Finite Group Databasebeta

← #13072276

Subgroups — #13072276

Order 1408.

780 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66999C212yesmaximal, complemented
2C2×C22⋊C4×D11C212yesmaximal
3C11×#393C211yesmaximal, characteristic, complemented
4#10622568C211yesmaximal, characteristic
5#10622562C211yesmaximal, characteristic, complemented
6#10622561C212yesmaximal, complemented
7#10622281C212yesmaximal, complemented
8#10622281C212yesmaximal, complemented
9#10622280C212yesmaximal, complemented
10C24×D11C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic, complemented
12C22×C4×D11C2212yes—
13C22×C4×D11C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2211yescharacteristic
18#66999—28no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2212yescomplemented
24C2×C4⋊Dic11C2211yescharacteristic, complemented
25C2×Dic11⋊C4C2212yescomplemented
26C2×Dic11⋊C4C2212yescomplemented
27C2×Dic11⋊C4C2212yescomplemented
28C22⋊C4×D11—28no—
29C11×#95C2211yescharacteristic, complemented
30C11×#95C2212yescomplemented
31C11⋊#95C2212yescomplemented
32C11⋊#95C2211yescharacteristic, complemented
33C24×C11C2311yescharacteristic
34C23×D11—24no—
35C23×D11—24no—
36C23×D11—41no—
37C23×D11—41no—
38C23×D11Q814yescomplemented
39C23×D11C2312yes—
40C2×Q8×C11—24no—
41C2×Q8×C11—41no—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C2×C4×D11—24no—
50C2×C4×D11—24no—
51C2×C4×D11—24no—
52C2×C4×D11—24no—
53C2×C4×D11—42no—
54C2×C4×D11—42no—
55C11×C22⋊C4—24no—
56C11×C22⋊C4—41no—
57C22⋊Dic11—24no—
58C22⋊Dic11—41no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4D418yes—
63C4⋊Dic11—24no—
64C4⋊Dic11—41no—
65Dic11⋊C4—24no—
66Dic11⋊C4—24no—
67Dic11⋊C4—42no—
68#2437—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—21no—
72C23×C11—21no—
73C23×C11C2×Q812yes—
74C23×C11C2411yescharacteristic
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—216no—
80C22×D11—44no—
81C22×D11—44no—
82C22×D11—48no—
83C22×D11—44no—
84C22×D11C2×D414yes—
85C22×D11C2×Q814yes—
86C22×D11#4114yes—
87Q8×C11—44no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11C2×D414yes—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11C2×D414yes—
107C4×D11—48no—
108C4×D11—48no—
109C2×C22⋊Q8—112no—
110C22×C22⋊C4—112no—
111#399—111no—
112#396—112no—
113#393D1111yescharacteristic, complemented
114#385—112no—
115#385—112no—
116#380—112no—
117#379—111no—
118C22×C11—24no—
119C22×C11—22no—
120C22×C11—41no—
121C22×C11—42no—
122C22×C11—41no—
123C22×C11C22×D412yes—
124C22×C11C22×Q811yescharacteristic
125C22×C11C2×#4112yes—
126C22×C11H(5,𝔽2)11yescharacteristic
127C22×C11H(5,𝔽2)11yescharacteristic
128C2×D11—24no—
129C2×D11—24no—
130C2×D11—24no—
131C2×D11—24no—
132C2×D11—24no—
133C2×D11—24no—
134C2×D11—416no—
135C2×D11C22⋊Q818yescomplemented
136C4×C11—24no—
137C4×C11—41no—
138C4×C11—42no—
139C4×C11—41no—
140Dic11—24no—
141Dic11—42no—
142Dic11—42no—
143C25—111no—
144C22×Q8C2×D1111yescharacteristic, complemented
145C23×C4—112no—
146C23×C4—112no—
147C22⋊Q8—228no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C22⋊C4—112no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—111no—
159C2×C22⋊C4—228no—
160C2×C22⋊C4C2×D1112yes—
161C2×C22⋊C4C2×D1111yescharacteristic
162#95—112no—
163#95—111no—
164#95C2×D1111yescharacteristic, complemented
165#95C2×D1112yescomplemented
166C2×C11—42no—
167C2×C11C2×C22⋊Q812yes—
168C2×C11#54311yescharacteristic
169C2×C11D4211yescharacteristic
170C2×C11#54612yes—
171C2×C11#55111yescharacteristic
172D11—28no—
173C24—112no—
174C24—114no—
175C24—224no—
176C24—224no—
177C24—441no—
178C24—441no—
179C24C22×D1111yescharacteristic
180C2×Q8—24no—
181C2×Q8—41no—
182C22×C4—112no—
183C22×C4—112no—
184C22×C4—112no—
185C22×C4—224no—
186C22×C4—224no—
187C22×C4—224no—
188C22×C4—224no—
189C22×C4—442no—
190C22×C4—442no—
191C22×C4C22×D1111yescharacteristic
192C22×C4C22×D1112yes—
193C22×C4C22×D1111yescharacteristic
194C22×C4C22×D1112yes—
195C4⋊C4—224no—
196C4⋊C4—224no—
197C4⋊C4—224no—
198C4⋊C4—442no—
199C4⋊C4—441no—
200C22⋊C4—24no—
201C22⋊C4—41no—
202C22⋊C4—118no—
203C22⋊C4—224no—
204C22⋊C4—224no—
205C22⋊C4—224no—
206C22⋊C4—224no—
207C22⋊C4—441no—
208C11#243711yescharacteristic, complemented, Sylow
209C23—22no—
210C23—21no—
211C23—22no—
212C23—21no—
213C23—114no—
214C23—114no—
215C23—114no—
216C23—2216no—
217C23—222no—
218C23—222no—
219C23—222no—
220C23—222no—
221C23—444no—
222C23—444no—
223C23—448no—
224C23—444no—
225C23Q8×D1112yes—
226C23C23×D1111yescharacteristic
227Q8—44no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—114no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—448no—
247C2×C4—448no—
248C2×C4D4×D1114yes—
249C22—24no—
250C22—22no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—118no—
255C22—224no—
256C22—224no—
257C22—224no—
258C22—224no—
259C22—224no—
260C22—224no—
261C22—4416no—
262C22C2×D4×D1112yes—
263C22#6703711yescharacteristic
264C22C2×Q8×D1111yescharacteristic
265C22#41×D1112yes—
266C22#6704211yescharacteristic
267C4—24no—
268C4—41no—
269C4—42no—
270C4—41no—
271C4—224no—
272C4—442no—
273C4—442no—
274C2—42no—
275C2—228no—
276C2#1062312111yescharacteristic
277C2D11×C22⋊Q812yes—
278C2#1062316511yescharacteristic
279C2#1062320712yes—
280C2#1062321011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×D11C22
hypercenter#393D11
hypocenterC11#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
3. C11×#393C2semidirect
5. #10622562C2semidirect
6. #10622561C2semidirect
7. #10622281C2semidirect
8. #10622281C2semidirect
9. #10622280C2semidirect
11. C22×Q8×C11C22semidirect
23. C2×C4⋊Dic11C22semidirect
24. C2×C4⋊Dic11C22semidirect
25. C2×Dic11⋊C4C22semidirect
26. C2×Dic11⋊C4C22semidirect
27. C2×Dic11⋊C4C22semidirect
29. C11×#95C22semidirect
30. C11×#95C22semidirect
31. C11⋊#95C22semidirect
32. C11⋊#95C22semidirect
38. C23×D11Q8semidirect
113. #393D11semidirect
135. C2×D11C22⋊Q8semidirect
144. C22×Q8C2×D11semidirect
164. #95C2×D11semidirect
165. #95C2×D11semidirect
208. C11#2437semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C22⋊C4×D112
C11×#3932
#106225682
#106225622
#106225612
#106222812
#106222802
#243711