Finite Group Databasebeta

← C11×#8962 #14586155

Subgroups — C11×#8962 #14586155

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2983C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic
3C11×#1479C212yesmaximal
4C11×#1461C211yesmaximal, characteristic
5C11×#1276C212yesmaximal
6C2×C11×C4⋊Q8C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C11×#446—24no—
10C11×#432—22no—
11C11×#431C2212yes—
12C11×#431C2212yes—
13C11×#391C411yescharacteristic
14C11×#391C411yescharacteristic
15C11×#389—22no—
16C11×#384C411yescharacteristic
17C4×C11×C4⋊C4—22no—
18C43×C11C2211yescharacteristic
19C11×Q8⋊C8—24no—
20C11×#324—22no—
21C22×Q8×C11C2×C411yescharacteristic
22C22×Q8×C11C2×C411yescharacteristic
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C4×Q8×C11—22no—
28C4×Q8×C11—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D412yes—
35C2×C42×C11—21no—
36C2×C42×C11—21no—
37C2×C42×C11—21no—
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D412yes—
41C2×C42×C11C2311yescharacteristic
42C11×C4⋊C8—24no—
43C11×C4⋊C8—22no—
44C11×C4⋊C8D414yes—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×#97—24no—
48C4×C8×C11—22no—
49C4×C8×C11—22no—
50C11×#95—22no—
51C11×#95—22no—
52#8962C1111yesmaximal, characteristic, direct product factor, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11—21no—
55C2×Q8×C11—21no—
56C2×Q8×C11—21no—
57C2×Q8×C11—22no—
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11M1612yes—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C2×C8×C11—24no—
71C2×C8×C11—42no—
72C11×C4⋊C4—28no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—42no—
78C42×C11—24no—
79C42×C11—22no—
80C42×C11—22no—
81C42×C11—21no—
82C42×C11—22no—
83C42×C11—42no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11M1612yes—
87C42×C11C2×D412yes—
88C42×C11#4112yes—
89#2983C2×C1111yescharacteristic
90C4×C4⋊Q8C2×C1111yescharacteristic
91#1479C2×C1112yes—
92#1461C2×C1111yescharacteristic
93#1276C2×C1112yes—
94C23×C11C2×C22⋊C411yescharacteristic
95Q8×C11—24no—
96Q8×C11—42no—
97Q8×C11—42no—
98Q8×C11—42no—
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—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11C4×D412yes—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11#12112yes—
120C2×C4×C11#12311yescharacteristic
121C2×C4×C11C2×M1611yescharacteristic
122C2×C4×C11C2×M1611yescharacteristic
123C2×C4×C11#13112yes—
124C8×C11—44no—
125C8×C11—82no—
126C2×C4⋊Q8C4×C1111yescharacteristic
127C2×C4×Q8C22×C1111yescharacteristic
128C2×C4×Q8C22×C1111yescharacteristic
129#446—24no—
130#432—22no—
131#431C22×C1112yes—
132#431C22×C1112yes—
133#391C4×C1111yescharacteristic
134#391C4×C1111yescharacteristic
135#389—22no—
136#384C4×C1111yescharacteristic
137C4×C4⋊C4—22no—
138C43C22×C1111yescharacteristic
139Q8⋊C8—24no—
140#324—22no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#38611yescharacteristic
144C22×C11#40711yescharacteristic
145C22×C11#40811yescharacteristic
146C4×C11—24no—
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—42no—
150C4×C11—42no—
151C4×C11—42no—
152C4×C11—42no—
153C4×C11—81no—
154C4×C11#43512yes—
155C4×C11#43612yes—
156C4×C11#45612yes—
157C22×Q8C2×C4×C1111yescharacteristic
158C22×Q8C2×C4×C1111yescharacteristic
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C2×C4×C1111yescharacteristic
169C2×C4⋊C4C2×C4×C1111yescharacteristic
170C2×C4⋊C4D4×C1112yes—
171C2×C42—21no—
172C2×C42—21no—
173C2×C42—21no—
174C2×C42C2×C4×C1111yescharacteristic
175C2×C42C2×C4×C1111yescharacteristic
176C2×C42D4×C1112yes—
177C2×C42C23×C1111yescharacteristic
178C4⋊C8—24no—
179C4⋊C8—22no—
180C4⋊C8D4×C1114yes—
181C22⋊C8—22no—
182C22⋊C8—22no—
183#97—24no—
184C4×C8—22no—
185C4×C8—22no—
186#95—22no—
187#95—22no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#187011yescharacteristic
191C2×C11#188411yescharacteristic
192C2×C11#188611yescharacteristic
193C2×Q8—22no—
194C2×Q8—21no—
195C2×Q8—21no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8C11×M1612yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4C11×C22⋊C412yes—
206C22×C4C11×C22⋊C412yes—
207C22×C4C22×C4×C1111yescharacteristic
208C22×C4C2×D4×C1111yescharacteristic
209C22×C4C2×D4×C1111yescharacteristic
210C2×C8—24no—
211C2×C8—42no—
212C4⋊C4—28no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—44no—
217C4⋊C4—42no—
218C42—24no—
219C42—22no—
220C42—22no—
221C42—21no—
222C42—22no—
223C42—42no—
224C42—41no—
225C42—41no—
226C42C11×M1612yes—
227C42C2×D4×C1112yes—
228C42C11×#4112yes—
229C11#896211yescharacteristic, direct product factor, Sylow
230C23C2×C11×C22⋊C411yescharacteristic
231Q8—24no—
232Q8—42no—
233Q8—42no—
234Q8—42no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4C4×D4×C1112yes—
254C2×C4C11×#12011yescharacteristic
255C2×C4C11×#12112yes—
256C2×C4C11×#12311yescharacteristic
257C2×C4C2×C11×M1611yescharacteristic
258C2×C4C2×C11×M1611yescharacteristic
259C2×C4C11×#13112yes—
260C8—44no—
261C8—82no—
262C22—21no—
263C22—21no—
264C22C11×#38611yescharacteristic
265C22C11×#40711yescharacteristic
266C22C11×#40811yescharacteristic
267C4—24no—
268C4—22no—
269C4—21no—
270C4—42no—
271C4—42no—
272C4—42no—
273C4—42no—
274C4—81no—
275C4C11×#43512yes—
276C4C11×#43612yes—
277C4C11×#45612yes—
278C2—21no—
279C2—21no—
280C2C11×#187011yescharacteristic
281C2C11×#188411yescharacteristic
282C2C11×#188611yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
52. #8962C11direct (N × H)
229. C11#8962direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29832
C4×C11×C4⋊Q82
C11×#14792
C11×#14612
C11×#12762
#896211