Finite Group Databasebeta

← C11×#14651 #14591844

Subgroups — C11×#14651 #14591844

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#392C211yesmaximal, characteristic
2C11×#1443C212yesmaximal, complemented
3C11×#1440C213yesmaximal, complemented
4C11×#1438C216yesmaximal, complemented
5C11×#1437C213yesmaximal, complemented
6C23×D4×C11C2213yes—
7C22×C11×C22⋊C4C2216yes—
8C22×C11×C22⋊C4C2213yes—
9C22×C11×C22⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C22×C42×C11C2211yescharacteristic
12C11×#392C418yescomplemented
13C2×C11×#95C2216yes—
14C2×C11×#95C2213yes—
15C2×C11×#95C2216yes—
16C2×C11×#95C2211yescharacteristic
17C25×C11C2313yes—
18C22×D4×C11—46no—
19C22×D4×C11—46no—
20C22×D4×C11—43no—
21C22×D4×C11—43no—
22C22×D4×C11C2×C4112yes—
23C23×C4×C11C2316yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×C4×C11C2312yes—
27C2×C11×C22⋊C4—212no—
28C2×C11×C22⋊C4—43no—
29C2×C11×C22⋊C4—43no—
30C2×C11×C22⋊C4—46no—
31C2×C11×C22⋊C4—46no—
32C2×C11×C22⋊C4—46no—
33C2×C11×C22⋊C4—46no—
34C2×C11×C22⋊C4—43no—
35C2×C11×C22⋊C4—43no—
36C2×C11×C22⋊C4C2×C4112yes—
37C2×C42×C11—43no—
38C11×#95—46no—
39C11×#95—43no—
40C11×#95—46no—
41C11×#95C2×C414yes—
42#14651C1111yesmaximal, characteristic, direct product factor, Sylow
43C24×C11—26no—
44C24×C11—23no—
45C24×C11—23no—
46C24×C11—26no—
47C24×C11—26no—
48C24×C11—26no—
49C24×C11—26no—
50C24×C11—26no—
51C24×C11C22×C416yes—
52C24×C11C2411yescharacteristic
53C2×D4×C11—412no—
54C2×D4×C11—424no—
55C2×D4×C11—424no—
56C2×D4×C11—412no—
57C2×D4×C11—412no—
58C22×C4×C11—23no—
59C22×C4×C11—26no—
60C22×C4×C11—26no—
61C22×C4×C11—26no—
62C22×C4×C11—23no—
63C22×C4×C11—26no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11—26no—
67C22×C4×C11—26no—
68C22×C4×C11—26no—
69C22×C4×C11—26no—
70C22×C4×C11—26no—
71C22×C4×C11—26no—
72C22×C4×C11—26no—
73C22×C4×C11C22×C416yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11#4114yes—
76C11×C22⋊C4—412no—
77C11×C22⋊C4—424no—
78C11×C22⋊C4—412no—
79C11×C22⋊C4—412no—
80C42×C11—44no—
81C2×#392C2×C1111yescharacteristic
82#1443C2×C1112yescomplemented
83#1440C2×C1113yescomplemented
84#1438C2×C1116yescomplemented
85#1437C2×C1113yescomplemented
86C23×C11—26no—
87C23×C11—26no—
88C23×C11—26no—
89C23×C11—212no—
90C23×C11—212no—
91C23×C11—46no—
92C23×C11—46no—
93C23×C11—46no—
94C23×C11—46no—
95C23×C11—46no—
96C23×C11—46no—
97C23×C11—43no—
98C23×C11—46no—
99C23×C11—46no—
100C23×C11—46no—
101C23×C11—46no—
102C23×C11—43no—
103C23×C11—43no—
104C23×C11—46no—
105C23×C11—43no—
106C23×C11—46no—
107C23×C11C23×C411yescharacteristic
108C23×C11C2×#4112yes—
109C23×C11H(5,𝔽2)13yes—
110C23×C11H(5,𝔽2)16yes—
111C23×C11H(5,𝔽2)13yes—
112D4×C11—448no—
113C2×C4×C11—26no—
114C2×C4×C11—26no—
115C2×C4×C11—212no—
116C2×C4×C11—212no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—46no—
120C2×C4×C11—43no—
121C2×C4×C11—46no—
122C2×C4×C11—43no—
123C2×C4×C11—43no—
124C2×C4×C11—46no—
125C2×C4×C11—46no—
126C2×C4×C11—46no—
127C2×C4×C11—46no—
128C2×C4×C11—46no—
129C2×C4×C11—46no—
130C2×C4×C11—46no—
131C23×D4C22×C1113yes—
132C22×C22⋊C4C22×C1116yes—
133C22×C22⋊C4C22×C1113yes—
134C22×C22⋊C4C22×C1113yes—
135C22×C22⋊C4C22×C1113yes—
136C22×C42C22×C1111yescharacteristic
137#392C4×C1118yescomplemented
138C2×#95C22×C1116yes—
139C2×#95C22×C1113yes—
140C2×#95C22×C1116yes—
141C2×#95C22×C1111yescharacteristic
142C22×C11—46no—
143C22×C11—412no—
144C22×C11—412no—
145C22×C11—46no—
146C22×C11—46no—
147C22×C11—86no—
148C22×C11—86no—
149C22×C11—86no—
150C22×C11—86no—
151C22×C11C4×#4111yescharacteristic
152C22×C11#51813yes—
153C22×C11#51813yes—
154C22×C11#53816yes—
155C22×C11#54016yes—
156C22×C11#56011yescharacteristic
157C22×C11#56016yes—
158C22×C11#56013yes—
159C22×C11#56013yes—
160C22×C11H(3,𝔽4)13yes—
161C4×C11—44no—
162C4×C11—46no—
163C4×C11—42no—
164C4×C11—86no—
165C25C23×C1113yes—
166C22×D4—46no—
167C22×D4—46no—
168C22×D4—43no—
169C22×D4—43no—
170C22×D4C2×C4×C11112yes—
171C23×C4C23×C1116yes—
172C23×C4C23×C1111yescharacteristic
173C23×C4C23×C1113yes—
174C23×C4C23×C1112yes—
175C2×C22⋊C4—212no—
176C2×C22⋊C4—43no—
177C2×C22⋊C4—43no—
178C2×C22⋊C4—46no—
179C2×C22⋊C4—46no—
180C2×C22⋊C4—46no—
181C2×C22⋊C4—46no—
182C2×C22⋊C4—43no—
183C2×C22⋊C4—43no—
184C2×C22⋊C4C2×C4×C11112yes—
185C2×C42—43no—
186#95—46no—
187#95—43no—
188#95—46no—
189#95C2×C4×C1114yes—
190C2×C11—86no—
191C2×C11#233313yes—
192C2×C11#237513yes—
193C2×C11#238011yescharacteristic
194C2×C11#282512yes—
195C2×C11#282816yes—
196C24—26no—
197C24—23no—
198C24—23no—
199C24—26no—
200C24—26no—
201C24—26no—
202C24—26no—
203C24—26no—
204C24C22×C4×C1116yes—
205C24C24×C1111yescharacteristic
206C2×D4—412no—
207C2×D4—424no—
208C2×D4—424no—
209C2×D4—412no—
210C2×D4—412no—
211C22×C4—23no—
212C22×C4—26no—
213C22×C4—26no—
214C22×C4—26no—
215C22×C4—23no—
216C22×C4—26no—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—26no—
220C22×C4—26no—
221C22×C4—26no—
222C22×C4—26no—
223C22×C4—26no—
224C22×C4—26no—
225C22×C4—26no—
226C22×C4C22×C4×C1116yes—
227C22×C4C22×C4×C1112yes—
228C22×C4C11×#4114yes—
229C22⋊C4—412no—
230C22⋊C4—424no—
231C22⋊C4—412no—
232C22⋊C4—412no—
233C42—44no—
234C11#1465111yescharacteristic, direct product factor, Sylow
235C23—26no—
236C23—26no—
237C23—26no—
238C23—212no—
239C23—212no—
240C23—46no—
241C23—46no—
242C23—46no—
243C23—46no—
244C23—46no—
245C23—46no—
246C23—43no—
247C23—46no—
248C23—46no—
249C23—46no—
250C23—43no—
251C23—46no—
252C23—46no—
253C23—43no—
254C23—43no—
255C23—46no—
256C23C23×C4×C1111yescharacteristic
257C23C2×C11×#4112yes—
258C23C11×H(5,𝔽2)13yes—
259C23C11×H(5,𝔽2)16yes—
260C23C11×H(5,𝔽2)13yes—
261D4—448no—
262C2×C4—26no—
263C2×C4—26no—
264C2×C4—212no—
265C2×C4—212no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—43no—
269C2×C4—46no—
270C2×C4—46no—
271C2×C4—43no—
272C2×C4—43no—
273C2×C4—46no—
274C2×C4—46no—
275C2×C4—46no—
276C2×C4—46no—
277C2×C4—46no—
278C2×C4—46no—
279C2×C4—46no—
280C22—46no—
281C22—46no—
282C22—412no—
283C22—412no—
284C22—46no—
285C22—86no—
286C22—86no—
287C22—86no—
288C22—86no—
289C22C4×C11×#4111yescharacteristic
290C22C11×#51813yes—
291C22C11×#51813yes—
292C22C11×#53816yes—
293C22C11×#54016yes—
294C22C11×#56011yescharacteristic
295C22C11×#56013yes—
296C22C11×#56016yes—
297C22C11×#56013yes—
298C22C11×H(3,𝔽4)13yes—
299C4—42no—
300C4—44no—
301C4—46no—
302C4—86no—
303C2—86no—
304C2C11×#233313yes—
305C2C11×#237513yes—
306C2C11×#238011yescharacteristic
307C2C11×#282512yes—
308C2C11×#282816yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1443C2semidirect
3. C11×#1440C2semidirect
4. C11×#1438C2semidirect
5. C11×#1437C2semidirect
12. C11×#392C4semidirect
42. #14651C11direct (N × H)
82. #1443C2×C11semidirect
83. #1440C2×C11semidirect
84. #1438C2×C11semidirect
85. #1437C2×C11semidirect
137. #392C4×C11semidirect
234. C11#14651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3922
C11×#14432
C11×#14402
C11×#14382
C11×#14372
#1465111