Finite Group Databasebeta

← #14647221

Subgroups — #14647221

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066930C212yesmaximal
2#13066449C212yesmaximal, complemented
3#13066445C212yesmaximal, complemented
4C4×C11×#117C211yesmaximal, characteristic
5C2×C11×#117C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C22×C42×C11C411yescharacteristic
8C4×C11×C4⋊C4—22no—
9C4×C11×C22⋊C4—22no—
10C11×#376C411yescharacteristic
11C11×#376C2211yescharacteristic
12C43×C11C411yescharacteristic
13C43×C11C2211yescharacteristic
14#10622538C2214yes—
15#10622166—22no—
16#10622163—22no—
17C23×C4×C11—21no—
18C23×C4×C11C2×C411yescharacteristic
19C11×#117—22no—
20C11×#117—22no—
21C11×#117—22no—
22C11×#117C814yescomplemented
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4D412yes—
25C2×C11×C22⋊C4—21no—
26C2×C11×C22⋊C4D412yes—
27C2×C42×C11—21no—
28C2×C42×C11—22no—
29C2×C42×C11—22no—
30C2×C42×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C11×#95—22no—
39C11×#95—22no—
40C22⋊(C11⋊C8)—24no—
41C4⋊(C11⋊C8)—24no—
42C4×C11⋊C8—24no—
43#8731—111nomaximal, Sylow
44C24×C11C22⋊C411yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—24no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—44no—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C2×C812yes—
58C22×C4×C11M1612yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D412yes—
61C11×C4⋊C4—24no—
62C11×C4⋊C4—24no—
63C11×C22⋊C4—24no—
64C11×C22⋊C4—24no—
65C42×C11—24no—
66C42×C11—21no—
67C42×C11—21no—
68C42×C11—21no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—44no—
73C42×C11—44no—
74C42×C11C2×C812yes—
75C42×C11C2×C812yes—
76C42×C11M1612yes—
77C42×C11M1612yes—
78C42×C11#4112yes—
79C42×C11#4112yes—
80C2×C11⋊C8—44no—
81C4×#117D1111yescharacteristic
82#1458—112no—
83#1276—112no—
84#1274—112no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—42no—
88C23×C11C22⋊C812yes—
89C23×C11C2×C22⋊C411yescharacteristic
90C2×C4×C11—24no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—42no—
103C2×C4×C11—48no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11C22⋊C812yes—
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11#11711yescharacteristic
111C2×C4×C11#12314yes—
112C2×C4×C11C22×C811yescharacteristic
113C2×C4×C11C2×M1611yescharacteristic
114C2×C4×C11C2×M1611yescharacteristic
115C2×C4×C11C2×M1611yescharacteristic
116C11⋊C8—84no—
117C2×#117Dic1111yescharacteristic
118C2×#117C2×D1111yescharacteristic
119C22×C42Dic1111yescharacteristic
120#431—114no—
121C4×C4⋊C4—22no—
122C4×C22⋊C4—22no—
123#376Dic1111yescharacteristic
124#376C2×D1111yescharacteristic
125C43Dic1111yescharacteristic
126C43C2×D1111yescharacteristic
127#324—222no—
128#323—222no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11#38111yescharacteristic
135C22×C11C2×C22⋊C811yescharacteristic
136C22×C11#40711yescharacteristic
137C4×C11—24no—
138C4×C11—22no—
139C4×C11—24no—
140C4×C11—42no—
141C4×C11—42no—
142C4×C11—42no—
143C4×C11—42no—
144C4×C11#43111yescharacteristic
145C4×C11#43111yescharacteristic
146C4×C11#43211yescharacteristic
147C4×C11#43211yescharacteristic
148C23×C4—21no—
149C23×C4C2×Dic1111yescharacteristic
150#117—22no—
151#117—22no—
152#117—22no—
153#117C11⋊C814yescomplemented
154C2×C4⋊C4—21no—
155C2×C4⋊C4C22⋊D1112yes—
156C2×C22⋊C4—21no—
157C2×C22⋊C4C22⋊D1112yes—
158C2×C42—21no—
159C2×C42—22no—
160C2×C42—22no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42C2×Dic1111yescharacteristic
164C2×C42C2×Dic1111yescharacteristic
165C2×C42C2×Dic1111yescharacteristic
166C2×C42C2×Dic1111yescharacteristic
167C2×C42C2×Dic1111yescharacteristic
168C2×C42C22×D1111yescharacteristic
169C4⋊C8—224no—
170C22⋊C8—224no—
171C4×C8—224no—
172#95—22no—
173#95—22no—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11—42no—
177C2×C11#181711yescharacteristic
178C2×C11#182712yes—
179C24C22⋊Dic1111yescharacteristic
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—24no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—44no—
190C22×C4C2×C11⋊C812yes—
191C22×C4#431812yes—
192C22×C4C22⋊Dic1111yescharacteristic
193C22×C4C22⋊Dic1112yes—
194C22×C4C22×Dic1111yescharacteristic
195C22×C4C2×C22⋊D1112yes—
196C2×C8—444no—
197C4⋊C4—24no—
198C4⋊C4—24no—
199C22⋊C4—24no—
200C22⋊C4—24no—
201C42—24no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—44no—
209C42—44no—
210C42C2×C11⋊C812yes—
211C42C2×C11⋊C812yes—
212C42#431812yes—
213C42#431812yes—
214C42#433912yes—
215C42#433912yes—
216C11#873111yescharacteristic, complemented, Sylow
217C23—21no—
218C23—21no—
219C23—42no—
220C23C22⋊(C11⋊C8)12yes—
221C23C2×C22⋊Dic1111yescharacteristic
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—48no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4C22⋊(C11⋊C8)12yes—
241C2×C4C22×C11⋊C811yescharacteristic
242C2×C4C2×#431811yescharacteristic
243C2×C4C2×#431811yescharacteristic
244C2×C4C2×#431811yescharacteristic
245C2×C4#6697911yescharacteristic
246C2×C4#6697911yescharacteristic
247C2×C4#6698214yes—
248C8—884no—
249C22—22no—
250C22—22no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×C22⋊(C11⋊C8)11yescharacteristic
255C22#1062282011yescharacteristic
256C22#1062282411yescharacteristic
257C4—24no—
258C4—22no—
259C4—24no—
260C4—42no—
261C4—42no—
262C4—42no—
263C4—42no—
264C4#1062253811yescharacteristic
265C4#1062253811yescharacteristic
266C4#1062253911yescharacteristic
267C4#1062253911yescharacteristic
268C2—21no—
269C2—21no—
270C2—42no—
271C2#1306868411yescharacteristic
272C2#1306872012yes—
subgroupG/H
centerC2×C4#66979
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC4×C11×#117C2
socleC22×C11#381
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×#117D11
hypocenterC11#8731
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #376 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #13066449C2semidirect
3. #13066445C2semidirect
22. C11×#117C8semidirect
153. #117C11⋊C8semidirect
216. C11#8731semidirect

Maximal subgroups

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

subgroupindex
#130669302
#130664492
#130664452
C4×C11×#1172
#873111