Finite Group Databasebeta

← #14753577

Subgroups — #14753577

Order 2816.

1470 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic
3#13068711C218yesmaximal, complemented
4#13068335C214yesmaximal, complemented
5C22×C11×#117C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#117—24no—
8C2×C11×#117—22no—
9C2×C11×#117C418yescomplemented
10C2×C11×#117C2214yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C22⋊C4—21no—
13C22×C42×C11—21no—
14C2×#66979C2212yes—
15C22×#4318C2212yes—
16#10622860—21no—
17#10622825C2214yes—
18#10622824—21no—
19C4×C22⋊Dic11—22no—
20#10622820—24no—
21C2×C22⋊(C11⋊C8)C2214yes—
22#10622167C22116yescomplemented
23C25×C11D411yescharacteristic
24C23×C4×C11—28no—
25C23×C4×C11—22no—
26C23×C4×C11C2×C414yes—
27C23×C4×C11D412yes—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D414yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C11×#117—216no—
33C11×#117—28no—
34C11×#117C2×C4116yes—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4C2×C418yes—
38C2×C11×C4⋊C4C2314yes—
39C2×C11×C22⋊C4—28no—
40C2×C11×C22⋊C4—24no—
41C2×C42×C11—28no—
42C2×C42×C11—24no—
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—24no—
45#66979—28no—
46C2×C4⋊Dic11C2314yes—
47C2×C4×Dic11—22no—
48C2×#4318—24no—
49C2×#4318—28no—
50C22×C11⋊C8C2314yes—
51C11⋊#95—24no—
52C22⋊(C11⋊C8)—28no—
53#20701—111nomaximal, Sylow
54C24×C11—24no—
55C24×C11—44no—
56C24×C11C22⋊C414yes—
57C24×C11C2×D412yes—
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—24no—
60C22×C4×C11—216no—
61C22×C4×C11—28no—
62C22×C4×C11—216no—
63C22×C4×C11—28no—
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11—48no—
67C22×C4×C11C22⋊C414yes—
68C22×C4×C11C22⋊C418yes—
69C22×C4×C11C22×C414yes—
70C22×C4×C11C22×C412yes—
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D414yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D412yes—
75C22×C4×C11#4118yes—
76C22×C4×C11C2411yescharacteristic
77C22×Dic11—24no—
78C11×C4⋊C4—28no—
79C11×C4⋊C4—24no—
80C11×C4⋊C4C22×C418yes—
81C11×C22⋊C4—216no—
82C42×C11—216no—
83C22⋊Dic11—48no—
84C22⋊Dic11—44no—
85C4⋊Dic11—28no—
86C4×Dic11—44no—
87#4318—48no—
88C2×C11⋊C8—24no—
89C2×C11⋊C8—28no—
90C22×#117D1111yescharacteristic
91C2×#407—111no—
92#2280—111no—
93#1825—118no—
94#1736—114no—
95C23×C11—24no—
96C23×C11—24no—
97C23×C11—24no—
98C23×C11—24no—
99C23×C11—28no—
100C23×C11—48no—
101C23×C11—416no—
102C23×C11C2×C22⋊C414yes—
103C23×C11C2×C22⋊C412yes—
104C23×C11#12314yes—
105C23×C11C22×D411yescharacteristic
106C2×C4×C11—24no—
107C2×C4×C11—28no—
108C2×C4×C11—28no—
109C2×C4×C11—28no—
110C2×C4×C11—216no—
111C2×C4×C11—28no—
112C2×C4×C11—416no—
113C2×C4×C11—48no—
114C2×C4×C11C2×C22⋊C414yes—
115C2×C4×C11C2×C22⋊C412yes—
116C2×C4×C11#11718yes—
117C2×C4×C11#12318yes—
118C2×C4×C11#12314yes—
119C2×C4×C11C23×C411yescharacteristic
120C2×C4×C11C22×D411yescharacteristic
121C2×C4×C11C2×#4114yes—
122C2×Dic11—44no—
123C2×Dic11—48no—
124C11⋊C8—44no—
125C24×C4C2×D1111yescharacteristic
126C22×M16—112no—
127C2×#117—24no—
128C2×#117—22no—
129C2×#117—112no—
130C2×#117Dic1118yescomplemented
131C2×#117C2×D1114yes—
132C22×C4⋊C4C2×D1112yes—
133C22×C22⋊C4—21no—
134C22×C42—21no—
135#407—224no—
136C2×C22⋊C8—114no—
137#381—221no—
138#380—114no—
139#379—221no—
140C4×C22⋊C4—222no—
141#340—1116no—
142C22×C11—28no—
143C22×C11—24no—
144C22×C11—24no—
145C22×C11—24no—
146C22×C11—24no—
147C22×C11—416no—
148C22×C11—48no—
149C22×C11#38114yes—
150C22×C11C22×C22⋊C411yescharacteristic
151C22×C11C2×#12312yes—
152C22×C11#57514yes—
153C4×C11—24no—
154C4×C11—48no—
155C4×C11#38114yes—
156C4×C11C2×#11712yes—
157C4×C11C2×#12312yes—
158Dic11—84no—
159C25C22⋊D1111yescharacteristic
160C23×C4—28no—
161C23×C4—22no—
162C23×C4C2×Dic1114yes—
163C23×C4C22⋊D1112yes—
164C23×C4C22⋊D1111yescharacteristic
165C23×C4C22⋊D1114yes—
166C23×C4C22×D1112yes—
167C23×C4C22×D1111yescharacteristic
168C2×M16—228no—
169C2×M16—224no—
170C22×C8—114no—
171#117—216no—
172#117—28no—
173#117—228no—
174#117C2×Dic11116yes—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—114no—
178C2×C4⋊C4C2×Dic1118yes—
179C2×C4⋊C4C22×D1114yes—
180C2×C22⋊C4—28no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—222no—
183C2×C22⋊C4—224no—
184C2×C42—28no—
185C2×C42—24no—
186C2×C42—222no—
187C22⋊C8—228no—
188#95—224no—
189C2×C11—24no—
190C2×C11—44no—
191C2×C11C2×#38111yescharacteristic
192C2×C11#289612yes—
193C2×C11#309314yes—
194C24—24no—
195C24—44no—
196C24C22⋊Dic1114yes—
197C24C2×C22⋊D1112yes—
198C24C2×C22⋊D1111yescharacteristic
199C22×C4—24no—
200C22×C4—216no—
201C22×C4—28no—
202C22×C4—216no—
203C22×C4—28no—
204C22×C4—28no—
205C22×C4—24no—
206C22×C4—48no—
207C22×C4—224no—
208C22×C4C22⋊Dic1114yes—
209C22×C4C22⋊Dic1118yes—
210C22×C4#433918yes—
211C22×C4C22×Dic1114yes—
212C22×C4C22×Dic1112yes—
213C22×C4C2×C22⋊D1112yes—
214C22×C4C2×C22⋊D1114yes—
215C22×C4C2×C22⋊D1111yescharacteristic
216C22×C4C2×C22⋊D1112yes—
217C22×C4C23×D1111yescharacteristic
218M16—448no—
219C2×C8—228no—
220C2×C8—224no—
221C4⋊C4—28no—
222C4⋊C4—24no—
223C4⋊C4—228no—
224C4⋊C4C22×Dic1118yes—
225C22⋊C4—216no—
226C22⋊C4—448no—
227C22⋊C4—444no—
228C42—216no—
229C42—444no—
230C11#2070111yescharacteristic, complemented, Sylow
231C23—24no—
232C23—24no—
233C23—28no—
234C23—24no—
235C23—24no—
236C23—48no—
237C23—416no—
238C23#6698214yes—
239C23C2×C22⋊Dic1114yes—
240C23C2×C22⋊Dic1112yes—
241C23C22×C22⋊D1111yescharacteristic
242C2×C4—24no—
243C2×C4—28no—
244C2×C4—28no—
245C2×C4—28no—
246C2×C4—216no—
247C2×C4—28no—
248C2×C4—416no—
249C2×C4—48no—
250C2×C4—444no—
251C2×C4—448no—
252C2×C4#6697918yes—
253C2×C4#6698218yes—
254C2×C4#6698214yes—
255C2×C4C2×C22⋊Dic1114yes—
256C2×C4C2×C22⋊Dic1112yes—
257C2×C4C2×#433914yes—
258C2×C4C23×Dic1111yescharacteristic
259C2×C4C22×C22⋊D1111yescharacteristic
260C8—444no—
261C22—28no—
262C22—24no—
263C22—24no—
264C22—24no—
265C22—24no—
266C22—416no—
267C22—48no—
268C22#1062282414yes—
269C22C2×#6698212yes—
270C22#1062335314yes—
271C22C22×C22⋊Dic1111yescharacteristic
272C4—24no—
273C4—48no—
274C4—884no—
275C4#1062282414yes—
276C4C2×#6697912yes—
277C4C2×#6698212yes—
278C2—24no—
279C2—44no—
280C2C2×#1062282411yescharacteristic
281C2#1307713512yes—
282C2#1307854714yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#117C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×#117D11
hypocenterC11#20701
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #13068711C2semidirect
4. #13068335C2semidirect
9. C2×C11×#117C4semidirect
22. #10622167C22semidirect
130. C2×#117Dic11semidirect
230. C11#20701semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130687112
#130683352
C22×C11×#1172
#2070111