Finite Group Databasebeta

← #13078664

Subgroups — #13078664

Order 1408.

454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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×D4×Dic11C211yesmaximal, characteristic, complemented
2#10623155C211yesmaximal, characteristic, complemented
3C11×#450C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic
5#10622778C212yesmaximal, complemented
6SD16×Dic11C212yesmaximal, complemented
7#10622657C211yesmaximal, characteristic, complemented
8#10622376C212yesmaximal, complemented
9#10622369C212yesmaximal, complemented
10#10622348C211yesmaximal, characteristic, complemented
11#10622331C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×Dic11—21no—
14C2×C11×SD16C2212yes—
15C11×C22⋊Q8C2211yescharacteristic
16C2×C22⋊Dic11—21no—
17#67000C2211yescharacteristic, complemented
18Q8×Dic11C2211yescharacteristic, complemented
19D4×Dic11—21no—
20D4×Dic11—21no—
21D4×Dic11C2212yes—
22D4×Dic11C2212yes—
23C2×#4323C2212yes—
24#66983C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27#66951—21no—
28#66946C2211yescharacteristic, complemented
29#66945—21no—
30#66943C2211yescharacteristic, complemented
31#66939—21no—
32(C22⋊D11)⋊C4—21no—
33C11×#102C2212yes—
34C11×C22⋊C8C2211yescharacteristic
35#66899C2212yescomplemented
36#66896C2212yes—
37C22⋊(C11⋊C8)C2211yescharacteristic
38#66885C2212yescomplemented
39#66881C2212yescomplemented
40Dic11⋊C8C2212yescomplemented
41C8×Dic11C2212yescomplemented
42#66871C2212yescomplemented
43C24×C11—21no—
44C2×Q8×C11C2311yescharacteristic
45C2×D4×C11—24no—
46C2×D4×C11—21no—
47C2×D4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—21no—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C22×Dic11—21no—
53C22×Dic11—44no—
54C22×Dic11D411yescharacteristic
55C22×Dic11D411yescharacteristic
56C2×D44C2311yescharacteristic
57C2×C4×D11—21no—
58C11×SD16—24no—
59C2×C8×C11C2312yes—
60C11×C4⋊C4—21no—
61C11×C4⋊C4C2311yescharacteristic
62C11×C22⋊C4—21no—
63C22⋊Dic11—22no—
64C22⋊Dic11—22no—
65#4323—24no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—21no—
69(C2×D11)⋊C4—21no—
70C4⋊Dic11—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11—21no—
73C4⋊Dic11C2312yes—
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—21no—
76C4×Dic11—21no—
77C4×Dic11D411yescharacteristic
78C4×Dic11D411yescharacteristic
79C4×Dic11C2311yescharacteristic
80C4×Dic11C2311yescharacteristic
81C2×C11⋊C8C2312yes—
82#3105—111nomaximal, Sylow
83C23×C11—24no—
84C23×C11—22no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11C2×D411yescharacteristic
88C22×D11—21no—
89Q8×C11—22no—
90D4×C11—24no—
91D4×C11—22no—
92D4×C11#4114yes—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2411yescharacteristic
98C22⋊D11—42no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—44no—
104C2×Dic11—42no—
105C2×Dic11—44no—
106C2×Dic11C2×D411yescharacteristic
107C2×Dic11C2×D411yescharacteristic
108C2×Dic11C2×D411yescharacteristic
109C2×Dic11C2×D411yescharacteristic
110D44—22no—
111C4×D11—42no—
112C8×C11—22no—
113C11⋊C8—22no—
114#529—111no—
115C2×C4×D4—111no—
116#484—111no—
117#481—111no—
118#478—112no—
119#463—112no—
120#450D1111yescharacteristic, complemented
121#447—111no—
122C4×SD16—112no—
123C4×D8—112no—
124#431—111no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—24no—
128C22×C11—48no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11#13512yes—
132C22×C11C22×D411yescharacteristic
133C2×D11—41no—
134C2×D11—41no—
135C2×D11—41no—
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11C2×#4112yes—
140Dic11—21no—
141Dic11—21no—
142Dic11—21no—
143Dic11—41no—
144Dic11—42no—
145Dic11AGL(1,ℤ/8)12yes—
146C22×D4C2×D1111yescharacteristic
147C23×C4—221no—
148C2×SD16C2×D1112yes—
149C2×D8—112no—
150#126—221no—
151#125—111no—
152#124—111no—
153#123—221no—
154C22⋊Q8C2×D1111yescharacteristic
155#121—111no—
156C4×Q8—111no—
157C4×D4—112no—
158C4×D4—112no—
159C4×D4—111no—
160C4×D4—221no—
161C4×D4—221no—
162C4×D4—221no—
163#117—221no—
164C2×C4⋊C4—111no—
165C2×C22⋊C4—221no—
166C2×C42—111no—
167#107—112no—
168#106—112no—
169C4⋊C8—112no—
170#103—112no—
171#102—112no—
172#102—112no—
173#102C2×D1112yes—
174C22⋊C8—111no—
175C22⋊C8C2×D1111yescharacteristic
176C4×C8—112no—
177C2×C11—22no—
178C2×C11—44no—
179C2×C11#52511yescharacteristic
180C2×C11C2×#13511yescharacteristic
181C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
182D11—81no—
183C24—21no—
184C2×Q8C22×D1111yescharacteristic
185C2×D4—24no—
186C2×D4—21no—
187C2×D4—111no—
188C2×D4—221no—
189C2×D4C22×D1112yes—
190C22×C4—111no—
191C22×C4—111no—
192C22×C4—221no—
193C22×C4—222no—
194C22×C4—222no—
195C22×C4—221no—
196C22×C4—444no—
197C22×C4C22×D1111yescharacteristic
198SD16—24no—
199D8—224no—
200C2×C8—112no—
201C2×C8C22×D1112yes—
202C4⋊C4—21no—
203C4⋊C4—111no—
204C4⋊C4—112no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4C22×D1111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—221no—
212C22⋊C4—221no—
213C22⋊C4—221no—
214C22⋊C4—222no—
215C22⋊C4—222no—
216C22⋊C4—221no—
217C42—111no—
218C42—111no—
219C42—111no—
220C42—111no—
221C42—221no—
222C11#310511yescharacteristic, complemented, Sylow
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—221no—
228C23D4×D1111yescharacteristic
229Q8—22no—
230D4—24no—
231D4—22no—
232D4—222no—
233D4—442no—
234D4#434114yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—111no—
239C2×C4—111no—
240C2×C4—111no—
241C2×C4—111no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—221no—
245C2×C4—222no—
246C2×C4—442no—
247C2×C4—444no—
248C2×C4—444no—
249C2×C4—442no—
250C2×C4D4×D1111yescharacteristic
251C2×C4C23×D1111yescharacteristic
252C8—22no—
253C8—222no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—441no—
261C22—441no—
262C22—441no—
263C22#6696912yes—
264C22C2×D4×D1111yescharacteristic
265C4—21no—
266C4—41no—
267C4—41no—
268C4—112no—
269C4—221no—
270C4—221no—
271C4—221no—
272C4—441no—
273C4—442no—
274C4C2×#434112yes—
275C2—22no—
276C2—44no—
277C2—881no—
278C2#1062311711yescharacteristic
279C2C2×#6696911yescharacteristic
280C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#450C2
socleC22×C11C22×D4
prime radical#10622830C2
hypercenter#450D11
hypocenterC11#3105
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic11C2semidirect
2. #10623155C2semidirect
3. C11×#450C2semidirect
5. #10622778C2semidirect
6. SD16×Dic11C2semidirect
7. #10622657C2semidirect
8. #10622376C2semidirect
9. #10622369C2semidirect
10. #10622348C2semidirect
11. #10622331C2semidirect
17. #67000C22semidirect
18. Q8×Dic11C22semidirect
28. #66946C22semidirect
30. #66943C22semidirect
35. #66899C22semidirect
38. #66885C22semidirect
39. #66881C22semidirect
40. Dic11⋊C8C22semidirect
41. C8×Dic11C22semidirect
42. #66871C22semidirect
120. #450D11semidirect
222. C11#3105semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
#106231552
C11×#4502
#106228302
#106227782
SD16×Dic112
#106226572
#106223762
#106223692
#106223482
#106223312
#310511