Finite Group Databasebeta

← C11×#60070 #14637263

Subgroups — C11×#60070 #14637263

Order 2816.

4892 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#585C211yesmaximal, characteristic
2C11×#3428C212yesmaximal, complemented
3C11×#2884C214yesmaximal, complemented
4C11×#2883C2112yesmaximal, complemented
5C2×C11×#410C2112yesmaximal, complemented
6C11×#585—28no—
7C11×#585—28no—
8C2×C11×2−1+4C414yescomplemented
9C2×C11×2−1+4C2212yes—
10C2×C11×H(5,𝔽2)C414yescomplemented
11C2×C11×H(5,𝔽2)C2216yes—
12C22×C11×#41C418yescomplemented
13C22×C11×#41C2216yes—
14C22×C11×#41C2211yescharacteristic
15C11×#520—28no—
16C11×#519C2214yescomplemented
17C11×#518C22112yescomplemented
18C4×C11×#41—28no—
19C2×C11×#117C22112yescomplemented
20C11×#410C22116yescomplemented
21C11×#410C22148yescomplemented
22C2×C11×#99C22148yescomplemented
23C11×2−1+4—232no—
24C11×2−1+4—216no—
25C11×H(5,𝔽2)—232no—
26C11×H(5,𝔽2)—248no—
27C2×C11×#41—232no—
28C2×C11×#41—232no—
29C2×C11×#41—224no—
30C2×C11×#41—224no—
31C2×C11×#41C2×C414yes—
32C2×C11×#41C2×C414yes—
33C2×C11×#41C2×C4112yescomplemented
34C2×C11×#41C2×C418yescomplemented
35C2×C11×#41C2×C4124yescomplemented
36C2×C11×#41C2×C4112yescomplemented
37C2×C11×#41D418yes—
38C2×C11×#41D418yes—
39C2×C11×#41C2314yes—
40C2×C11×#41C23112yes—
41C22×Q8×C11C2×C418yescomplemented
42C22×Q8×C11C2×C416yescomplemented
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2×C4124yescomplemented
45C22×D4×C11C2×C416yescomplemented
46C22×D4×C11C23112yes—
47C22×D4×C11C2313yes—
48C23×C4×C11C2×C4112yescomplemented
49C23×C4×C11C2313yes—
50C4×Q8×C11—216no—
51C4×D4×C11—248no—
52C11×#117—212no—
53C11×#117—212no—
54C11×#117C2318yes—
55C11×#117C23124yes—
56C2×C11×C4⋊C4—212no—
57C2×C11×C22⋊C4C23124yes—
58C2×C42×C11—212no—
59C11×#99C23164yes—
60#60070C1111yesmaximal, characteristic, direct product factor, Sylow
61C24×C11C22×C4112yes—
62C24×C11C2413yes—
63C11×#41—232no—
64C11×#41—296no—
65C11×#41—224no—
66C11×#41—224no—
67C11×#41—248no—
68C11×#41—28no—
69C11×#41—28no—
70C11×#41—248no—
71C11×#41C22⋊C4116yes—
72C11×#41C22⋊C4116yes—
73C11×#41C22⋊C4132yes—
74C2×Q8×C11—232no—
75C2×Q8×C11—224no—
76C2×Q8×C11C22×C4112yes—
77C2×Q8×C11C22×C414yes—
78C2×Q8×C11C22×C414yes—
79C2×Q8×C11C2×D418yes—
80C2×D4×C11—248no—
81C2×D4×C11—296no—
82C2×D4×C11—224no—
83C2×D4×C11C22×C4112yes—
84C2×D4×C11C22×C414yes—
85C2×D4×C11C22×C4124yes—
86C2×D4×C11C22×C4112yes—
87C2×D4×C11C2×D4124yes—
88C2×D4×C11C2418yes—
89C22×C4×C11—224no—
90C22×C4×C11—224no—
91C22×C4×C11—224no—
92C22×C4×C11C22×C418yes—
93C22×C4×C11C22×C4124yes—
94C22×C4×C11C22×C4112yes—
95C22×C4×C11C22×C416yes—
96C22×C4×C11C22×C416yes—
97C22×C4×C11C2×D4112yes—
98C22×C4×C11C2×D4112yes—
99C22×C4×C11C2411yescharacteristic
100C22×C4×C11C2413yes—
101C11×C4⋊C4—28no—
102C11×C4⋊C4—224no—
103C11×C22⋊C4—224no—
104C11×C22⋊C4C24116yes—
105C42×C11—28no—
106C42×C11—224no—
107C2×#585C2×C1111yescharacteristic
108#3428C2×C1112yescomplemented
109#2884C2×C1114yescomplemented
110#2883C2×C11112yescomplemented
111C2×#410C2×C11112yescomplemented
112C23×C11—224no—
113C23×C11—83no—
114C23×C11—812no—
115C23×C11C23×C418yes—
116C23×C11C23×C416yes—
117C23×C11C22×D4112yes—
118C23×C11C2511yescharacteristic
119Q8×C11—224no—
120Q8×C11—28no—
121Q8×C11C2×C22⋊C4116yes—
122D4×C11—248no—
123D4×C11—216no—
124D4×C11—224no—
125D4×C11—28no—
126D4×C11C2×C22⋊C4148yes—
127C2×C4×C11—224no—
128C2×C4×C11—28no—
129C2×C4×C11—248no—
130C2×C4×C11—28no—
131C2×C4×C11—216no—
132C2×C4×C11—824no—
133C2×C4×C11C2×C22⋊C4112yes—
134C2×C4×C11C2×C22⋊C4124yes—
135C2×C4×C11C2×C22⋊C4112yes—
136C2×C4×C11C23×C418yes—
137C2×C4×C11C23×C416yes—
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C23×C411yescharacteristic
140C2×C4×C11C22×D4112yes—
141C2×C4×C11C22×D412yes—
142C2×C4×C11C22×D412yes—
143#585—28no—
144#585—28no—
145C2×2−1+4C4×C1114yescomplemented
146C2×2−1+4C22×C1112yes—
147C2×H(5,𝔽2)C4×C1114yescomplemented
148C2×H(5,𝔽2)C22×C1116yes—
149C22×#41C4×C1118yescomplemented
150C22×#41C22×C1116yes—
151C22×#41C22×C1111yescharacteristic
152#520—28no—
153#519C22×C1114yescomplemented
154#518C22×C11112yescomplemented
155C4×#41—28no—
156C2×#117C22×C11112yescomplemented
157#410C22×C11116yescomplemented
158#410C22×C11148yescomplemented
159C2×#99C22×C11148yescomplemented
160C22×C11—28no—
161C22×C11—412no—
162C22×C11—46no—
163C22×C11—41no—
164C22×C11—48no—
165C22×C11—824no—
166C22×C11C22×C22⋊C4112yes—
167C22×C11C24×C411yescharacteristic
168C22×C11C23×D412yes—
169C4×C11—28no—
170C4×C11—416no—
171C4×C11C22×C22⋊C411yescharacteristic
172C4×C11C22×C22⋊C4112yes—
173C4×C11C22×C22⋊C412yes—
174C4×C11C22×C22⋊C411yescharacteristic
1752−1+4—232no—
1762−1+4—216no—
177H(5,𝔽2)—232no—
178H(5,𝔽2)—248no—
179C2×#41—232no—
180C2×#41—232no—
181C2×#41—224no—
182C2×#41—224no—
183C2×#41C2×C4×C1114yes—
184C2×#41C2×C4×C1114yes—
185C2×#41C2×C4×C11112yescomplemented
186C2×#41C2×C4×C1118yescomplemented
187C2×#41C2×C4×C11124yescomplemented
188C2×#41C2×C4×C11112yescomplemented
189C2×#41D4×C1118yes—
190C2×#41D4×C1118yes—
191C2×#41C23×C1114yes—
192C2×#41C23×C11112yes—
193C22×Q8C2×C4×C1118yescomplemented
194C22×Q8C2×C4×C1116yescomplemented
195C22×Q8C23×C1111yescharacteristic
196C22×D4C2×C4×C11124yescomplemented
197C22×D4C2×C4×C1116yescomplemented
198C22×D4C23×C11112yes—
199C22×D4C23×C1113yes—
200C23×C4C2×C4×C11112yescomplemented
201C23×C4C23×C1113yes—
202C4×Q8—216no—
203C4×D4—248no—
204#117—212no—
205#117—212no—
206#117C23×C1118yes—
207#117C23×C11124yes—
208C2×C4⋊C4—212no—
209C2×C22⋊C4C23×C11124yes—
210C2×C42—212no—
211#99C23×C11164yes—
212C2×C11—22no—
213C2×C11—21no—
214C2×C11—212no—
215C2×C11—48no—
216C2×C11C23×C22⋊C411yescharacteristic
217C24C22×C4×C11112yes—
218C24C24×C1113yes—
219#41—232no—
220#41—296no—
221#41—224no—
222#41—224no—
223#41—248no—
224#41—28no—
225#41—28no—
226#41—248no—
227#41C11×C22⋊C4116yes—
228#41C11×C22⋊C4116yes—
229#41C11×C22⋊C4132yes—
230C2×Q8—232no—
231C2×Q8—224no—
232C2×Q8C22×C4×C11112yes—
233C2×Q8C22×C4×C1114yes—
234C2×Q8C22×C4×C1114yes—
235C2×Q8C2×D4×C1118yes—
236C2×D4—248no—
237C2×D4—296no—
238C2×D4—224no—
239C2×D4C22×C4×C11112yes—
240C2×D4C22×C4×C1114yes—
241C2×D4C22×C4×C11124yes—
242C2×D4C22×C4×C11112yes—
243C2×D4C2×D4×C11124yes—
244C2×D4C24×C1118yes—
245C22×C4—224no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4C22×C4×C1118yes—
249C22×C4C22×C4×C11124yes—
250C22×C4C22×C4×C11112yes—
251C22×C4C22×C4×C1116yes—
252C22×C4C22×C4×C1116yes—
253C22×C4C2×D4×C11112yes—
254C22×C4C2×D4×C11112yes—
255C22×C4C24×C1111yescharacteristic
256C22×C4C24×C1113yes—
257C4⋊C4—28no—
258C4⋊C4—224no—
259C22⋊C4—224no—
260C22⋊C4C24×C11116yes—
261C42—28no—
262C42—224no—
263C11#6007011yescharacteristic, direct product factor, Sylow
264C23—224no—
265C23—83no—
266C23—812no—
267C23C23×C4×C1118yes—
268C23C23×C4×C1116yes—
269C23C22×D4×C11112yes—
270C23C25×C1111yescharacteristic
271Q8—224no—
272Q8—28no—
273Q8C2×C11×C22⋊C4116yes—
274D4—248no—
275D4—216no—
276D4—224no—
277D4—28no—
278D4C2×C11×C22⋊C4148yes—
279C2×C4—224no—
280C2×C4—28no—
281C2×C4—28no—
282C2×C4—248no—
283C2×C4—216no—
284C2×C4—824no—
285C2×C4C2×C11×C22⋊C4112yes—
286C2×C4C2×C11×C22⋊C4112yes—
287C2×C4C2×C11×C22⋊C4124yes—
288C2×C4C23×C4×C1118yes—
289C2×C4C23×C4×C1111yescharacteristic
290C2×C4C23×C4×C1116yes—
291C2×C4C23×C4×C1111yescharacteristic
292C2×C4C22×D4×C1112yes—
293C2×C4C22×D4×C11112yes—
294C2×C4C22×D4×C1112yes—
295C22—28no—
296C22—412no—
297C22—46no—
298C22—41no—
299C22—48no—
300C22—824no—
301C22C22×C11×C22⋊C4112yes—
302C22C24×C4×C1111yescharacteristic
303C22C23×D4×C1112yes—
304C4—28no—
305C4—416no—
306C4C22×C11×C22⋊C411yescharacteristic
307C4C22×C11×C22⋊C411yescharacteristic
308C4C22×C11×C22⋊C4112yes—
309C4C22×C11×C22⋊C412yes—
310C2—22no—
311C2—21no—
312C2—212no—
313C2—48no—
314C2C23×C11×C22⋊C411yescharacteristic
subgroupG/H
centerC4×C11C22×C22⋊C4
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
socleC2×C11C23×C22⋊C4
prime radicalC2×C11×#585C2
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3428C2semidirect
3. C11×#2884C2semidirect
4. C11×#2883C2semidirect
5. C2×C11×#410C2semidirect
8. C2×C11×2−1+4C4semidirect
10. C2×C11×H(5,𝔽2)C4semidirect
12. C22×C11×#41C4semidirect
16. C11×#519C22semidirect
17. C11×#518C22semidirect
19. C2×C11×#117C22semidirect
20. C11×#410C22semidirect
21. C11×#410C22semidirect
22. C2×C11×#99C22semidirect
33. C2×C11×#41C2×C4semidirect
34. C2×C11×#41C2×C4semidirect
35. C2×C11×#41C2×C4semidirect
36. C2×C11×#41C2×C4semidirect
41. C22×Q8×C11C2×C4semidirect
42. C22×Q8×C11C2×C4semidirect
44. C22×D4×C11C2×C4semidirect
45. C22×D4×C11C2×C4semidirect
48. C23×C4×C11C2×C4semidirect
60. #60070C11direct (N × H)
108. #3428C2×C11semidirect
109. #2884C2×C11semidirect
110. #2883C2×C11semidirect
111. C2×#410C2×C11semidirect
145. C2×2−1+4C4×C11semidirect
147. C2×H(5,𝔽2)C4×C11semidirect
149. C22×#41C4×C11semidirect
153. #519C22×C11semidirect
154. #518C22×C11semidirect
156. C2×#117C22×C11semidirect
157. #410C22×C11semidirect
158. #410C22×C11semidirect
159. C2×#99C22×C11semidirect
185. C2×#41C2×C4×C11semidirect
186. C2×#41C2×C4×C11semidirect
187. C2×#41C2×C4×C11semidirect
188. C2×#41C2×C4×C11semidirect
193. C22×Q8C2×C4×C11semidirect
194. C22×Q8C2×C4×C11semidirect
196. C22×D4C2×C4×C11semidirect
197. C22×D4C2×C4×C11semidirect
200. C23×C4C2×C4×C11semidirect
263. C11#60070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5852
C11×#34282
C11×#28842
C11×#28832
C2×C11×#4102
#6007011