Finite Group Databasebeta

← C11×#22249 #14599442

Subgroups — C11×#22249 #14599442

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#499C211yesmaximal, characteristic
2C4×C11×#125C212yesmaximal
3C11×#1991C212yesmaximal
4C11×#1921C212yesmaximal
5C11×#1920C212yesmaximal
6C11×#1919C212yesmaximal
7C11×#1918C212yesmaximal
8C11×#1835C211yesmaximal, characteristic
9C11×#1744C211yesmaximal, characteristic
10C2×C11×#125C2212yes—
11C11×#499C418yescomplemented
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#106C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#389C2212yes—
18C11×#389C2212yes—
19C11×#387—22no—
20C11×#387—22no—
21C11×#382C2212yes—
22C4×C11×C4⋊C4—22no—
23C4×C11×C4⋊C4—22no—
24C4×C11×C4⋊C4C2212yes—
25C4×C11×C4⋊C4C2212yes—
26C43×C11C2211yescharacteristic
27C11×#340C2212yes—
28C11×#340C2212yes—
29C11×#340C2212yes—
30C11×#340C2211yescharacteristic
31C11×#340C2212yes—
32C11×#340C2211yescharacteristic
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×C8×C11C2312yes—
37C22×C8×C11C2311yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C11×#125—24no—
40C11×#125C2×C418yes—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11D412yes—
52C2×C42×C11D411yescharacteristic
53C2×C42×C11D411yescharacteristic
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56C11×#107C2×C414yes—
57C11×#107C2×C414yes—
58C11×#106C2×C418yes—
59C4×C8×C11—22no—
60C4×C8×C11C2×C414yes—
61C11×#95—22no—
62C11×#95—22no—
63C11×#95—22no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—22no—
67#22249C1111yesmaximal, characteristic, direct product factor, Sylow
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2411yescharacteristic
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11C22×C412yes—
83C2×C8×C11C22×C412yes—
84C11×C4⋊C4—28no—
85C11×C4⋊C4—28no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—44no—
93C11×C4⋊C4—44no—
94C11×C4⋊C4C22×C414yes—
95C11×C4⋊C4C22×C414yes—
96C42×C11—24no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—41no—
100C42×C11—41no—
101C42×C11—44no—
102C42×C11—44no—
103C42×C11C22×C412yes—
104C42×C11#4112yes—
105C2×#499C2×C1111yescharacteristic
106C4×#125C2×C1112yes—
107#1991C2×C1112yes—
108#1921C2×C1112yes—
109#1920C2×C1112yes—
110#1919C2×C1112yes—
111#1918C2×C1112yes—
112#1835C2×C1111yescharacteristic
113#1744C2×C1111yescharacteristic
114C23×C11C22×D411yescharacteristic
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C4×D412yes—
136C2×C4×C11C4×D412yes—
137C2×C4×C11#13514yes—
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C2×#4111yescharacteristic
140C2×C4×C112−1+412yes—
141C2×C4×C112−1+412yes—
142C8×C11—22no—
143C8×C11—22no—
144C8×C11—42no—
145C2×#125C22×C1112yes—
146#499C4×C1118yescomplemented
147C2×#107C22×C1111yescharacteristic
148C2×#107C22×C1111yescharacteristic
149C2×#106C22×C1112yes—
150C2×C4×C8C22×C1111yescharacteristic
151C2×C4×C8C22×C1111yescharacteristic
152#389C22×C1112yes—
153#389C22×C1112yes—
154#387—22no—
155#387—22no—
156#382C22×C1112yes—
157C4×C4⋊C4—22no—
158C4×C4⋊C4—22no—
159C4×C4⋊C4C22×C1112yes—
160C4×C4⋊C4C22×C1112yes—
161C43C22×C1111yescharacteristic
162#340C22×C1112yes—
163#340C22×C1111yescharacteristic
164#340C22×C1111yescharacteristic
165#340C22×C1112yes—
166#340C22×C1112yes—
167#340C22×C1112yes—
168#340C22×C1112yes—
169#336C22×C1112yes—
170#336C22×C1112yes—
171C22×C11C2×C4×D411yescharacteristic
172C22×C11#53612yes—
173C22×C11C2×#13512yes—
174C22×C11#57511yescharacteristic
175C22×C11#57511yescharacteristic
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—24no—
179C4×C11—44no—
180C4×C11—44no—
181C4×C11—42no—
182C4×C11—82no—
183C4×C11—82no—
184C4×C11#51911yescharacteristic
185C4×C11#51911yescharacteristic
186C4×C11#54112yes—
187C22×C8C23×C1112yes—
188C22×C8C23×C1111yescharacteristic
189C22×C8C23×C1111yescharacteristic
190#125—24no—
191#125C2×C4×C1118yes—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4C23×C1112yes—
197C2×C4⋊C4C23×C1112yes—
198C2×C4⋊C4C23×C1112yes—
199C2×C4⋊C4C23×C1112yes—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42D4×C1112yes—
203C2×C42D4×C1111yescharacteristic
204C2×C42D4×C1111yescharacteristic
205C2×C42C23×C1112yes—
206C2×C42C23×C1111yescharacteristic
207#107C2×C4×C1114yes—
208#107C2×C4×C1114yes—
209#106C2×C4×C1118yes—
210C4×C8—22no—
211C4×C8C2×C4×C1114yes—
212#95—22no—
213#95—22no—
214#95—22no—
215#95—22no—
216#95—22no—
217#95—22no—
218C2×C11#232711yescharacteristic
219C2×C11C4×#13511yescharacteristic
220C2×C11#294311yescharacteristic
221C2×C11#323212yes—
222C2×C11#323312yes—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4C2×D4×C1112yes—
228C22×C4C2×D4×C1111yescharacteristic
229C22×C4C2×D4×C1111yescharacteristic
230C22×C4C2×D4×C1112yes—
231C22×C4C24×C1111yescharacteristic
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8C22×C4×C1112yes—
238C2×C8C22×C4×C1112yes—
239C4⋊C4—28no—
240C4⋊C4—28no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—44no—
248C4⋊C4—44no—
249C4⋊C4C22×C4×C1114yes—
250C4⋊C4C22×C4×C1114yes—
251C42—24no—
252C42—22no—
253C42—22no—
254C42—41no—
255C42—41no—
256C42—44no—
257C42—44no—
258C42C22×C4×C1112yes—
259C42C11×#4112yes—
260C11#2224911yescharacteristic, direct product factor, Sylow
261C23C22×D4×C1111yescharacteristic
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4C4×D4×C1112yes—
283C2×C4C4×D4×C1112yes—
284C2×C4C11×#13514yes—
285C2×C4C23×C4×C1111yescharacteristic
286C2×C4C2×C11×#4111yescharacteristic
287C2×C4C11×2−1+412yes—
288C2×C4C11×2−1+412yes—
289C8—22no—
290C8—22no—
291C8—42no—
292C22C2×C4×D4×C1111yescharacteristic
293C22C11×#53612yes—
294C22C2×C11×#13512yes—
295C22C11×#57511yescharacteristic
296C22C11×#57511yescharacteristic
297C4—22no—
298C4—22no—
299C4—24no—
300C4—44no—
301C4—44no—
302C4—42no—
303C4—82no—
304C4—82no—
305C4C11×#51911yescharacteristic
306C4C11×#51911yescharacteristic
307C4C11×#54112yes—
308C2C11×#232711yescharacteristic
309C2C4×C11×#13511yescharacteristic
310C2C11×#294311yescharacteristic
311C2C11×#323212yes—
312C2C11×#323312yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
11. C11×#499C4semidirect
67. #22249C11direct (N × H)
146. #499C4×C11semidirect
260. C11#22249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4992
C4×C11×#1252
C11×#19912
C11×#19212
C11×#19202
C11×#19192
C11×#19182
C11×#18352
C11×#17442
#2224911