Finite Group Databasebeta

← #13072492

Subgroups — #13072492

Order 1408.

660 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66988C212yesmaximal, complemented
2C2×D4×Dic11C212yesmaximal, complemented
3C11×#392C211yesmaximal, characteristic
4#10622835C212yesmaximal, complemented
5#10622563C212yesmaximal, complemented
6#10622562C211yesmaximal, characteristic, complemented
7#10622559C211yesmaximal, characteristic, complemented
8#10622558C212yesmaximal, complemented
9#10622260C212yesmaximal, complemented
10C22×D4×C11C2212yes—
11C22×D4×C11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C23×Dic11C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21#66988—28no—
22D4×Dic11—28no—
23C2×C4⋊Dic11C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2212yes—
29C11×#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C24×C11C2312yes—
34C24×C11C2311yescharacteristic
35C2×D4×C11—24no—
36C2×D4×C11—24no—
37C2×D4×C11—24no—
38C2×D4×C11—24no—
39C2×D4×C11—41no—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×Dic11—24no—
44C22×Dic11—24no—
45C22×Dic11—24no—
46C22×Dic11—41no—
47C22×Dic11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C11×C22⋊C4—24no—
53C11×C22⋊C4—41no—
54C22⋊Dic11—24no—
55C22⋊Dic11—24no—
56C22⋊Dic11—24no—
57C22⋊Dic11—22no—
58C22⋊Dic11D418yescomplemented
59C4⋊Dic11—24no—
60C4⋊Dic11—41no—
61Dic11⋊C4—24no—
62Dic11⋊C4—24no—
63Dic11⋊C4—24no—
64C4×Dic11—24no—
65#2455—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11C2×D414yes—
77C23×C11#4112yes—
78C23×C11C2411yescharacteristic
79D4×C11—216no—
80D4×C11—44no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11#4114yes—
88C2×Dic11—22no—
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—
98C2×Dic11—44no—
99C2×Dic11—48no—
100C2×Dic11C2×D414yes—
101C2×Dic11C2×D414yes—
102C2×#123—112no—
103C2×C4×D4—112no—
104#399—111no—
105#394—112no—
106#392D1111yescharacteristic
107#389—112no—
108#388—112no—
109#385—111no—
110#385—112no—
111C22×C11—24no—
112C22×C11—24no—
113C22×C11—22no—
114C22×C11—24no—
115C22×C11—24no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11—41no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—41no—
123C22×C11C22×D412yes—
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4112yes—
126C22×C11H(5,𝔽2)11yescharacteristic
127C22×C112−1+411yescharacteristic
128C4×C11—24no—
129C4×C11—41no—
130C4×C11—41no—
131Dic11—24no—
132Dic11—24no—
133Dic11—42no—
134Dic11—42no—
135C22×D4C2×D1112yes—
136C22×D4C2×D1111yescharacteristic
137C23×C4—111no—
138C23×C4—112no—
139#123—228no—
140C4×D4—228no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—111no—
146C2×C22⋊C4—112no—
147C2×C22⋊C4—112no—
148C2×C22⋊C4—112no—
149C2×C22⋊C4—112no—
150C2×C22⋊C4—111no—
151C2×C22⋊C4C2×D1112yes—
152C2×C22⋊C4C2×D1111yescharacteristic
153C2×C42—112no—
154#95—112no—
155#95—112no—
156#95—111no—
157#95C2×D1111yescharacteristic
158C2×C11—44no—
159C2×C11—42no—
160C2×C11#52512yes—
161C2×C11#53911yescharacteristic
162C2×C11D4211yescharacteristic
163C2×C11#54712yes—
164C2×C11#55911yescharacteristic
165C24C22×D1112yes—
166C24C22×D1111yescharacteristic
167C2×D4—24no—
168C2×D4—24no—
169C2×D4—24no—
170C2×D4—24no—
171C2×D4—41no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—112no—
175C22×C4—112no—
176C22×C4—224no—
177C22×C4—224no—
178C22×C4—224no—
179C22×C4—441no—
180C22×C4—442no—
181C22×C4C22×D1111yescharacteristic
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1112yes—
184C4⋊C4—224no—
185C4⋊C4—224no—
186C4⋊C4—224no—
187C4⋊C4—224no—
188C4⋊C4—441no—
189C22⋊C4—24no—
190C22⋊C4—41no—
191C22⋊C4—118no—
192C22⋊C4—224no—
193C22⋊C4—224no—
194C22⋊C4—224no—
195C22⋊C4—222no—
196C42—224no—
197C11#245511yescharacteristic, complemented, Sylow
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23D4×D1114yes—
209C23#434112yes—
210C23C23×D1111yescharacteristic
211D4—216no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—114no—
220C2×C4—114no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—444no—
232C2×C4—448no—
233C2×C4#434114yes—
234C22—24no—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—24no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22C2×D4×D1112yes—
247C22C2×#434112yes—
248C22C2×#434111yescharacteristic
249C22#6703711yescharacteristic
250C22#6704311yescharacteristic
251C4—24no—
252C4—41no—
253C4—41no—
254C4—224no—
255C4—224no—
256C4—442no—
257C4—442no—
258C2—44no—
259C2—42no—
260C2#1062311712yes—
261C2#1062312111yescharacteristic
262C2#1062313311yescharacteristic
263C2#1062314212yes—
264C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC11×#392C2
hypercenter#392D11
hypocenterC11#2455
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66988C2semidirect
2. C2×D4×Dic11C2semidirect
4. #10622835C2semidirect
5. #10622563C2semidirect
6. #10622562C2semidirect
7. #10622559C2semidirect
8. #10622558C2semidirect
9. #10622260C2semidirect
58. C22⋊Dic11D4semidirect
197. C11#2455semidirect

Maximal subgroups

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

subgroupindex
C2×#669882
C2×D4×Dic112
C11×#3922
#106228352
#106225632
#106225622
#106225592
#106225582
#106222602
#245511