Finite Group Databasebeta

← C11×#22252 #14599445

Subgroups — C11×#22252 #14599445

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#499C211yesmaximal, characteristic
2C11×#2330C212yesmaximal
3C11×#1992C212yesmaximal
4C11×#1921C212yesmaximal
5C11×#1920C212yesmaximal
6C11×#1919C212yesmaximal
7C11×#1918C212yesmaximal
8C11×#1834C211yesmaximal, characteristic
9C11×#1746C211yesmaximal, characteristic
10C2×C11×#125C2212yes—
11C11×#499C418yescomplemented
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#106C2212yes—
15C2×C11×#97C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#389—22no—
18C11×#389—22no—
19C11×#389C2212yes—
20C11×#389C2212yes—
21C11×#387—22no—
22C11×#387—22no—
23C11×#384C2212yes—
24C4×C11×C4⋊C4C2212yes—
25C4×C11×C4⋊C4C2212yes—
26C11×#376C2211yescharacteristic
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⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11C2312yes—
54C2×C42×C11C2311yescharacteristic
55C11×#107C2×C414yes—
56C11×#107C2×C414yes—
57C11×#106C2×C418yes—
58C11×#97—22no—
59C4×C8×C11C2×C414yes—
60C11×#95—22no—
61C11×#95—22no—
62C11×#95—22no—
63C11×#95—22no—
64C11×#95D411yescharacteristic
65C11×#95D412yes—
66C11×#95D411yescharacteristic
67#22252C1111yesmaximal, 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×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
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—82no—
93C11×C4⋊C4—82no—
94C11×C4⋊C4—82no—
95C11×C4⋊C4—82no—
96C11×C4⋊C4C22×C414yes—
97C11×C4⋊C4C22×C414yes—
98C42×C11—22no—
99C42×C11—22no—
100C42×C11—82no—
101C42×C11—82no—
102C42×C11C22×C412yes—
103C42×C11#4112yes—
104C2×#499C2×C1111yescharacteristic
105#2330C2×C1112yes—
106#1992C2×C1112yes—
107#1921C2×C1112yes—
108#1920C2×C1112yes—
109#1919C2×C1112yes—
110#1918C2×C1112yes—
111#1834C2×C1111yescharacteristic
112#1746C2×C1111yescharacteristic
113C23×C11C22×D411yescharacteristic
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
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×C11C23×C411yescharacteristic
138C2×C4×C11C2×#4111yescharacteristic
139C2×C4×C112−1+412yes—
140C2×C4×C112−1+412yes—
141C8×C11—22no—
142C8×C11—22no—
143C8×C11—42no—
144C2×#125C22×C1112yes—
145#499C4×C1118yescomplemented
146C2×#107C22×C1111yescharacteristic
147C2×#107C22×C1111yescharacteristic
148C2×#106C22×C1112yes—
149C2×#97C22×C1111yescharacteristic
150C2×C4×C8C22×C1111yescharacteristic
151#389—22no—
152#389—22no—
153#389C22×C1112yes—
154#389C22×C1112yes—
155#387—22no—
156#387—22no—
157#384C22×C1112yes—
158C4×C4⋊C4C22×C1112yes—
159C4×C4⋊C4C22×C1112yes—
160#376C22×C1111yescharacteristic
161#340C22×C1112yes—
162#340C22×C1111yescharacteristic
163#340C22×C1111yescharacteristic
164#340C22×C1112yes—
165#340C22×C1112yes—
166#340C22×C1112yes—
167#340C22×C1112yes—
168#336C22×C1112yes—
169#336C22×C1112yes—
170C22×C11C2×C4×D411yescharacteristic
171C22×C11#53612yes—
172C22×C11#57611yescharacteristic
173C22×C11#57712yes—
174C22×C11#57811yescharacteristic
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—44no—
178C4×C11—44no—
179C4×C11—42no—
180C4×C11—42no—
181C4×C11—82no—
182C4×C11—82no—
183C4×C11#51911yescharacteristic
184C4×C11#51911yescharacteristic
185C4×C11#54112yes—
186C22×C8C23×C1112yes—
187C22×C8C23×C1111yescharacteristic
188C22×C8C23×C1111yescharacteristic
189#125—24no—
190#125C2×C4×C1118yes—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4C23×C1112yes—
198C2×C4⋊C4C23×C1112yes—
199C2×C4⋊C4C23×C1112yes—
200C2×C4⋊C4C23×C1112yes—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42C23×C1112yes—
204C2×C42C23×C1111yescharacteristic
205#107C2×C4×C1114yes—
206#107C2×C4×C1114yes—
207#106C2×C4×C1118yes—
208#97—22no—
209C4×C8C2×C4×C1114yes—
210#95—22no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95D4×C1111yescharacteristic
215#95D4×C1112yes—
216#95D4×C1111yescharacteristic
217C2×C11#232711yescharacteristic
218C2×C11#295111yescharacteristic
219C2×C11#295211yescharacteristic
220C2×C11#324112yes—
221C2×C11#324212yes—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4C2×D4×C1112yes—
227C22×C4C2×D4×C1112yes—
228C22×C4C2×D4×C1111yescharacteristic
229C22×C4C2×D4×C1111yescharacteristic
230C22×C4C24×C1111yescharacteristic
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8C22×C4×C1112yes—
237C2×C8C22×C4×C1112yes—
238C4⋊C4—28no—
239C4⋊C4—28no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—82no—
247C4⋊C4—82no—
248C4⋊C4—82no—
249C4⋊C4—82no—
250C4⋊C4C22×C4×C1114yes—
251C4⋊C4C22×C4×C1114yes—
252C42—22no—
253C42—22no—
254C42—82no—
255C42—82no—
256C42C22×C4×C1112yes—
257C42C11×#4112yes—
258C11#2225211yescharacteristic, direct product factor, Sylow
259C23C22×D4×C1111yescharacteristic
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
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×C4C4×D4×C1112yes—
282C2×C4C4×D4×C1112yes—
283C2×C4C23×C4×C1111yescharacteristic
284C2×C4C2×C11×#4111yescharacteristic
285C2×C4C11×2−1+412yes—
286C2×C4C11×2−1+412yes—
287C8—22no—
288C8—22no—
289C8—42no—
290C22C2×C4×D4×C1111yescharacteristic
291C22C11×#53612yes—
292C22C11×#57611yescharacteristic
293C22C11×#57712yes—
294C22C11×#57811yescharacteristic
295C4—22no—
296C4—22no—
297C4—44no—
298C4—44no—
299C4—42no—
300C4—42no—
301C4—82no—
302C4—82no—
303C4C11×#51911yescharacteristic
304C4C11×#51911yescharacteristic
305C4C11×#54112yes—
306C2C11×#232711yescharacteristic
307C2C11×#295111yescharacteristic
308C2C11×#295211yescharacteristic
309C2C11×#324112yes—
310C2C11×#324212yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
11. C11×#499C4semidirect
67. #22252C11direct (N × H)
145. #499C4×C11semidirect
258. C11#22252direct (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
C11×#23302
C11×#19922
C11×#19212
C11×#19202
C11×#19192
C11×#19182
C11×#18342
C11×#17462
#2225211