Finite Group Databasebeta

← C11×#2697 #13065535

Subgroups — C11×#2697 #13065535

Order 1408.

680 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×C11×#120C211yesmaximal, characteristic
3C11×#397C212yesmaximal, complemented
4C11×#396C212yesmaximal, complemented
5C11×#394C212yesmaximal, complemented
6C11×#390C211yesmaximal, characteristic, complemented
7C11×#388C212yesmaximal, complemented
8C11×#386C212yesmaximal, complemented
9C11×#379C212yesmaximal, complemented
10C25×C11C2211yescharacteristic
11C22×D4×C11C2212yes—
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic, complemented
14C11×#123—24no—
15C11×#120—24no—
16C2×C11×C4⋊C4C2212yescomplemented
17C2×C11×C4⋊C4C2211yescharacteristic, complemented
18C2×C11×C4⋊C4C2212yescomplemented
19C2×C11×C22⋊C4C2212yes—
20C2×C11×C22⋊C4C2212yes—
21C2×C11×C22⋊C4C2212yes—
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2212yes—
24C2×C11×C22⋊C4C2212yes—
25C2×C11×C22⋊C4C2212yes—
26C2×C11×C22⋊C4C2212yes—
27C2×C11×C22⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2212yescomplemented
29C2×C42×C11C2211yescharacteristic, complemented
30C11×#95C2212yescomplemented
31C11×#95C2212yescomplemented
32C11×#95C2212yescomplemented
33C24×C11—22no—
34C24×C11—24no—
35C24×C11—42no—
36C24×C11—41no—
37C24×C11—41no—
38C24×C11C2311yescharacteristic
39C24×C11C2311yescharacteristic
40C24×C11C2312yes—
41C2×D4×C11—24no—
42C2×D4×C11—24no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C2×D4×C11—42no—
46C2×D4×C11D414yes—
47C22×C4×C11—22no—
48C22×C4×C11—41no—
49C22×C4×C11—41no—
50C22×C4×C11C2312yes—
51C22×C4×C11C2312yes—
52C22×C4×C11C2312yes—
53C22×C4×C11C2312yes—
54C22×C4×C11C2312yes—
55C22×C4×C11C2311yescharacteristic
56C11×C4⋊C4—24no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—42no—
59C11×C22⋊C4—22no—
60C11×C22⋊C4—24no—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—24no—
63C11×C22⋊C4—24no—
64C11×C22⋊C4—42no—
65C11×C22⋊C4—42no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—42no—
69C42×C11—41no—
70#2697C1111yesmaximal, characteristic, direct product factor, Sylow
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—22no—
85C23×C11—48no—
86C23×C11—44no—
87C23×C11—44no—
88C23×C11—48no—
89C23×C11—44no—
90C23×C11C2×D412yes—
91C23×C11C2×D412yes—
92C23×C11#4114yes—
93C23×C11C2411yescharacteristic
94D4×C11—44no—
95D4×C11—48no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—44no—
114C2×C4×C11C2×D412yes—
115C2×#123C2×C1111yescharacteristic, complemented
116C2×#120C2×C1111yescharacteristic
117#397C2×C1112yescomplemented
118#396C2×C1112yescomplemented
119#394C2×C1112yescomplemented
120#390C2×C1111yescharacteristic, complemented
121#388C2×C1112yescomplemented
122#386C2×C1112yescomplemented
123#379C2×C1112yescomplemented
124C22×C11—22no—
125C22×C11—22no—
126C22×C11—24no—
127C22×C11—24no—
128C22×C11—24no—
129C22×C11—24no—
130C22×C11—24no—
131C22×C11—416no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—42no—
142C22×C11C22×D411yescharacteristic
143C22×C11C2×#4112yes—
144C22×C11H(5,𝔽2)11yescharacteristic
145C22×C11H(5,𝔽2)11yescharacteristic
146C22×C11H(5,𝔽2)12yes—
147C4×C11—22no—
148C4×C11—42no—
149C4×C11—42no—
150C4×C11—42no—
151C4×C11—42no—
152C4×C11—42no—
153C25C22×C1111yescharacteristic
154C22×D4C22×C1112yes—
155C22×D4C22×C1111yescharacteristic
156C23×C4C22×C1111yescharacteristic, complemented
157#123—24no—
158#120—24no—
159C2×C4⋊C4C22×C1112yescomplemented
160C2×C4⋊C4C22×C1111yescharacteristic, complemented
161C2×C4⋊C4C22×C1112yescomplemented
162C2×C22⋊C4C22×C1112yes—
163C2×C22⋊C4C22×C1111yescharacteristic
164C2×C22⋊C4C22×C1112yes—
165C2×C22⋊C4C22×C1112yes—
166C2×C22⋊C4C22×C1112yes—
167C2×C22⋊C4C22×C1112yes—
168C2×C22⋊C4C22×C1112yes—
169C2×C22⋊C4C22×C1112yes—
170C2×C22⋊C4C22×C1111yescharacteristic, complemented
171C2×C22⋊C4C22×C1112yescomplemented
172C2×C42C22×C1111yescharacteristic, complemented
173#95C22×C1112yescomplemented
174#95C22×C1112yescomplemented
175#95C22×C1112yescomplemented
176C2×C11—42no—
177C2×C11—42no—
178C2×C11—44no—
179C2×C11#53411yescharacteristic
180C2×C11#53812yes—
181C2×C11#54612yes—
182C2×C11#55111yescharacteristic
183C2×C11#56011yescharacteristic
184C24—22no—
185C24—24no—
186C24—42no—
187C24—41no—
188C24—41no—
189C24C23×C1111yescharacteristic
190C24C23×C1111yescharacteristic
191C24C23×C1112yes—
192C2×D4—24no—
193C2×D4—24no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—42no—
197C2×D4D4×C1114yes—
198C22×C4—22no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4C23×C1112yes—
202C22×C4C23×C1112yes—
203C22×C4C23×C1112yes—
204C22×C4C23×C1112yes—
205C22×C4C23×C1112yes—
206C22×C4C23×C1111yescharacteristic
207C4⋊C4—24no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C22⋊C4—22no—
211C22⋊C4—24no—
212C22⋊C4—22no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C42—41no—
221C11#269711yescharacteristic, direct product factor, Sylow
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—48no—
237C23—44no—
238C23—44no—
239C23—48no—
240C23—44no—
241C23C2×D4×C1112yes—
242C23C2×D4×C1112yes—
243C23C11×#4114yes—
244C23C24×C1111yescharacteristic
245D4—44no—
246D4—48no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—44no—
265C2×C4C2×D4×C1112yes—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—24no—
271C22—24no—
272C22—24no—
273C22—416no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—42no—
283C22—41no—
284C22C22×D4×C1111yescharacteristic
285C22C2×C11×#4112yes—
286C22C11×H(5,𝔽2)11yescharacteristic
287C22C11×H(5,𝔽2)11yescharacteristic
288C22C11×H(5,𝔽2)12yes—
289C4—22no—
290C4—42no—
291C4—42no—
292C4—42no—
293C4—42no—
294C4—42no—
295C2—42no—
296C2—44no—
297C2—42no—
298C2C11×#53411yescharacteristic
299C2C11×#53812yes—
300C2C11×#54612yes—
301C2C11×#55111yescharacteristic
302C2C11×#56011yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC2×C11×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C11×#397C2semidirect
4. C11×#396C2semidirect
5. C11×#394C2semidirect
6. C11×#390C2semidirect
7. C11×#388C2semidirect
8. C11×#386C2semidirect
9. C11×#379C2semidirect
13. C23×C4×C11C22semidirect
16. C2×C11×C4⋊C4C22semidirect
17. C2×C11×C4⋊C4C22semidirect
18. C2×C11×C4⋊C4C22semidirect
27. C2×C11×C22⋊C4C22semidirect
28. C2×C11×C22⋊C4C22semidirect
29. C2×C42×C11C22semidirect
30. C11×#95C22semidirect
31. C11×#95C22semidirect
32. C11×#95C22semidirect
70. #2697C11direct (N × H)
115. C2×#123C2×C11semidirect
117. #397C2×C11semidirect
118. #396C2×C11semidirect
119. #394C2×C11semidirect
120. #390C2×C11semidirect
121. #388C2×C11semidirect
122. #386C2×C11semidirect
123. #379C2×C11semidirect
156. C23×C4C22×C11semidirect
159. C2×C4⋊C4C22×C11semidirect
160. C2×C4⋊C4C22×C11semidirect
161. C2×C4⋊C4C22×C11semidirect
170. C2×C22⋊C4C22×C11semidirect
171. C2×C22⋊C4C22×C11semidirect
172. C2×C42C22×C11semidirect
173. #95C22×C11semidirect
174. #95C22×C11semidirect
175. #95C22×C11semidirect
221. C11#2697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×C11×#1202
C11×#3972
C11×#3962
C11×#3942
C11×#3902
C11×#3882
C11×#3862
C11×#3792
#269711