Finite Group Databasebeta

← C11×#21951 #14599144

Subgroups — C11×#21951 #14599144

Order 2816.

978 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×#431C212yesmaximal
2C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#1939C218yesmaximal, complemented
4C11×#1797C214yesmaximal
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C42×C11C2212yes—
8C22×C42×C11C2211yescharacteristic
9C11×#431—28no—
10C2×C11×C4⋊C8C2214yes—
11C2×C11×C4⋊C8C2218yes—
12C2×C11×C22⋊C8C2214yes—
13C2×C4×C8×C11C2214yes—
14C4×C11×C4⋊C4C414yes—
15C4×C11×C4⋊C4C2214yes—
16C2×C11×#95C412yes—
17C11×#336C2218yes—
18C23×C4×C11C2×C412yes—
19C23×C4×C11C2×C411yescharacteristic
20C23×C4×C11C2×C412yes—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C22×C8×C11C2318yes—
24C2×C11×C4⋊C4—24no—
25C2×C11×C4⋊C4C818yescomplemented
26C2×C11×C4⋊C4C2×C414yes—
27C2×C11×C4⋊C4C2×C414yes—
28C2×C42×C11—44no—
29C2×C42×C11C2×C414yes—
30C2×C42×C11C2×C412yes—
31C2×C42×C11D414yes—
32C2×C42×C11Q814yes—
33C2×C42×C11C2314yes—
34C2×C42×C11C2312yes—
35C11×C4⋊C8—28no—
36C11×C4⋊C8—48no—
37C11×C22⋊C8—28no—
38C4×C8×C11—28no—
39C11×#95C2×C418yes—
40#21951C1111yesmaximal, characteristic, direct product factor, Sylow
41C24×C11C22×C411yescharacteristic
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—24no—
45C22×C4×C11—42no—
46C22×C4×C11—42no—
47C22×C4×C11—41no—
48C22×C4×C11—41no—
49C22×C4×C11—42no—
50C22×C4×C11—42no—
51C22×C4×C11C4⋊C414yes—
52C22×C4×C11C4⋊C414yes—
53C22×C4×C11C2×C818yes—
54C22×C4×C11C2×C814yes—
55C22×C4×C11M1614yes—
56C22×C4×C11C22×C414yes—
57C22×C4×C11C22×C412yes—
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C22×C414yes—
60C22×C4×C11C22×C412yes—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×Q812yes—
63C22×C4×C11C2411yescharacteristic
64C2×C8×C11—28no—
65C2×C8×C11—28no—
66C2×C8×C11—28no—
67C11×C4⋊C4—28no—
68C11×C4⋊C4C2×C8116yes—
69C42×C11—28no—
70C42×C11—44no—
71C42×C11C4⋊C418yes—
72C42×C11C2×D414yes—
73C42×C11C2×Q814yes—
74C2×#431C2×C1112yes—
75C2×C4×C4⋊C4C2×C1111yescharacteristic
76#1939C2×C1118yescomplemented
77#1797C2×C1114yes—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11C2×C4⋊C412yes—
83C23×C11C22×C812yes—
84C23×C11C2×M1612yes—
85C23×C11C23×C411yescharacteristic
86C2×C4×C11—24no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—24no—
92C2×C4×C11—24no—
93C2×C4×C11—24no—
94C2×C4×C11—24no—
95C2×C4×C11—24no—
96C2×C4×C11—24no—
97C2×C4×C11—44no—
98C2×C4×C11—48no—
99C2×C4×C11—48no—
100C2×C4×C11C4⋊C8116yescomplemented
101C2×C4×C11C2×C4⋊C412yes—
102C2×C4×C11C2×C4⋊C414yes—
103C2×C4×C11C2×C4⋊C414yes—
104C2×C4×C11C22×C818yes—
105C2×C4×C11C22×C814yes—
106C2×C4×C11C2×M1614yes—
107C2×C4×C11C22×D411yescharacteristic
108C2×C4×C11C22×Q811yescharacteristic
109C2×C4×C11H(5,𝔽2)12yes—
110C2×C4×C112−1+412yes—
111C8×C11—48no—
112C22×C4⋊C4C4×C1111yescharacteristic
113C22×C4⋊C4C4×C1111yescharacteristic
114C22×C42C22×C1112yes—
115C22×C42C22×C1111yescharacteristic
116#431—28no—
117C2×C4⋊C8C22×C1114yes—
118C2×C4⋊C8C22×C1118yes—
119C2×C22⋊C8C22×C1114yes—
120C2×C4×C8C22×C1114yes—
121C4×C4⋊C4C4×C1114yes—
122C4×C4⋊C4C22×C1114yes—
123C2×#95C4×C1112yes—
124#336C22×C1118yes—
125C22×C11—22no—
126C22×C11—22no—
127C22×C11—22no—
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11C2×C4⋊C814yes—
132C22×C11C22×C4⋊C411yescharacteristic
133C22×C11#51811yescharacteristic
134C22×C11#51911yescharacteristic
135C22×C11C23×C811yescharacteristic
136C22×C11C22×M1611yescharacteristic
137C22×C11#56811yescharacteristic
138C22×C11#56811yescharacteristic
139C4×C11—22no—
140C4×C11—24no—
141C4×C11—28no—
142C4×C11—44no—
143C4×C11C2×C4⋊C818yes—
144C4×C11#53712yes—
145C4×C11#54412yes—
146C23×C4C2×C4×C1112yes—
147C23×C4C2×C4×C1111yescharacteristic
148C23×C4C2×C4×C1112yes—
149C23×C4C2×C4×C1111yescharacteristic
150C23×C4C23×C1111yescharacteristic
151C22×C8C23×C1118yes—
152C2×C4⋊C4—24no—
153C2×C4⋊C4C8×C1118yescomplemented
154C2×C4⋊C4C2×C4×C1114yes—
155C2×C4⋊C4C2×C4×C1114yes—
156C2×C42—44no—
157C2×C42C2×C4×C1114yes—
158C2×C42C2×C4×C1112yes—
159C2×C42D4×C1114yes—
160C2×C42Q8×C1114yes—
161C2×C42C23×C1114yes—
162C2×C42C23×C1112yes—
163C4⋊C8—28no—
164C4⋊C8—48no—
165C22⋊C8—28no—
166C4×C8—28no—
167#95C2×C4×C1118yes—
168C2×C11—24no—
169C2×C11#231611yescharacteristic
170C2×C11C22×C4⋊C811yescharacteristic
171C2×C11#290511yescharacteristic
172C2×C11#297211yescharacteristic
173C2×C11#297511yescharacteristic
174C2×C11#298211yescharacteristic
175C2×C11#298311yescharacteristic
176C24C22×C4×C1111yescharacteristic
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—24no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4C11×C4⋊C414yes—
187C22×C4C11×C4⋊C414yes—
188C22×C4C2×C8×C1118yes—
189C22×C4C2×C8×C1114yes—
190C22×C4C11×M1614yes—
191C22×C4C22×C4×C1114yes—
192C22×C4C22×C4×C1112yes—
193C22×C4C22×C4×C1111yescharacteristic
194C22×C4C22×C4×C1114yes—
195C22×C4C22×C4×C1112yes—
196C22×C4C2×D4×C1112yes—
197C22×C4C2×Q8×C1112yes—
198C22×C4C24×C1111yescharacteristic
199C2×C8—28no—
200C2×C8—28no—
201C2×C8—28no—
202C4⋊C4—28no—
203C4⋊C4C2×C8×C11116yes—
204C42—28no—
205C42—44no—
206C42C11×C4⋊C418yes—
207C42C2×D4×C1114yes—
208C42C2×Q8×C1114yes—
209C11#2195111yescharacteristic, direct product factor, Sylow
210C23—21no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23C2×C11×C4⋊C412yes—
215C23C22×C8×C1112yes—
216C23C2×C11×M1612yes—
217C23C23×C4×C1111yescharacteristic
218C2×C4—24no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—24no—
224C2×C4—24no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—44no—
230C2×C4—48no—
231C2×C4—48no—
232C2×C4C11×C4⋊C8116yescomplemented
233C2×C4C2×C11×C4⋊C412yes—
234C2×C4C2×C11×C4⋊C414yes—
235C2×C4C2×C11×C4⋊C414yes—
236C2×C4C22×C8×C1118yes—
237C2×C4C22×C8×C1114yes—
238C2×C4C2×C11×M1614yes—
239C2×C4C22×D4×C1111yescharacteristic
240C2×C4C22×Q8×C1111yescharacteristic
241C2×C4C11×H(5,𝔽2)12yes—
242C2×C4C11×2−1+412yes—
243C8—48no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22C2×C11×C4⋊C814yes—
251C22C22×C11×C4⋊C411yescharacteristic
252C22C11×#51811yescharacteristic
253C22C11×#51911yescharacteristic
254C22C23×C8×C1111yescharacteristic
255C22C22×C11×M1611yescharacteristic
256C22C11×#56811yescharacteristic
257C22C11×#56811yescharacteristic
258C4—24no—
259C4—28no—
260C4—22no—
261C4—44no—
262C4C2×C11×C4⋊C818yes—
263C4C11×#53712yes—
264C4C11×#54412yes—
265C2—24no—
266C2C11×#231611yescharacteristic
267C2C22×C11×C4⋊C811yescharacteristic
268C2C11×#290511yescharacteristic
269C2C11×#297211yescharacteristic
270C2C11×#297511yescharacteristic
271C2C11×#298211yescharacteristic
272C2C11×#298311yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC22C23×C8×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1939C2semidirect
25. C2×C11×C4⋊C4C8semidirect
40. #21951C11direct (N × H)
76. #1939C2×C11semidirect
100. C2×C4×C11C4⋊C8semidirect
153. C2×C4⋊C4C8×C11semidirect
209. C11#21951direct (N × H)
232. C2×C4C11×C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4312
C2×C4×C11×C4⋊C42
C11×#19392
C11×#17972
#2195111