Finite Group Databasebeta

← C11×#23158 #14600351

Subgroups — C11×#23158 #14600351

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#500C211yesmaximal, characteristic
2C11×#2369C212yesmaximal
3C11×#1987C212yesmaximal
4C11×#1942C212yesmaximal
5C11×#1921C214yesmaximal
6C4×C11×#107C211yesmaximal, characteristic
7C4×C11×#107C212yesmaximal
8C8×C11×C4⋊C4C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2212yes—
10C11×#500C418yescomplemented
11C2×C11×#107C2211yescharacteristic
12C2×C11×#107C2212yes—
13C2×C11×#107C2212yes—
14C2×C11×#107C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C4×C8×C11C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C11×#391—24no—
19C11×#389—22no—
20C11×#389C2214yes—
21C4×C11×C4⋊C4—22no—
22C4×C11×C4⋊C4C2214yes—
23C4×C11×C4⋊C4C2212yes—
24C4×C11×C4⋊C4C2211yescharacteristic
25C11×#340C2212yes—
26C11×#340C2214yes—
27C11×#340C2214yes—
28C11×#336C2212yes—
29C22×Q8×C11—22no—
30C22×C8×C11C2312yes—
31C22×C8×C11C2311yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8C2×C418yes—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4C2312yes—
40C2×C11×C4⋊C4C2314yes—
41C2×C11×C4⋊C4C2312yes—
42C2×C42×C11—22no—
43C2×C42×C11—24no—
44C2×C42×C11C2312yes—
45C2×C42×C11C2311yescharacteristic
46C11×#107—22no—
47C11×#107C2×C418yes—
48C11×#107C2×C418yes—
49C11×#107Q814yescomplemented
50C11×C4⋊C8—22no—
51C4×C8×C11—24no—
52C4×C8×C11C2×C414yes—
53C11×#95—24no—
54C11×#95—24no—
55C11×#95—22no—
56C11×#95D412yes—
57#23158C1111yesmaximal, characteristic, direct product factor, Sylow
58C2×Q8×C11—28no—
59C2×Q8×C11—82no—
60C2×Q8×C11—82no—
61C22×C4×C11—22no—
62C22×C4×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11C2×D412yes—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D412yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2411yescharacteristic
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—22no—
74C2×C8×C11C22×C412yes—
75C2×C8×C11C22×C412yes—
76C2×C8×C11C2×Q812yes—
77C2×C8×C11#4112yes—
78C11×C4⋊C4—28no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—24no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—84no—
85C11×C4⋊C4Q1614yes—
86C11×C4⋊C4C22×C418yes—
87C11×C4⋊C4C2×Q814yes—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11—44no—
91C42×C11—84no—
92C42×C11C22×C412yes—
93C42×C11#4112yes—
94C2×#500C2×C1111yescharacteristic
95#2369C2×C1112yes—
96#1987C2×C1112yes—
97#1942C2×C1112yes—
98#1921C2×C1114yes—
99C4×#107C2×C1111yescharacteristic
100C4×#107C2×C1112yes—
101C8×C4⋊C4C2×C1111yescharacteristic
102C23×C11C22×D411yescharacteristic
103Q8×C11—88no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—28no—
109C2×C4×C11—22no—
110C2×C4×C11—24no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11C4×D412yes—
121C2×C4×C11C4×D412yes—
122C2×C4×C11C2×Q1614yes—
123C2×C4×C11C2×Q1612yes—
124C2×C4×C11#13512yes—
125C2×C4×C11C23×C411yescharacteristic
126C2×C4×C11C22×Q811yescharacteristic
127C2×C4×C11C2×#4111yescharacteristic
128C2×C4×C11C2×#4111yescharacteristic
129C2×C4×C112−1+411yescharacteristic
130C2×C4×C112−1+411yescharacteristic
131C8×C11—22no—
132C8×C11—42no—
133C8×C11C4×Q814yes—
134C2×C4⋊Q8C22×C1112yes—
135#500C4×C1118yescomplemented
136C2×#107C22×C1111yescharacteristic
137C2×#107C22×C1112yes—
138C2×#107C22×C1112yes—
139C2×#107C22×C1111yescharacteristic
140C2×C4⋊C8C22×C1111yescharacteristic
141C2×C4×C8C22×C1112yes—
142C2×C4×C8C22×C1111yescharacteristic
143#391—24no—
144#389—22no—
145#389C22×C1114yes—
146C4×C4⋊C4—22no—
147C4×C4⋊C4C22×C1114yes—
148C4×C4⋊C4C22×C1112yes—
149C4×C4⋊C4C22×C1111yescharacteristic
150#340C22×C1112yes—
151#340C22×C1114yes—
152#340C22×C1114yes—
153#336C22×C1112yes—
154C22×C11C2×C4×D411yescharacteristic
155C22×C11#54711yescharacteristic
156C22×C11D4×Q811yescharacteristic
157C22×C11C22×Q1611yescharacteristic
158C22×C11C2×#13511yescharacteristic
159C22×C11#57611yescharacteristic
160C22×C11#57611yescharacteristic
161C4×C11—24no—
162C4×C11—22no—
163C4×C11—42no—
164C4×C11—44no—
165C4×C11—48no—
166C4×C11—82no—
167C4×C11C4×Q1614yes—
168C4×C11C2×C4×Q811yescharacteristic
169C4×C11#51911yescharacteristic
170C4×C11#55611yescharacteristic
171C4×C11#55711yescharacteristic
172C22×Q8—22no—
173C22×C8C23×C1112yes—
174C22×C8C23×C1111yescharacteristic
175C22×C8C23×C1111yescharacteristic
176C4⋊Q8—24no—
177C4⋊Q8C2×C4×C1118yes—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4D4×C1111yescharacteristic
181C2×C4⋊C4D4×C1111yescharacteristic
182C2×C4⋊C4C23×C1112yes—
183C2×C4⋊C4C23×C1114yes—
184C2×C4⋊C4C23×C1112yes—
185C2×C42—22no—
186C2×C42—24no—
187C2×C42C23×C1112yes—
188C2×C42C23×C1111yescharacteristic
189#107—22no—
190#107C2×C4×C1118yes—
191#107C2×C4×C1118yes—
192#107Q8×C1114yescomplemented
193C4⋊C8—22no—
194C4×C8—24no—
195C4×C8C2×C4×C1114yes—
196#95—24no—
197#95—24no—
198#95—22no—
199#95D4×C1112yes—
200C2×C11#236511yescharacteristic
201C2×C11C2×C4×Q1611yescharacteristic
202C2×C11#294811yescharacteristic
203C2×C11#333811yescharacteristic
204C2×C11#334111yescharacteristic
205C2×C11#338011yescharacteristic
206C2×C11Q8×Q1611yescharacteristic
207C2×Q8—28no—
208C2×Q8—82no—
209C2×Q8—82no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—22no—
213C22×C4C2×D4×C1112yes—
214C22×C4C2×D4×C1111yescharacteristic
215C22×C4C2×D4×C1112yes—
216C22×C4C2×D4×C1111yescharacteristic
217C22×C4C24×C1111yescharacteristic
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—22no—
221C2×C8—22no—
222C2×C8—22no—
223C2×C8C22×C4×C1112yes—
224C2×C8C22×C4×C1112yes—
225C2×C8C2×Q8×C1112yes—
226C2×C8C11×#4112yes—
227C4⋊C4—28no—
228C4⋊C4—22no—
229C4⋊C4—24no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—84no—
234C4⋊C4C11×Q1614yes—
235C4⋊C4C22×C4×C1118yes—
236C4⋊C4C2×Q8×C1114yes—
237C42—22no—
238C42—22no—
239C42—44no—
240C42—84no—
241C42C22×C4×C1112yes—
242C42C11×#4112yes—
243C11#2315811yescharacteristic, direct product factor, Sylow
244C23C22×D4×C1111yescharacteristic
245Q8—88no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—28no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4C4×D4×C1112yes—
263C2×C4C4×D4×C1112yes—
264C2×C4C2×C11×Q1614yes—
265C2×C4C2×C11×Q1612yes—
266C2×C4C11×#13512yes—
267C2×C4C23×C4×C1111yescharacteristic
268C2×C4C22×Q8×C1111yescharacteristic
269C2×C4C2×C11×#4111yescharacteristic
270C2×C4C2×C11×#4111yescharacteristic
271C2×C4C11×2−1+411yescharacteristic
272C2×C4C11×2−1+411yescharacteristic
273C8—22no—
274C8—42no—
275C8C4×Q8×C1114yes—
276C22C2×C4×D4×C1111yescharacteristic
277C22C11×#54711yescharacteristic
278C22D4×Q8×C1111yescharacteristic
279C22C22×C11×Q1611yescharacteristic
280C22C2×C11×#13511yescharacteristic
281C22C11×#57611yescharacteristic
282C22C11×#57611yescharacteristic
283C4—22no—
284C4—24no—
285C4—48no—
286C4—42no—
287C4—44no—
288C4—82no—
289C4C4×C11×Q1614yes—
290C4C2×C4×Q8×C1111yescharacteristic
291C4C11×#51911yescharacteristic
292C4C11×#55611yescharacteristic
293C4C11×#55711yescharacteristic
294C2C11×#236511yescharacteristic
295C2C2×C4×C11×Q1611yescharacteristic
296C2C11×#294811yescharacteristic
297C2C11×#333811yescharacteristic
298C2C11×#334111yescharacteristic
299C2C11×#338011yescharacteristic
300C2Q8×C11×Q1611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
10. C11×#500C4semidirect
49. C11×#107Q8semidirect
57. #23158C11direct (N × H)
135. #500C4×C11semidirect
192. #107Q8×C11semidirect
243. C11#23158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5002
C11×#23692
C11×#19872
C11×#19422
C11×#19212
C4×C11×#1072
C8×C11×C4⋊C42
#2315811