Finite Group Databasebeta

← C11×#2662 #13065500

Subgroups — C11×#2662 #13065500

Order 1408.

534 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#126C211yesmaximal, characteristic, complemented
2C2×C11×#124C211yesmaximal, characteristic, complemented
3C11×#396C212yesmaximal, complemented
4C11×#395C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#394C212yesmaximal, complemented
7C11×#393C211yesmaximal, characteristic, complemented
8C11×#392C211yesmaximal, characteristic
9C11×#390C212yesmaximal, complemented
10C11×#388C212yesmaximal, complemented
11C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C22×D4×C11C2212yes—
15C11×#126—24no—
16C11×#124—24no—
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2212yes—
22C2×C11×C22⋊C4C2212yes—
23C2×C11×C22⋊C4C2212yes—
24C2×C11×C22⋊C4C2212yes—
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2212yes—
29C2×C11×C22⋊C4C2212yes—
30C2×C11×C22⋊C4C2212yes—
31C2×C42×C11C2212yes—
32C2×C42×C11C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11×#95C2212yes—
36C11×#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2312yes—
39C2×Q8×C11—22no—
40C2×Q8×C11—42no—
41C2×D4×C11—22no—
42C2×D4×C11—24no—
43C2×D4×C11—42no—
44C2×D4×C11—42no—
45C2×D4×C11—42no—
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2312yes—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—24no—
59C11×C4⋊C4—42no—
60C11×C22⋊C4—24no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—22no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4—24no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—42no—
69C42×C11—42no—
70C42×C11D414yescomplemented
71#2662C1111yesmaximal, characteristic, direct product factor, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—22no—
84C23×C11C2411yescharacteristic
85Q8×C11—44no—
86D4×C11—44no—
87D4×C11—48no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11C2×D412yes—
108C2×C4×C11C2×D412yes—
109C2×C4×C11C2×D412yes—
110C2×C4×C11#4114yes—
111C2×#126C2×C1111yescharacteristic, complemented
112C2×#124C2×C1111yescharacteristic, complemented
113#396C2×C1112yescomplemented
114#395C2×C1111yescharacteristic, complemented
115#394C2×C1111yescharacteristic, complemented
116#394C2×C1112yescomplemented
117#393C2×C1111yescharacteristic, complemented
118#392C2×C1111yescharacteristic
119#390C2×C1112yescomplemented
120#388C2×C1112yescomplemented
121C4×C4⋊C4C2×C1111yescharacteristic, complemented
122C22×C11—41no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11C22×D411yescharacteristic
135C22×C11C2×#4112yes—
136C22×C11H(5,𝔽2)12yes—
137C22×C11H(5,𝔽2)11yescharacteristic
138C22×C112−1+411yescharacteristic
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—24no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11—42no—
146C4×C11—41no—
147C4×C11—42no—
148C22×Q8C22×C1111yescharacteristic
149C22×D4C22×C1111yescharacteristic
150C22×D4C22×C1112yes—
151#126—24no—
152#124—24no—
153C2×C4⋊C4C22×C1111yescharacteristic
154C2×C4⋊C4C22×C1111yescharacteristic
155C2×C4⋊C4C22×C1111yescharacteristic
156C2×C4⋊C4C22×C1112yes—
157C2×C4⋊C4C22×C1112yes—
158C2×C22⋊C4C22×C1112yes—
159C2×C22⋊C4C22×C1112yes—
160C2×C22⋊C4C22×C1111yescharacteristic
161C2×C22⋊C4C22×C1111yescharacteristic
162C2×C22⋊C4C22×C1111yescharacteristic
163C2×C22⋊C4C22×C1112yes—
164C2×C22⋊C4C22×C1112yes—
165C2×C22⋊C4C22×C1112yes—
166C2×C22⋊C4C22×C1112yes—
167C2×C42C22×C1112yes—
168C2×C42C22×C1111yescharacteristic
169#95C22×C1111yescharacteristic
170#95C22×C1111yescharacteristic
171#95C22×C1112yes—
172#95C22×C1112yes—
173C2×C11—82no—
174C2×C11—81no—
175C2×C11#53211yescharacteristic
176C2×C11#53511yescharacteristic
177C2×C11#53711yescharacteristic
178C2×C11#53812yes—
179C2×C11#54212yes—
180C24C23×C1111yescharacteristic
181C24C23×C1112yes—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—42no—
189C22×C4C23×C1112yes—
190C22×C4C23×C1111yescharacteristic
191C22×C4C23×C1111yescharacteristic
192C22×C4C23×C1112yes—
193C22×C4C23×C1111yescharacteristic
194C22×C4C23×C1111yescharacteristic
195C22×C4C23×C1111yescharacteristic
196C22×C4C23×C1111yescharacteristic
197C22×C4C23×C1112yes—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—24no—
202C4⋊C4—42no—
203C22⋊C4—24no—
204C22⋊C4—24no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—24no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C42—42no—
213C42D4×C1114yescomplemented
214C11#266211yescharacteristic, direct product factor, Sylow
215C23—21no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23C24×C1111yescharacteristic
228Q8—44no—
229D4—44no—
230D4—48no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4C2×D4×C1112yes—
251C2×C4C2×D4×C1112yes—
252C2×C4C2×D4×C1112yes—
253C2×C4C11×#4114yes—
254C22—41no—
255C22—42no—
256C22—42no—
257C22—41no—
258C22—41no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22C22×D4×C1111yescharacteristic
267C22C2×C11×#4112yes—
268C22C11×H(5,𝔽2)12yes—
269C22C11×H(5,𝔽2)11yescharacteristic
270C22C11×2−1+411yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—24no—
275C4—41no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—42no—
280C2—82no—
281C2—81no—
282C2C11×#53211yescharacteristic
283C2C11×#53511yescharacteristic
284C2C11×#53711yescharacteristic
285C2C11×#53812yes—
286C2C11×#54212yes—
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
2. C2×C11×#124C2semidirect
3. C11×#396C2semidirect
4. C11×#395C2semidirect
5. C11×#394C2semidirect
6. C11×#394C2semidirect
7. C11×#393C2semidirect
9. C11×#390C2semidirect
10. C11×#388C2semidirect
11. C4×C11×C4⋊C4C2semidirect
70. C42×C11D4semidirect
71. #2662C11direct (N × H)
111. C2×#126C2×C11semidirect
112. C2×#124C2×C11semidirect
113. #396C2×C11semidirect
114. #395C2×C11semidirect
115. #394C2×C11semidirect
116. #394C2×C11semidirect
117. #393C2×C11semidirect
119. #390C2×C11semidirect
120. #388C2×C11semidirect
121. C4×C4⋊C4C2×C11semidirect
213. C42D4×C11semidirect
214. C11#2662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C11×#1242
C11×#3962
C11×#3952
C11×#3942
C11×#3932
C11×#3922
C11×#3902
C11×#3882
C4×C11×C4⋊C42
#266211