Finite Group Databasebeta

← #14684568

Subgroups — #14684568

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066878C212yesmaximal, complemented
2#13066869C216yesmaximal, complemented
3#13066861C213yesmaximal
4#13066838C213yesmaximal
5C2×C11×#399C211yesmaximal, characteristic
6C24×Dic11C2211yescharacteristic
7C22×C11×C4⋊C4C2213yes—
8C22×C11×C22⋊C4C2213yes—
9C22×C22⋊Dic11C2213yes—
10C22×C4⋊Dic11C2213yes—
11C11×#399C418yescomplemented
12C2×C11×#95C2211yescharacteristic
13C2×C11⋊#95C2216yes—
14C2×C11⋊#95C2216yes—
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2216yes—
17C25×C11C2311yescharacteristic
18C23×C4×C11C2313yes—
19C23×C4×C11C2313yes—
20C23×Dic11—43no—
21C23×Dic11—43no—
22C23×Dic11Q814yes—
23C23×Dic11C2316yes—
24C23×Dic11C2312yes—
25C2×C11×C4⋊C4—43no—
26C2×C11×C4⋊C4—43no—
27C2×C11×C4⋊C4C2×C4112yescomplemented
28C2×C11×C22⋊C4—43no—
29C2×C11×C22⋊C4—43no—
30C2×C11×C22⋊C4C2×C4112yes—
31C2×C22⋊Dic11—26no—
32C2×C22⋊Dic11—43no—
33C2×C22⋊Dic11—43no—
34C2×C4⋊Dic11—43no—
35C2×C4⋊Dic11—46no—
36C11×#95C2×C414yescomplemented
37C11⋊#95—46no—
38C11⋊#95—46no—
39C11⋊#95—46no—
40C11⋊#95—43no—
41#14636—111nomaximal, Sylow
42C24×C11—23no—
43C24×C11—23no—
44C24×C11—23no—
45C24×C11—23no—
46C24×C11C22×C412yes—
47C24×C11C2×Q812yes—
48C24×C11#4112yes—
49C24×C11C2411yescharacteristic
50C22×C4×C11—26no—
51C22×C4×C11—23no—
52C22×C4×C11—26no—
53C22×C4×C11—23no—
54C22×C4×C11—26no—
55C22×C4×C11—23no—
56C22×C4×C11—23no—
57C22×C4×C11—26no—
58C22×C4×C11C22×C416yes—
59C22×C4×C11C22×C416yes—
60C22×Dic11—26no—
61C22×Dic11—26no—
62C22×Dic11—26no—
63C22×Dic11—26no—
64C22×Dic11—26no—
65C22×Dic11—26no—
66C22×Dic11—26no—
67C22×Dic11—26no—
68C22×Dic11—26no—
69C22×Dic11—412no—
70C22×Dic11—44no—
71C22×Dic11—412no—
72C22×Dic11C2×Q814yes—
73C11×C4⋊C4—412no—
74C11×C22⋊C4—412no—
75C22⋊Dic11—412no—
76C4⋊Dic11—412no—
77C2×#399D1111yescharacteristic
78#1443—112no—
79#1441—116no—
80#1439—113no—
81C22⋊#95—113no—
82C23×C11—26no—
83C23×C11—26no—
84C23×C11—26no—
85C23×C11—26no—
86C23×C11—26no—
87C23×C11—26no—
88C23×C11—41no—
89C23×C11—43no—
90C23×C11—43no—
91C23×C11—46no—
92C23×C11—43no—
93C23×C11C4×Q814yes—
94C23×C11C23×C411yescharacteristic
95C23×C11C22×Q811yescharacteristic
96C23×C11C2×#4111yescharacteristic
97C23×C11H(5,𝔽2)13yes—
98C23×C11H(5,𝔽2)13yes—
99C23×C11H(5,𝔽2)13yes—
100C23×C112−1+413yes—
101C2×C4×C11—26no—
102C2×C4×C11—26no—
103C2×C4×C11—212no—
104C2×C4×C11—212no—
105C2×C4×C11—43no—
106C2×C4×C11—46no—
107C2×C4×C11—43no—
108C2×C4×C11—43no—
109C2×C4×C11—46no—
110C2×C4×C11—43no—
111C2×Dic11—212no—
112C2×Dic11—416no—
113C2×Dic11—42no—
114C2×Dic11—46no—
115C2×Dic11—46no—
116C2×Dic11—46no—
117C2×Dic11—46no—
118C2×Dic11—46no—
119C2×Dic11—46no—
120C2×Dic11—46no—
121C2×Dic11—46no—
122C24×C4—111no—
123C22×C4⋊C4—113no—
124C22×C4⋊C4C2×D1113yes—
125C22×C22⋊C4—113no—
126C22×C22⋊C4C2×D1113yes—
127#399Dic1118yescomplemented
128C2×#95—116no—
129C2×#95—116no—
130C2×#95—113no—
131C2×#95—116no—
132C2×#95C2×D1111yescharacteristic
133C22×C11—212no—
134C22×C11—46no—
135C22×C11—42no—
136C22×C11—46no—
137C22×C11—42no—
138C22×C11—46no—
139C22×C11—42no—
140C22×C11C2×C4×Q811yescharacteristic
141C22×C11#51813yes—
142C22×C11#52013yes—
143C22×C11#53813yes—
144C22×C11#53913yes—
145C22×C11#54313yes—
146C22×C11#54413yes—
147C22×C11#56013yes—
148C22×C11#56011yescharacteristic
149C22×C11#56013yes—
150C22×C11#56216yes—
151C22×C11#56313yes—
152C4×C11—46no—
153C4×C11—46no—
154Dic11—44no—
155Dic11—86no—
156C25C22×D1111yescharacteristic
157C23×C4—112no—
158C23×C4—114no—
159C23×C4—116no—
160C23×C4—443no—
161C23×C4—443no—
162C23×C4C22×D1113yes—
163C23×C4C22×D1113yes—
164C2×C4⋊C4—43no—
165C2×C4⋊C4—43no—
166C2×C4⋊C4—443no—
167C2×C4⋊C4—446no—
168C2×C4⋊C4C2×Dic11112yescomplemented
169C2×C22⋊C4—43no—
170C2×C22⋊C4—43no—
171C2×C22⋊C4—226no—
172C2×C22⋊C4—443no—
173C2×C22⋊C4—443no—
174C2×C22⋊C4C2×Dic11112yes—
175#95—443no—
176#95—446no—
177#95—446no—
178#95—446no—
179#95C2×Dic1114yescomplemented
180C2×C11—44no—
181C2×C11#232913yes—
182C2×C11#237613yes—
183C2×C11#238011yescharacteristic
184C2×C11#282613yes—
185C2×C11#283411yescharacteristic
186C2×C11#284113yes—
187C2×C11#284211yescharacteristic
188C24—23no—
189C24—23no—
190C24—23no—
191C24—23no—
192C24Q8×D1112yes—
193C24#434312yes—
194C24C22×Dic1112yes—
195C24C23×D1111yescharacteristic
196C22×C4—23no—
197C22×C4—26no—
198C22×C4—23no—
199C22×C4—23no—
200C22×C4—23no—
201C22×C4—26no—
202C22×C4—26no—
203C22×C4—26no—
204C22×C4—114no—
205C22×C4—226no—
206C22×C4—226no—
207C22×C4—226no—
208C22×C4—226no—
209C22×C4—226no—
210C22×C4—226no—
211C22×C4—226no—
212C22×C4—226no—
213C22×C4—226no—
214C22×C4—4412no—
215C22×C4—444no—
216C22×C4—4412no—
217C22×C4C22×Dic1116yes—
218C22×C4C22×Dic1116yes—
219C4⋊C4—412no—
220C4⋊C4—4412no—
221C22⋊C4—412no—
222C22⋊C4—4412no—
223C11#1463611yescharacteristic, complemented, Sylow
224C23—26no—
225C23—26no—
226C23—26no—
227C23—26no—
228C23—26no—
229C23—26no—
230C23—41no—
231C23—43no—
232C23—43no—
233C23—43no—
234C23—46no—
235C23Q8×Dic1114yes—
236C23#6703713yes—
237C23#6703713yes—
238C23C2×Q8×D1111yescharacteristic
239C23C2×#434311yescharacteristic
240C23#6704213yes—
241C23#6704313yes—
242C23C23×Dic1111yescharacteristic
243C2×C4—26no—
244C2×C4—26no—
245C2×C4—212no—
246C2×C4—212no—
247C2×C4—43no—
248C2×C4—43no—
249C2×C4—46no—
250C2×C4—43no—
251C2×C4—43no—
252C2×C4—46no—
253C2×C4—2212no—
254C2×C4—4416no—
255C2×C4—442no—
256C2×C4—446no—
257C2×C4—446no—
258C2×C4—446no—
259C2×C4—446no—
260C2×C4—446no—
261C2×C4—446no—
262C2×C4—446no—
263C2×C4—446no—
264C22—212no—
265C22—42no—
266C22—46no—
267C22—42no—
268C22—46no—
269C22—42no—
270C22—46no—
271C22#1062315413yes—
272C22#1062316513yes—
273C22#1062317513yes—
274C22#1062317613yes—
275C22#1062318213yes—
276C22#1062319713yes—
277C22#1062319816yes—
278C22#1062325111yescharacteristic
279C22#1062325113yes—
280C22#1062332913yes—
281C22C2×Q8×Dic1111yescharacteristic
282C22#1062335813yes—
283C4—46no—
284C4—46no—
285C4—444no—
286C4—886no—
287C2—44no—
288C2#1307135113yes—
289C2#1307176413yes—
290C2#1307179311yescharacteristic
291C2#1307671613yes—
292C2#1307680211yescharacteristic
293C2#1307687813yes—
294C2#1307688111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#399C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#399D11
hypocenterC11#14636
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. #13066878C2semidirect
2. #13066869C2semidirect
11. C11×#399C4semidirect
27. C2×C11×C4⋊C4C2×C4semidirect
36. C11×#95C2×C4semidirect
127. #399Dic11semidirect
168. C2×C4⋊C4C2×Dic11semidirect
179. #95C2×Dic11semidirect
223. C11#14636semidirect

Maximal subgroups

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

subgroupindex
#130668782
#130668692
#130668612
#130668382
C2×C11×#3992
#1463611