Finite Group Databasebeta

← #13074951

Subgroups — #13074951

Order 1408.

1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#66990C212yesmaximal, complemented
2C2×#66935C214yesmaximal, complemented
3C11×#390C211yesmaximal, characteristic, complemented
4#10622604C212yesmaximal, complemented
5#10622574C214yesmaximal, complemented
6#10622552C212yesmaximal, complemented
7C24×D11C2212yescomplemented
8C22×D4×C11C2211yescharacteristic
9C22×C22⋊D11C2214yes—
10C22×D44C2212yes—
11C22×D44C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic, complemented
13C2×C11×C22⋊C4C2214yescomplemented
14C2×C42×C11C2211yescharacteristic, complemented
15C2×C22⋊Dic11C2212yescomplemented
16#66990—28no—
17C2×(C2×D11)⋊C4C2214yescomplemented
18C2×(C2×D11)⋊C4C2214yescomplemented
19C2×(C2×D11)⋊C4C2214yescomplemented
20C2×C4⋊Dic11C2212yescomplemented
21#66935—216no—
22C11⋊#95C2212yescomplemented
23C24×C11C2312yes—
24C23×D11—24no—
25C23×D11—28no—
26C23×D11—42no—
27C23×D11—42no—
28C23×D11—44no—
29C23×D11C2314yes—
30C2×D4×C11—41no—
31C2×D4×C11—41no—
32C2×D4×C11D414yescomplemented
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—28no—
37C2×C22⋊D11—28no—
38C2×C22⋊D11—44no—
39C22×Dic11C2314yes—
40C2×D44—28no—
41C2×D44—42no—
42C2×D44—42no—
43C2×D44—42no—
44C2×D44D418yescomplemented
45C11×C4⋊C4—41no—
46C11×C22⋊C4—28no—
47C42×C11—41no—
48C22⋊Dic11—24no—
49(C2×D11)⋊C4—28no—
50(C2×D11)⋊C4—28no—
51(C2×D11)⋊C4—28no—
52C4⋊Dic11—42no—
53#2679—111nomaximal, Sylow
54C23×C11—24no—
55C23×C11—24no—
56C23×C11—22no—
57C23×C11—22no—
58C23×C11C2×D414yes—
59C23×C11C2411yescharacteristic
60C22×D11—24no—
61C22×D11—24no—
62C22×D11—24no—
63C22×D11—24no—
64C22×D11—24no—
65C22×D11—24no—
66C22×D11—48no—
67C22×D11—416no—
68C22×D11—416no—
69C22×D11—48no—
70C22×D11—48no—
71C22×D11C2×D418yes—
72D4×C11—44no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—24no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×D414yes—
81C22⋊D11—416no—
82C2×Dic11—24no—
83C2×Dic11—24no—
84C2×Dic11—24no—
85D44—48no—
86D44—48no—
87C2×#120—112no—
88C2×#120—114no—
89#394—112no—
90#394—114no—
91#390—112no—
92#390D1111yescharacteristic, complemented
93C22×C11—24no—
94C22×C11—28no—
95C22×C11—44no—
96C22×C11—42no—
97C22×C11—42no—
98C22×C11C22×D411yescharacteristic
99C22×C11C22×D412yes—
100C22×C11H(5,𝔽2)11yescharacteristic
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)12yes—
103C2×D11—28no—
104C2×D11—28no—
105C2×D11—28no—
106C2×D11—432no—
107C2×D11—44no—
108C2×D11—44no—
109C2×D11—44no—
110C2×D11—44no—
111C4×C11—22no—
112C4×C11—24no—
113C4×C11—42no—
114Dic11—44no—
115C25—112no—
116C22×D4—114no—
117C22×D4—112no—
118C22×D4—112no—
119C22×D4C2×D1111yescharacteristic
120#120—2216no—
121#120—228no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4C2×D1111yescharacteristic, complemented
124C2×C22⋊C4—112no—
125C2×C22⋊C4—114no—
126C2×C22⋊C4—114no—
127C2×C22⋊C4—114no—
128C2×C22⋊C4C2×D1114yescomplemented
129C2×C42C2×D1111yescharacteristic, complemented
130#95—112no—
131C2×C11—44no—
132C2×C11#53411yescharacteristic
133C2×C11#53412yes—
134C2×C11D4211yescharacteristic
135C2×C11D4212yes—
136C2×C11H(3,𝔽4)11yescharacteristic
137D11—48no—
138C24—114no—
139C24—228no—
140C24—224no—
141C24—442no—
142C24—442no—
143C24—444no—
144C24C22×D1112yes—
145C2×D4—41no—
146C2×D4—41no—
147C2×D4—118no—
148C2×D4—228no—
149C2×D4—228no—
150C2×D4—228no—
151C2×D4—442no—
152C2×D4—442no—
153C2×D4—442no—
154C2×D4—444no—
155C2×D4D4414yescomplemented
156C22×C4—114no—
157C22×C4C22×D1112yes—
158C22×C4C22×D1111yescharacteristic
159C22×C4C22×D1112yes—
160C4⋊C4—41no—
161C4⋊C4—442no—
162C22⋊C4—28no—
163C22⋊C4—228no—
164C22⋊C4—224no—
165C22⋊C4—228no—
166C22⋊C4—228no—
167C42—41no—
168C11#267911yescharacteristic, complemented, Sylow
169C23—24no—
170C23—22no—
171C23—22no—
172C23—24no—
173C23—118no—
174C23—224no—
175C23—224no—
176C23—224no—
177C23—224no—
178C23—224no—
179C23—224no—
180C23—4416no—
181C23—448no—
182C23—448no—
183C23—4416no—
184C23—448no—
185C23C2×D4414yes—
186C23C23×D1111yescharacteristic
187D4—44no—
188D4—448no—
189D4—448no—
190D4—4416no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—224no—
198C2×C4—224no—
199C2×C4—224no—
200C2×C4C2×D4412yes—
201C2×C4D4×D1114yes—
202C22—24no—
203C22—28no—
204C22—42no—
205C22—44no—
206C22—42no—
207C22—228no—
208C22—228no—
209C22—228no—
210C22—4432no—
211C22—444no—
212C22—444no—
213C22—444no—
214C22—444no—
215C22C22×D4411yescharacteristic
216C22C2×D4×D1112yes—
217C22#6703711yescharacteristic
218C22#6703711yescharacteristic
219C22#6704212yes—
220C4—22no—
221C4—24no—
222C4—42no—
223C4—444no—
224C2—44no—
225C2—448no—
226C2#1062302411yescharacteristic
227C2D4×D4412yes—
228C2#1062313612yes—
229C2#1062321411yescharacteristic
230C2#1062324811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2679
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66990C2semidirect
2. C2×#66935C2semidirect
3. C11×#390C2semidirect
4. #10622604C2semidirect
5. #10622574C2semidirect
6. #10622552C2semidirect
7. C24×D11C22semidirect
12. C2×C11×C4⋊C4C22semidirect
13. C2×C11×C22⋊C4C22semidirect
14. C2×C42×C11C22semidirect
15. C2×C22⋊Dic11C22semidirect
17. C2×(C2×D11)⋊C4C22semidirect
18. C2×(C2×D11)⋊C4C22semidirect
19. C2×(C2×D11)⋊C4C22semidirect
20. C2×C4⋊Dic11C22semidirect
22. C11⋊#95C22semidirect
32. C2×D4×C11D4semidirect
44. C2×D44D4semidirect
92. #390D11semidirect
123. C2×C4⋊C4C2×D11semidirect
128. C2×C22⋊C4C2×D11semidirect
129. C2×C42C2×D11semidirect
155. C2×D4D44semidirect
168. C11#2679semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669352
C11×#3902
#106226042
#106225742
#106225522
#267911