Finite Group Databasebeta

← #13076909

Subgroups — #13076909

Order 1408.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D11C211yesmaximal, characteristic, complemented
2C2×#66982C211yesmaximal, characteristic, complemented
3C2×#66939C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic
5C11×#381C211yesmaximal, characteristic, complemented
6#10622568C211yesmaximal, characteristic, complemented
7#10622556C211yesmaximal, characteristic, complemented
8#10622281C214yesmaximal, complemented
9#10622278C214yesmaximal, complemented
10C24×D11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×C22⋊D11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C22×D44C2212yes—
15C22×C4×D11—24no—
16C22×C4×D11—24no—
17C22×C4×D11—24no—
18C22×C4×D11C2214yes—
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22#66982—24no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2214yes—
25C2×(C2×D11)⋊C4C2212yescomplemented
26C2×(C2×D11)⋊C4C2212yescomplemented
27C2×C4⋊Dic11C2212yescomplemented
28C2×Dic11⋊C4C2212yescomplemented
29#66939—24no—
30#66935—24no—
31C11×#95C2214yescomplemented
32C11⋊#95C2214yescomplemented
33C24×C11C2311yescharacteristic
34C23×D11—22no—
35C23×D11—22no—
36C23×D11—28no—
37C23×D11D414yes—
38C23×D11C2311yescharacteristic
39C23×D11C2312yes—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11D414yescomplemented
43C22×C4×C11C2312yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2312yes—
46C2×C22⋊D11—22no—
47C2×C22⋊D11—22no—
48C2×C22⋊D11—22no—
49C22×Dic11—22no—
50C22×Dic11—22no—
51C22×Dic11D414yescomplemented
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2312yes—
55C2×D44—24no—
56C2×D44—28no—
57C2×C4×D11—232no—
58C2×C4×D11—28no—
59C2×C4×D11—28no—
60C2×C4×D11—28no—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—22no—
63C22⋊Dic11—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—28no—
67(C2×D11)⋊C4—24no—
68C4⋊Dic11—24no—
69Dic11⋊C4—24no—
70#2849—111nomaximal, Sylow
71C23×C11—24no—
72C23×C11C2×D412yes—
73C23×C11C2×D412yes—
74C23×C11C2×D412yes—
75C23×C11C2411yescharacteristic
76C22×D11—216no—
77C22×D11—216no—
78C22×D11—28no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—24no—
82C22×D11—216no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—24no—
87C22×D11C2×D414yes—
88C22×D11#4118yes—
89C2×C4×C11—28no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—24no—
95C2×C4×C11—24no—
96C2×C4×C11C2×D414yes—
97C22⋊D11—44no—
98C2×Dic11—28no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—24no—
106C2×Dic11C2×D414yes—
107D44—48no—
108C4×D11—232no—
109C24×C4—111no—
110C2×#123—111no—
111C2×#123—111no—
112C2×#120—111no—
113#386—114no—
114#385—114no—
115#381—111no—
116#381D1111yescharacteristic, complemented
117#379—111no—
118C22×C11—24no—
119C22×C11—24no—
120C22×C11—24no—
121C22×C11#12014yes—
122C22×C11C22×D411yescharacteristic
123C22×C11C22×D411yescharacteristic
124C22×C11C22×D411yescharacteristic
125C22×C11C2×#4114yes—
126C2×D11—232no—
127C2×D11—24no—
128C2×D11—24no—
129C2×D11—28no—
130C2×D11—28no—
131C2×D11—41no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11#12318yescomplemented
136C4×C11—24no—
137C4×C11—42no—
138C4×C11—42no—
139Dic11—24no—
140Dic11—41no—
141Dic11—42no—
142C25—111no—
143C22×D4—111no—
144C22×D4—112no—
145C23×C4—111no—
146C23×C4—114no—
147C23×C4—224no—
148C23×C4—224no—
149C23×C4—224no—
150C23×C4C2×D1111yescharacteristic
151#123—224no—
152#123—224no—
153#120—224no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C22⋊C4—111no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4—114no—
161C2×C22⋊C4C2×D1111yescharacteristic
162C2×C22⋊C4C2×D1111yescharacteristic
163#95—114no—
164#95C2×D1114yescomplemented
165C2×C11—24no—
166C2×C11C2×#12011yescharacteristic
167C2×C11C2×#12312yes—
168C2×C11#52512yes—
169C2×C11#52512yes—
170D11—28no—
171D11—81no—
172C24—112no—
173C24—114no—
174C24—111no—
175C24—228no—
176C24—222no—
177C24—222no—
178C24C22×D1111yescharacteristic
179C2×D4—224no—
180C2×D4—228no—
181C2×D4—222no—
182C2×D4—222no—
183C2×D4—222no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—114no—
187C22×C4—112no—
188C22×C4—112no—
189C22×C4—111no—
190C22×C4—228no—
191C22×C4—228no—
192C22×C4—2232no—
193C22×C4—222no—
194C22×C4—222no—
195C22×C4—228no—
196C22×C4D4414yescomplemented
197C22×C4C22×D1112yes—
198C22×C4C22×D1112yes—
199C22×C4C22×D1112yes—
200C4⋊C4—224no—
201C4⋊C4—224no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C22⋊C4—224no—
205C22⋊C4—224no—
206C22⋊C4—228no—
207C22⋊C4—222no—
208C22⋊C4—224no—
209C11#284911yescharacteristic, complemented, Sylow
210C23—24no—
211C23—114no—
212C23—118no—
213C23—2216no—
214C23—2216no—
215C23—2216no—
216C23—228no—
217C23—222no—
218C23—222no—
219C23—224no—
220C23—221no—
221C23—221no—
222C23—221no—
223C23—224no—
224C23C2×D4412yes—
225C23D4×D1112yes—
226C23D4×D1112yes—
227C23C23×D1111yescharacteristic
228D4—448no—
229D4—444no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—114no—
238C2×C4—2232no—
239C2×C4—228no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—221no—
246C2×C4—224no—
247C2×C4C2×D4414yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—118no—
252C22—2232no—
253C22—224no—
254C22—228no—
255C22—224no—
256C22—228no—
257C22—441no—
258C22—442no—
259C22—442no—
260C22—442no—
261C22#6693514yes—
262C22C22×D4411yescharacteristic
263C22C2×D4×D1111yescharacteristic
264C22C2×D4×D1111yescharacteristic
265C22#41×D1114yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—224no—
270C4—441no—
271C4—442no—
272C2—24no—
273C2—228no—
274C2—881no—
275C2C2×#6693511yescharacteristic
276C2#1062305512yes—
277C2D11×#12312yes—
278C2#1062318712yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC2×#66935C2
hypercenter#381D11
hypocenterC11#2849
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D11C2semidirect
2. C2×#66982C2semidirect
3. C2×#66939C2semidirect
5. C11×#381C2semidirect
6. #10622568C2semidirect
7. #10622556C2semidirect
8. #10622281C2semidirect
9. #10622278C2semidirect
25. C2×(C2×D11)⋊C4C22semidirect
26. C2×(C2×D11)⋊C4C22semidirect
27. C2×C4⋊Dic11C22semidirect
28. C2×Dic11⋊C4C22semidirect
31. C11×#95C22semidirect
32. C11⋊#95C22semidirect
42. C22×C4×C11D4semidirect
51. C22×Dic11D4semidirect
116. #381D11semidirect
135. C2×D11#123semidirect
164. #95C2×D11semidirect
196. C22×C4D44semidirect
209. C11#2849semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D112
C2×#669822
C2×#669392
C2×#669352
C11×#3812
#106225682
#106225562
#106222812
#106222782
#284911