Finite Group Databasebeta

← #13072498

Subgroups — #13072498

Order 1408.

660 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×C22⋊D11C212yesmaximal, complemented
2C2×#66947C212yesmaximal, complemented
3C11×#385C211yesmaximal, characteristic, complemented
4#10622585C212yesmaximal, complemented
5#10622573C211yesmaximal, characteristic
6#10622572C212yesmaximal, complemented
7#10622562C211yesmaximal, characteristic, complemented
8#10622282C212yesmaximal, complemented
9#10622281C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C4×C22⋊D11—28no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2212yes—
28#66947—28no—
29C11×#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2211yescharacteristic
33C24×C11C2311yescharacteristic
34C23×D11C2312yes—
35C22×C4×C11—24no—
36C22×C4×C11—41no—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C2×C22⋊D11—24no—
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×D44—24no—
48C2×D44—41no—
49C2×C4×D11—24no—
50C2×C4×D11—24no—
51C2×C4×D11—42no—
52C11×C4⋊C4—24no—
53C11×C22⋊C4—22no—
54C11×C22⋊C4—41no—
55C22⋊Dic11—24no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—24no—
58(C2×D11)⋊C4—24no—
59(C2×D11)⋊C4D418yescomplemented
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—21no—
69C23×C11—21no—
70C23×C11#4112yes—
71C23×C11C2411yescharacteristic
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11C2×D414yes—
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—21no—
87C2×C4×C11—21no—
88C2×C4×C11—44no—
89C2×C4×C11C2×D414yes—
90C22⋊D11—216no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11C2×D414yes—
99C2×Dic11#4114yes—
100D44—44no—
101C4×D11—48no—
102C2×#123—112no—
103C2×C4×D4—112no—
104#399—111no—
105#394—112no—
106#392—111no—
107#389—112no—
108#388—112no—
109#385—112no—
110#385D1111yescharacteristic, complemented
111C22×C11—24no—
112C22×C11—22no—
113C22×C11—41no—
114C22×C11—42no—
115C22×C11—41no—
116C22×C11C22×D412yes—
117C22×C11C2×#4111yescharacteristic
118C22×C11C2×#4112yes—
119C22×C11H(5,𝔽2)11yescharacteristic
120C22×C112−1+411yescharacteristic
121C2×D11—24no—
122C2×D11—24no—
123C2×D11—24no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—42no—
128C4×C11—24no—
129C4×C11—42no—
130C4×C11—41no—
131C4×C11—41no—
132Dic11—24no—
133Dic11—24no—
134Dic11—42no—
135C22×D4—112no—
136C22×D4—111no—
137C23×C4—112no—
138C23×C4C2×D1111yescharacteristic
139#123—228no—
140C4×D4—228no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4C2×D1112yes—
146C2×C22⋊C4—112no—
147C2×C22⋊C4—112no—
148C2×C22⋊C4—112no—
149C2×C22⋊C4—112no—
150C2×C22⋊C4—112no—
151C2×C22⋊C4C2×D1111yescharacteristic
152C2×C22⋊C4C2×D1111yescharacteristic
153C2×C42—112no—
154#95—112no—
155#95—111no—
156#95—111no—
157#95C2×D1112yes—
158C2×C11—42no—
159C2×C11#52512yes—
160C2×C11#53911yescharacteristic
161C2×C11D4211yescharacteristic
162C2×C11#54712yes—
163C2×C11#55911yescharacteristic
164D11—44no—
165C24—112no—
166C24C22×D1111yescharacteristic
167C2×D4—224no—
168C2×D4—224no—
169C2×D4—224no—
170C2×D4—224no—
171C2×D4—441no—
172C22×C4—24no—
173C22×C4—41no—
174C22×C4—112no—
175C22×C4—112no—
176C22×C4—112no—
177C22×C4—224no—
178C22×C4—224no—
179C22×C4—442no—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1112yes—
184C4⋊C4—24no—
185C4⋊C4—224no—
186C4⋊C4—224no—
187C4⋊C4—224no—
188C4⋊C4—441no—
189C22⋊C4—22no—
190C22⋊C4—41no—
191C22⋊C4—118no—
192C22⋊C4—224no—
193C22⋊C4—224no—
194C22⋊C4—224no—
195C22⋊C4—224no—
196C42—224no—
197C11#245511yescharacteristic, complemented, Sylow
198C23—22no—
199C23—21no—
200C23—21no—
201C23—22no—
202C23—114no—
203C23—222no—
204C23—222no—
205C23—222no—
206C23—222no—
207C23—222no—
208C23—222no—
209C23#433912yes—
210C23C23×D1111yescharacteristic
211D4—2216no—
212D4—444no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—44no—
223C2×C4—114no—
224C2×C4—114no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—448no—
233C2×C4D4×D1114yes—
234C22—22no—
235C22—24no—
236C22—41no—
237C22—42no—
238C22—41no—
239C22—224no—
240C22—224no—
241C22—224no—
242C22—442no—
243C22—442no—
244C22—442no—
245C22—442no—
246C22C2×#433911yescharacteristic
247C22C2×D4×D1112yes—
248C22#6703711yescharacteristic
249C22#6704011yescharacteristic
250C22#41×D1112yes—
251C4—24no—
252C4—42no—
253C4—41no—
254C4—41no—
255C4—224no—
256C4—224no—
257C4—442no—
258C2—42no—
259C2—444no—
260C2#1062304611yescharacteristic
261C2#1062307812yes—
262C2#1062312111yescharacteristic
263C2#1062316212yes—
264C2#1062319511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radical#10622573C2
hypercenter#385D11
hypocenterC11#2455
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D11C2semidirect
2. C2×#66947C2semidirect
3. C11×#385C2semidirect
4. #10622585C2semidirect
6. #10622572C2semidirect
7. #10622562C2semidirect
8. #10622282C2semidirect
9. #10622281C2semidirect
59. (C2×D11)⋊C4D4semidirect
110. #385D11semidirect
197. C11#2455semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C2×#669472
C11×#3852
#106225852
#106225732
#106225722
#106225622
#106222822
#106222812
#245511