Finite Group Databasebeta

← #13075663

Subgroups — #13075663

Order 1408.

560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#397C211yesmaximal, characteristic, complemented
2#10622603C212yesmaximal, complemented
3#10622568C212yesmaximal
4#10622568C211yesmaximal, characteristic
5#10622564C212yesmaximal, complemented
6#10622560C211yesmaximal, characteristic, complemented
7#10622287C212yesmaximal, complemented
8#10622286C212yesmaximal, complemented
9#10622283C212yesmaximal, complemented
10C24×D11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic, complemented
12C2×C11×C4⋊C4C2211yescharacteristic, complemented
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2212yescomplemented
24C2×C4×Dic11C2212yescomplemented
25C11×#95C2212yescomplemented
26C11×#95C2211yescharacteristic, complemented
27C11⋊#95C2211yescharacteristic, complemented
28C11⋊#95C2212yescomplemented
29C11⋊#95C2212yescomplemented
30C11⋊#95C2212yescomplemented
31C24×C11C2311yescharacteristic
32C23×D11—22no—
33C23×D11—24no—
34C23×D11—41no—
35C23×D11—42no—
36C23×D11—41no—
37C23×D11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C2×Dic22—42no—
46C2×Dic22—41no—
47C11×C4⋊C4—41no—
48C11×C22⋊C4—24no—
49C11×C22⋊C4—41no—
50C22⋊Dic11—41no—
51C22⋊Dic11—42no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—42no—
55(C2×D11)⋊C4—42no—
56(C2×D11)⋊C4—42no—
57(C2×D11)⋊C4—42no—
58C4⋊Dic11—42no—
59C4×Dic11—42no—
60#2736—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—21no—
63C23×C11—22no—
64C23×C11—21no—
65C23×C11#4112yes—
66C23×C11C2411yescharacteristic
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—44no—
74C22×D11—48no—
75C22×D11—48no—
76C22×D11—44no—
77C22×D11—44no—
78C22×D11#4114yes—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98Dic22—44no—
99#397—112no—
100#397D1111yescharacteristic, complemented
101#393—111no—
102#393—112no—
103#388—112no—
104#388—112no—
105#388—112no—
106#379—111no—
107#379—112no—
108C22×C11—22no—
109C22×C11—24no—
110C22×C11—42no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11C2×#4111yescharacteristic
114C22×C11C2×#4112yes—
115C22×C11H(5,𝔽2)11yescharacteristic
116C22×C11H(5,𝔽2)11yescharacteristic
117C22×C11H(5,𝔽2)12yes—
118C2×D11—24no—
119C2×D11—24no—
120C2×D11—24no—
121C2×D11—416no—
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C4×C11—42no—
127C4×C11—42no—
128C4×C11—41no—
129C4×C11—41no—
130Dic11—42no—
131Dic11—42no—
132Dic11—42no—
133C25—111no—
134C22×Q8—111no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4C2×D1111yescharacteristic, complemented
137C2×C22⋊C4—112no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—111no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4—112no—
142C2×C22⋊C4—112no—
143C2×C22⋊C4—112no—
144C2×C22⋊C4—112no—
145C2×C22⋊C4C2×D1112yes—
146C2×C22⋊C4C2×D1111yescharacteristic
147C2×C42—112no—
148#95—112no—
149#95—111no—
150#95—112no—
151#95—112no—
152#95C2×D1112yescomplemented
153#95C2×D1111yescharacteristic, complemented
154C2×C11—42no—
155C2×C11#53812yes—
156C2×C11#53811yescharacteristic
157C2×C11#55112yes—
158C2×C11#55111yescharacteristic
159C2×C11H(3,𝔽4)11yescharacteristic
160D11—44no—
161C24—112no—
162C24—224no—
163C24—222no—
164C24—441no—
165C24—442no—
166C24—441no—
167C24C22×D1111yescharacteristic
168C2×Q8—441no—
169C2×Q8—442no—
170C22×C4—112no—
171C22×C4—112no—
172C22×C4—112no—
173C22×C4C22×D1111yescharacteristic
174C22×C4C22×D1112yes—
175C22×C4C22×D1111yescharacteristic
176C22×C4C22×D1112yes—
177C4⋊C4—41no—
178C4⋊C4—442no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—224no—
182C22⋊C4—224no—
183C22⋊C4—442no—
184C22⋊C4—442no—
185C22⋊C4—442no—
186C22⋊C4—442no—
187C22⋊C4—441no—
188C22⋊C4—442no—
189C42—442no—
190C11#273611yescharacteristic, complemented, Sylow
191C23—21no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—114no—
196C23—222no—
197C23—222no—
198C23—222no—
199C23—222no—
200C23—222no—
201C23—222no—
202C23—448no—
203C23—444no—
204C23—444no—
205C23—448no—
206C23—444no—
207C23#434112yes—
208C23C23×D1111yescharacteristic
209Q8—444no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C22—22no—
230C22—24no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22—224no—
235C22—224no—
236C22—224no—
237C22—4416no—
238C22—442no—
239C22—442no—
240C22—442no—
241C22—442no—
242C22C2×#434111yescharacteristic
243C22#6703711yescharacteristic
244C22#41×D1112yes—
245C22#6704211yescharacteristic
246C22#6704212yes—
247C4—42no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—442no—
252C4—442no—
253C4—442no—
254C2—42no—
255C2—444no—
256C2#1062314811yescharacteristic
257C2#1062318912yes—
258C2#1062319011yescharacteristic
259C2#1062321411yescharacteristic
260C2#1062323512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×D11C22
hypercenter#397D11
hypocenterC11#2736
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C11×#397C2semidirect
2. #10622603C2semidirect
5. #10622564C2semidirect
6. #10622560C2semidirect
7. #10622287C2semidirect
8. #10622286C2semidirect
9. #10622283C2semidirect
11. C22×Dic22C22semidirect
12. C2×C11×C4⋊C4C22semidirect
23. C2×C4⋊Dic11C22semidirect
24. C2×C4×Dic11C22semidirect
25. C11×#95C22semidirect
26. C11×#95C22semidirect
27. C11⋊#95C22semidirect
28. C11⋊#95C22semidirect
29. C11⋊#95C22semidirect
30. C11⋊#95C22semidirect
100. #397D11semidirect
136. C2×C4⋊C4C2×D11semidirect
152. #95C2×D11semidirect
153. #95C2×D11semidirect
190. C11#2736semidirect

Maximal subgroups

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

subgroupindex
C11×#3972
#106226032
#106225682
#106225642
#106225602
#106222872
#106222862
#106222832
#273611