H)
3. C2×C11×#510C2semidirect
4. C2×C11×#509C2semidirect
5. C2×C11×#508C2semidirect
6. C22×C11×M32C2semidirect
12. C2×C11×#135C22semidirect
13. C2×C11×#135C22semidirect
14. C22×C11×Q16C22semidirect
16. C22×C11×D8C22semidirect
18. C11×#510C22semidirect
19. C11×#509C22semidirect
20. C11×#508C22semidirect
21. C2×C11×Q32C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×D16C22semidirect
24. C2×C11×M32C22semidirect
25. C2×C11×M32C22semidirect
26. C22×C11×C16C22semidirect
43. C11×#135C23semidirect
47. C2×C11×Q16C23semidirect
54. C2×C11×D8C23semidirect
61. C11×Q32C23semidirect
62. C11×SD32C23semidirect
63. C11×D16C23semidirect
64. C11×M32C23semidirect
66. C2×C11×C16C23semidirect
67. C2×#3414C11direct (N × H)
115. C22×#135C2×C11semidirect
116. #3414C2×C11direct (N × H)
117. C2×#510C2×C11semidirect
118. C2×#509C2×C11semidirect
119. C2×#508C2×C11semidirect
120. C22×M32C2×C11semidirect
158. C2×#135C22×C11semidirect
159. C2×#135C22×C11semidirect
160. C22×Q16C22×C11semidirect
162. C22×D8C22×C11semidirect
164. #510C22×C11semidirect
165. #509C22×C11semidirect
166. #508C22×C11semidirect
167. C2×Q32C22×C11semidirect
168. C2×SD32C22×C11semidirect
169. C2×D16C22×C11semidirect
170. C2×M32C22×C11semidirect
171. C2×M32C22×C11semidirect
172. C22×C16C22×C11semidirect
203. #135C23×C11semidirect
207. C2×Q16C23×C11semidirect
214. C2×D8C23×C11semidirect
221. Q32C23×C11semidirect
222. SD32C23×C11semidirect
223. D16C23×C11semidirect
224. M32C23×C11semidirect
226. C2×C16C23×C11semidirect
230. C2×C11#3414direct (N × H)
279. C11C2×#3414direct (N × H)
329. C2C11×#3414direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C11×#34142
C2×C11×#5102
C2×C11×#5092
C2×C11×#5082
C22×C11×M322
C2×#341411