Finite Group Databasebeta

← #13079558

Subgroups — #13079558

Order 1408.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#10623259C211yesmaximal, characteristic, complemented
2D11×#127C211yesmaximal, characteristic
3C11×#486C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5#10622689C211yesmaximal, characteristic, complemented
6#10622389C214yesmaximal, complemented
7#10622375C214yesmaximal, complemented
8#10622306C211yesmaximal, characteristic, complemented
9#10622298C211yesmaximal, characteristic, complemented
10C2×D4×D11—21no—
11C2×D4×D11—21no—
12C2×D4×D11C2212yes—
13C11×C4⋊Q8C2211yescharacteristic, complemented
14C11×#127C2211yescharacteristic
15#66999—21no—
16Q8×Dic11—21no—
17#66993—21no—
18#66993—21no—
19#66993C2212yes—
20C2×#4324C2214yescomplemented
21C2×#4314C2214yescomplemented
22#66950C2212yes—
23#66945—21no—
24#66943—21no—
25#66940C2212yescomplemented
26#66927C2211yescharacteristic
27C42×D11C2211yescharacteristic
28#66922C2211yescharacteristic, complemented
29C11×#102C2214yescomplemented
30C4×C8×C11C2211yescharacteristic, complemented
31(C2×D11)⋊C8C2212yes—
32Dic11⋊C8C2212yescomplemented
33#66873C2214yescomplemented
34C4×C11⋊C8C2211yescharacteristic, complemented
35C23×D11—22no—
36C2×Q8×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11C2312yes—
40C2×C22⋊D11—22no—
41C2×C22⋊D11—22no—
42C2×C22⋊D11—22no—
43D4×D11—44no—
44D4×D11—44no—
45D4×D11—44no—
46C2×D44—21no—
47C2×D44—21no—
48C2×D44C2312yes—
49C2×C4×D11D411yescharacteristic
50C2×C4×D11D411yescharacteristic
51C2×C4×D11C2311yescharacteristic
52C2×Dic22C2312yes—
53C2×C8×C11C2312yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4C2312yes—
56C42×C11C2311yescharacteristic
57#4324—44no—
58(C2×D11)⋊C4—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11—21no—
61C4⋊Dic11—21no—
62Dic11⋊C4—22no—
63C4×Dic11—22no—
64C4×Dic11D411yescharacteristic
65C4×Dic11D411yescharacteristic
66C4×Dic11C2311yescharacteristic
67C2×C11⋊C8C2312yes—
68#4314—44no—
69#3208—111nomaximal, Sylow
70C23×C11—22no—
71C22×D11—22no—
72C22×D11—44no—
73C22×D11—44no—
74C22×D11—44no—
75C22×D11C2×D411yescharacteristic
76Q8×C11—42no—
77D4×C11—24no—
78D4×C11—42no—
79D4×C11—42no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2411yescharacteristic
84C22⋊D11—44no—
85C22⋊D11—44no—
86C22⋊D11—44no—
87C2×Dic11—22no—
88C2×Dic11C2×D411yescharacteristic
89C2×Dic11C2×D411yescharacteristic
90C2×Dic11C2×D411yescharacteristic
91D44—24no—
92D44—42no—
93D44—42no—
94C4×D11—22no—
95C4×D11—22no—
96C4×D11SD1614yescomplemented
97Dic22—24no—
98C8×C11—22no—
99C11⋊C8—22no—
100#533—111no—
101C2×#127—111no—
102#492—111no—
103#492—111no—
104#486—111no—
105#486D1111yescharacteristic, complemented
106#460—114no—
107#450—114no—
108#431—111no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11C22×D411yescharacteristic
113C2×D11—21no—
114C2×D11—21no—
115C2×D11—42no—
116C2×D11—42no—
117C2×D11—42no—
118C2×D11—88no—
119C2×D11C2×SD1612yes—
120C4×C11—42no—
121C4×C11C2×SD1612yes—
122C4×C11AGL(1,ℤ/8)12yes—
123C4×C11H(5,𝔽2)12yes—
124Dic11—21no—
125Dic11—21no—
126Dic11—42no—
127Dic11C2×SD1612yes—
128C22×D4—112no—
129C22×D4—221no—
130C22×D4—221no—
131C2×SD16—114no—
132C2×SD16—114no—
133C4⋊Q8—111no—
134C4⋊Q8C2×D1111yescharacteristic, complemented
135#127—112no—
136#127—111no—
137#127—221no—
138#127—221no—
139#127C2×D1111yescharacteristic
140#125—221no—
141C22⋊Q8—112no—
142C22⋊Q8—221no—
143C4×Q8—112no—
144C4×Q8—221no—
145#117—221no—
146C2×C42—111no—
147C4⋊C8—112no—
148#102—114no—
149#102C2×D1114yescomplemented
150C22⋊C8—112no—
151C4×C8—111no—
152C4×C8C2×D1111yescharacteristic, complemented
153C2×C11—82no—
154C2×C11#53511yescharacteristic
155C2×C11C22×SD1611yescharacteristic
156C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
157D11—22no—
158D11—82no—
159C24—222no—
160C2×Q8—21no—
161C2×Q8—112no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—112no—
165C2×D4—222no—
166C2×D4—222no—
167C2×D4—222no—
168C2×D4—221no—
169C2×D4—221no—
170C2×D4—444no—
171C2×D4—444no—
172C2×D4—444no—
173C2×D4C22×D1112yes—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—111no—
177SD16—444no—
178SD16—444no—
179C2×C8—112no—
180C2×C8C22×D1112yes—
181C4⋊C4—21no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4C22×D1112yes—
187C22⋊C4—222no—
188C42—111no—
189C42—111no—
190C42—111no—
191C42—222no—
192C42C22×D1111yescharacteristic
193C11#320811yescharacteristic, complemented, Sylow
194C23—22no—
195C23—111no—
196C23—222no—
197C23—444no—
198C23—444no—
199C23—444no—
200Q8—42no—
201Q8—224no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—224no—
206D4—444no—
207D4—444no—
208D4—444no—
209D4—442no—
210D4—442no—
211C2×C4—22no—
212C2×C4—111no—
213C2×C4—114no—
214C2×C4—111no—
215C2×C4—111no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4D4×D1111yescharacteristic
220C2×C4D4×D1111yescharacteristic
221C2×C4C23×D1111yescharacteristic
222C8—22no—
223C8—222no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—112no—
228C22—221no—
229C22—221no—
230C22—442no—
231C22—442no—
232C22—442no—
233C22—888no—
234C22C2×D4×D1111yescharacteristic
235C4—42no—
236C4—112no—
237C4—221no—
238C4—221no—
239C4—442no—
240C4#6696412yes—
241C4SD16×D1112yes—
242C4#6704212yes—
243C2—82no—
244C2—222no—
245C2—882no—
246C2#1062320511yescharacteristic
247C2C2×#6696411yescharacteristic
248C2C2×SD16×D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
prime radicalD11×#127C2
hypercenter#486D11
hypocenterC11#3208
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#486C2semidirect
4. #10622701C2semidirect
5. #10622689C2semidirect
6. #10622389C2semidirect
7. #10622375C2semidirect
8. #10622306C2semidirect
9. #10622298C2semidirect
13. C11×C4⋊Q8C22semidirect
20. C2×#4324C22semidirect
21. C2×#4314C22semidirect
25. #66940C22semidirect
28. #66922C22semidirect
29. C11×#102C22semidirect
30. C4×C8×C11C22semidirect
32. Dic11⋊C8C22semidirect
33. #66873C22semidirect
34. C4×C11⋊C8C22semidirect
96. C4×D11SD16semidirect
105. #486D11semidirect
134. C4⋊Q8C2×D11semidirect
149. #102C2×D11semidirect
152. C4×C8C2×D11semidirect
193. C11#3208semidirect

Maximal subgroups

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

subgroupindex
#106232592
D11×#1272
C11×#4862
#106227012
#106226892
#106223892
#106223752
#106223062
#106222982
#320811