Finite Group Databasebeta

← C11×#13201 #14590394

Subgroups — C11×#13201 #14590394

Order 2816.

420 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2930C211yesmaximal, characteristic
2C11×#2153C211yesmaximal, characteristic, complemented
3C11×#2117C212yesmaximal, complemented
4C2×C11×#349C212yesmaximal, complemented
5C11×#2110C211yesmaximal, characteristic, complemented
6C2×C11×#131C2211yescharacteristic
7C22×C11×M16C2211yescharacteristic
8C11×#525C411yescharacteristic
9C2×C11×M32C2212yes—
10C2×C11×M32C2212yes—
11C11×#436—22no—
12C11×#435—22no—
13C11×#424C411yescharacteristic
14C11×#408C411yescharacteristic
15C11×#407C411yescharacteristic
16C11×#405C2211yescharacteristic
17C11×#364—22no—
18C11×#350—24no—
19C11×#349—24no—
20C11×#347—22no—
21C2×C11×#41C2×C411yescharacteristic
22C23×C4×C11C2×C411yescharacteristic
23C11×#131—22no—
24C11×#131—22no—
25C2×C11×M16—22no—
26C2×C11×M16—21no—
27C2×C11×M16—21no—
28C2×C11×M16—21no—
29C2×C11×M16—22no—
30C2×C11×M16C2×C411yescharacteristic
31C2×C11×M16C2×C411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11C2×C411yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C11×#123—21no—
36C11×C22⋊Q8—21no—
37C11×#121—21no—
38C11×#120—21no—
39C4×D4×C11—22no—
40C11×#117C2×C411yescharacteristic
41C11×M32—22no—
42C11×M32—22no—
43C11×M32—22no—
44C11×M32D414yescomplemented
45C2×C11×C16—22no—
46C2×C11×C16—22no—
47C11×C4⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×#97D412yes—
51C4×C8×C11D412yes—
52#13201C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11M1611yescharacteristic
54C11×#41—22no—
55C11×#41—22no—
56C2×Q8×C11M1611yescharacteristic
57C2×D4×C11—21no—
58C2×D4×C11—22no—
59C2×D4×C11M1611yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11M1611yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C11×M16—22no—
68C11×M16—22no—
69C11×M16—42no—
70C11×M16—41no—
71C11×M16—41no—
72C11×M16—41no—
73C11×M16—41no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—22no—
77C2×C8×C11—42no—
78C2×C8×C11C22⋊C412yes—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×D412yes—
82C2×C8×C11#4112yes—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—21no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—21no—
88C42×C11C22⋊C412yes—
89C11×C16—24no—
90C11×C16—42no—
91#2930C2×C1111yescharacteristic
92#2153C2×C1111yescharacteristic, complemented
93#2117C2×C1112yescomplemented
94C2×#349C2×C1112yescomplemented
95#2110C2×C1111yescharacteristic, complemented
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—22no—
99C23×C11—81no—
100C23×C11C2×M1611yescharacteristic
101Q8×C11—22no—
102D4×C11—22no—
103D4×C11—42no—
104D4×C11—82no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C4×D412yes—
116C2×C4×C11C2×M1611yescharacteristic
117C2×C4×C11#13112yes—
118C8×C11—22no—
119C8×C11—41no—
120C8×C11—41no—
121C8×C11#12112yes—
122C8×C11#12411yescharacteristic
123C8×C11#12711yescharacteristic
124C2×#131C22×C1111yescharacteristic
125C22×M16C22×C1111yescharacteristic
126#525C4×C1111yescharacteristic
127C2×M32C22×C1112yes—
128C2×M32C22×C1112yes—
129#436—22no—
130#435—22no—
131#424C4×C1111yescharacteristic
132#408C4×C1111yescharacteristic
133#407C4×C1111yescharacteristic
134#405C22×C1111yescharacteristic
135#364—22no—
136#350—24no—
137#349—24no—
138#347—22no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—42no—
142C22×C11—41no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11—82no—
146C22×C11#40711yescharacteristic
147C22×C11#43512yes—
148C4×C11—42no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11#39011yescharacteristic
152C4×C11#40811yescharacteristic
153C4×C11#43512yes—
154C2×#41C2×C4×C1111yescharacteristic
155C23×C4C2×C4×C1111yescharacteristic
156#131—22no—
157#131—22no—
158C2×M16—22no—
159C2×M16—21no—
160C2×M16—21no—
161C2×M16—21no—
162C2×M16—22no—
163C2×M16C2×C4×C1111yescharacteristic
164C2×M16C2×C4×C1111yescharacteristic
165C22×C8—21no—
166C22×C8C2×C4×C1111yescharacteristic
167C22×C8C23×C1111yescharacteristic
168#123—21no—
169C22⋊Q8—21no—
170#121—21no—
171#120—21no—
172C4×D4—22no—
173#117C2×C4×C1111yescharacteristic
174M32—22no—
175M32—22no—
176M32—22no—
177M32D4×C1114yescomplemented
178C2×C16—22no—
179C2×C16—22no—
180C4⋊C8—22no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183#97D4×C1112yes—
184C4×C8D4×C1112yes—
185C2×C11—21no—
186C2×C11—22no—
187C2×C11—81no—
188C2×C11—81no—
189C2×C11#195511yescharacteristic
190C24C11×M1611yescharacteristic
191#41—22no—
192#41—22no—
193C2×Q8C11×M1611yescharacteristic
194C2×D4—21no—
195C2×D4—22no—
196C2×D4C11×M1611yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4C11×M1611yescharacteristic
203C22×C4C22×C4×C1111yescharacteristic
204M16—22no—
205M16—22no—
206M16—42no—
207M16—41no—
208M16—41no—
209M16—41no—
210M16—41no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—22no—
214C2×C8—42no—
215C2×C8C11×C22⋊C412yes—
216C2×C8C2×D4×C1111yescharacteristic
217C2×C8C2×D4×C1112yes—
218C2×C8C2×D4×C1111yescharacteristic
219C2×C8C11×#4112yes—
220C4⋊C4—22no—
221C4⋊C4—21no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—21no—
225C42C11×C22⋊C412yes—
226C16—24no—
227C16—42no—
228C11#1320111yescharacteristic, direct product factor, Sylow
229C23—21no—
230C23—21no—
231C23—22no—
232C23—81no—
233C23C2×C11×M1611yescharacteristic
234Q8—22no—
235D4—22no—
236D4—42no—
237D4—82no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4C2×C11×C22⋊C411yescharacteristic
248C2×C4C4×D4×C1112yes—
249C2×C4C2×C11×M1611yescharacteristic
250C2×C4C11×#13112yes—
251C8—22no—
252C8—41no—
253C8—41no—
254C8C11×#12112yes—
255C8C11×#12411yescharacteristic
256C8C11×#12711yescharacteristic
257C22—41no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—82no—
264C22C11×#40711yescharacteristic
265C22C11×#43512yes—
266C4—42no—
267C4—41no—
268C4—41no—
269C4C11×#39011yescharacteristic
270C4C11×#40811yescharacteristic
271C4C11×#43512yes—
272C2—21no—
273C2—22no—
274C2—81no—
275C2—81no—
276C2C11×#195511yescharacteristic
subgroupG/H
centerC4×C11#390
commutatorC22×C4C22×C4×C11
Frattini, cosocleC22×C8C23×C11
socleC2×C11#1955
prime radicalC11×#525C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2153C2semidirect
3. C11×#2117C2semidirect
4. C2×C11×#349C2semidirect
5. C11×#2110C2semidirect
44. C11×M32D4semidirect
52. #13201C11direct (N × H)
92. #2153C2×C11semidirect
93. #2117C2×C11semidirect
94. C2×#349C2×C11semidirect
95. #2110C2×C11semidirect
177. M32D4×C11semidirect
228. C11#13201direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29302
C11×#21532
C11×#21172
C2×C11×#3492
C11×#21102
#1320111