Finite Group Databasebeta

← C11×#2814 #13065652

Subgroups — C11×#2814 #13065652

Order 1408.

478 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic
2C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C11×#398C211yesmaximal, characteristic, complemented
4C11×#398C212yesmaximal, complemented
5C11×#397C211yesmaximal, characteristic, complemented
6C11×#397C212yesmaximal, complemented
7C11×#396C212yesmaximal, complemented
8C11×#395C211yesmaximal, characteristic, complemented
9C11×#394C212yesmaximal
10C11×#393C211yesmaximal, characteristic, complemented
11C11×#380C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C11×#123—24no—
16C11×C22⋊Q8—24no—
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2212yes—
22C2×C11×C4⋊C4C2212yes—
23C2×C11×C4⋊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—
31C11×#95C2211yescharacteristic
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11×#95C2212yes—
35C11×#95C2212yes—
36C11×#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2311yescharacteristic
39C2×Q8×C11—22no—
40C2×Q8×C11—42no—
41C2×D4×C11—22no—
42C2×D4×C11—42no—
43C22×C4×C11—42no—
44C22×C4×C11D414yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2312yes—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C22×C4×C11C2312yes—
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C11×C4⋊C4—22no—
55C11×C4⋊C4—24no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—22no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4—42no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68#2814C1111yesmaximal, characteristic, direct product factor, Sylow
69C23×C11—21no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—21no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—21no—
78C23×C11C2×D412yes—
79C23×C11C2411yescharacteristic
80Q8×C11—44no—
81D4×C11—44no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—44no—
104C2×C4×C11C2×D412yes—
105C2×C4×C11C2×D412yes—
106C2×#123C2×C1111yescharacteristic
107C2×C22⋊Q8C2×C1111yescharacteristic, complemented
108#398C2×C1111yescharacteristic, complemented
109#398C2×C1112yescomplemented
110#397C2×C1111yescharacteristic, complemented
111#397C2×C1112yescomplemented
112#396C2×C1112yescomplemented
113#395C2×C1111yescharacteristic, complemented
114#394C2×C1112yes—
115#393C2×C1111yescharacteristic, complemented
116#380C2×C1111yescharacteristic, complemented
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11C22×D411yescharacteristic
128C22×C11H(5,𝔽2)12yes—
129C22×C11H(5,𝔽2)11yescharacteristic
130C22×C112−1+412yes—
131C22×C112−1+411yescharacteristic
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—41no—
135C4×C11—42no—
136C4×C11—41no—
137C4×C11—41no—
138C4×C11—42no—
139C4×C11—42no—
140C4×C11—42no—
141C22×Q8C22×C1111yescharacteristic
142C22×D4C22×C1111yescharacteristic
143C23×C4C22×C1111yescharacteristic
144#123—24no—
145C22⋊Q8—24no—
146C2×C4⋊C4C22×C1112yes—
147C2×C4⋊C4C22×C1111yescharacteristic
148C2×C4⋊C4C22×C1111yescharacteristic
149C2×C4⋊C4C22×C1111yescharacteristic
150C2×C4⋊C4C22×C1112yes—
151C2×C4⋊C4C22×C1112yes—
152C2×C4⋊C4C22×C1112yes—
153C2×C22⋊C4C22×C1112yes—
154C2×C22⋊C4C22×C1111yescharacteristic
155C2×C22⋊C4C22×C1111yescharacteristic
156C2×C22⋊C4C22×C1111yescharacteristic
157C2×C22⋊C4C22×C1112yes—
158C2×C22⋊C4C22×C1112yes—
159C2×C22⋊C4C22×C1112yes—
160#95C22×C1111yescharacteristic
161#95C22×C1111yescharacteristic
162#95C22×C1112yes—
163#95C22×C1112yes—
164#95C22×C1112yes—
165#95C22×C1112yes—
166C2×C11—42no—
167C2×C11—81no—
168C2×C11#53411yescharacteristic
169C2×C11#53611yescharacteristic
170C2×C11#53711yescharacteristic
171C2×C11#56212yes—
172C2×C11#56312yes—
173C24C23×C1111yescharacteristic
174C24C23×C1111yescharacteristic
175C2×Q8—22no—
176C2×Q8—42no—
177C2×D4—22no—
178C2×D4—42no—
179C22×C4—42no—
180C22×C4D4×C1114yes—
181C22×C4C23×C1111yescharacteristic
182C22×C4C23×C1112yes—
183C22×C4C23×C1112yes—
184C22×C4C23×C1111yescharacteristic
185C22×C4C23×C1112yes—
186C22×C4C23×C1112yes—
187C22×C4C23×C1111yescharacteristic
188C22×C4C23×C1111yescharacteristic
189C22×C4C23×C1111yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C22⋊C4—24no—
198C22⋊C4—22no—
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C11#281411yescharacteristic, direct product factor, Sylow
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—22no—
213C23—21no—
214C23C2×D4×C1112yes—
215C23C24×C1111yescharacteristic
216Q8—44no—
217D4—44no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—44no—
240C2×C4C2×D4×C1112yes—
241C2×C4C2×D4×C1112yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—42no—
252C22C22×D4×C1111yescharacteristic
253C22C11×H(5,𝔽2)12yes—
254C22C11×H(5,𝔽2)11yescharacteristic
255C22C11×2−1+412yes—
256C22C11×2−1+411yescharacteristic
257C4—22no—
258C4—22no—
259C4—41no—
260C4—42no—
261C4—41no—
262C4—41no—
263C4—42no—
264C4—42no—
265C4—42no—
266C2—42no—
267C2—81no—
268C2C11×#53411yescharacteristic
269C2C11×#53611yescharacteristic
270C2C11×#53711yescharacteristic
271C2C11×#56212yes—
272C2C11×#56312yes—
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC22×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×C22⋊Q8C2semidirect
3. C11×#398C2semidirect
4. C11×#398C2semidirect
5. C11×#397C2semidirect
6. C11×#397C2semidirect
7. C11×#396C2semidirect
8. C11×#395C2semidirect
10. C11×#393C2semidirect
11. C11×#380C2semidirect
68. #2814C11direct (N × H)
107. C2×C22⋊Q8C2×C11semidirect
108. #398C2×C11semidirect
109. #398C2×C11semidirect
110. #397C2×C11semidirect
111. #397C2×C11semidirect
112. #396C2×C11semidirect
113. #395C2×C11semidirect
115. #393C2×C11semidirect
116. #380C2×C11semidirect
204. C11#2814direct (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×C22⋊Q82
C11×#3982
C11×#3972
C11×#3962
C11×#3952
C11×#3942
C11×#3932
C11×#3802
#281411