Finite Group Databasebeta

← #13078118

Subgroups — #13078118

Order 1408.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623336C211yesmaximal, characteristic, complemented
2C22×#4323C211yesmaximal, characteristic, complemented
3C2×#66961C211yesmaximal, characteristic, complemented
4#10623052C211yesmaximal, characteristic, complemented
5C11×#418C211yesmaximal, characteristic, complemented
6#10622732C211yesmaximal, characteristic, complemented
7#10622615C211yesmaximal, characteristic, complemented
8#10622400C214yesmaximal, complemented
9#10622399C214yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C2×#4339C2211yescharacteristic
12C22×D44C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#67006—22no—
16#66993C2212yescomplemented
17#66991—22no—
18#66989C2212yescomplemented
19C2×#4323—24no—
20C2×#4323C2214yes—
21#66979C2211yescharacteristic
22C22×C11⋊C8C2211yescharacteristic
23#66961—24no—
24C2×D88C2212yescomplemented
25C2×#4314C2212yescomplemented
26#66946C2214yescomplemented
27C22⋊C4×D11—22no—
28C4×D44—22no—
29C11×#102C2214yescomplemented
30Dic11⋊C8C2214yescomplemented
31#66874C2212yescomplemented
32#66873C2212yescomplemented
33C24×C11—21no—
34C23×D11—21no—
35C2×D4×C11—22no—
36C2×D4×C11—21no—
37C2×D4×C11—22no—
38C2×D4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—24no—
41C2×C22⋊D11—21no—
42#4339—22no—
43#4339—22no—
44C2×D44—21no—
45C2×D44—22no—
46C2×D44D414yescomplemented
47C2×D44C2311yescharacteristic
48C2×D44C2312yes—
49C2×C4×D11—24no—
50C2×C4×D11—21no—
51C2×Dic22C2311yescharacteristic
52C11×M16—22no—
53C2×C8×C11C2312yes—
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—21no—
56C42×C11—21no—
57C22⋊Dic11—24no—
58C22⋊Dic11D412yes—
59#4323—28no—
60(C2×D11)⋊C4—24no—
61C4⋊Dic11D412yes—
62C4×Dic11C2312yes—
63C2×C11⋊C8—22no—
64C2×C11⋊C8C2312yes—
65D88—24no—
66#4314—24no—
67#3041—111nomaximal, Sylow
68C23×C11—22no—
69C23×C11—42no—
70C23×C11—82no—
71C23×C11C2×D411yescharacteristic
72C22×D11—22no—
73C22×D11—24no—
74C22×D11—21no—
75C22×D11—82no—
76D4×C11—22no—
77D4×C11—22no—
78D4×C11—42no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D412yes—
82C2×C4×C11#4112yes—
83C2×C4×C11C2411yescharacteristic
84C22⋊D11—42no—
85C22⋊D11—84no—
86C2×Dic11—21no—
87C2×Dic11C2×D414yes—
88D44—24no—
89D44—21no—
90D44—22no—
91D44—21no—
92D44C2×D414yes—
93C4×D11—42no—
94C4×D11—84no—
95Dic22—21no—
96Dic22—21no—
97C8×C11—22no—
98C11⋊C8—22no—
99C2×AGL(1,ℤ/8)—111no—
100C22×D8—111no—
101#535—111no—
102#518—111no—
103#463—114no—
104#459—114no—
105#424—111no—
106#418D1111yescharacteristic, complemented
107#416—111no—
108C22×C11—22no—
109C22×C11—42no—
110C22×C11—44no—
111C22×C11—84no—
112C22×C11#12112yes—
113C22×C11C22×D411yescharacteristic
114C2×D11—24no—
115C2×D11—44no—
116C2×D11—41no—
117C2×D11—42no—
118C2×D11—84no—
119C4×C11—42no—
120C4×C11#12112yes—
121C4×C11C22×D411yescharacteristic
122C4×C11C2×#4111yescharacteristic
123Dic11—24no—
124Dic11—41no—
125C2×#41—111no—
126C22×D4—111no—
127C22×D4C2×D1111yescharacteristic
128AGL(1,ℤ/8)—224no—
129C2×SD16—112no—
130C2×D8—114no—
131C2×D8—112no—
132C2×D8—224no—
133C2×M16C2×D1111yescharacteristic
134C22×C8—111no—
135#127—112no—
136#124—112no—
137#121—222no—
138#120—222no—
139C4×D4—114no—
140C4×D4—222no—
141#117—111no—
142#117C2×D1111yescharacteristic
143C2×C22⋊C4—222no—
144C4⋊C8—114no—
145#103—112no—
146#102—112no—
147#102C2×D1114yescomplemented
148C2×C11—22no—
149C2×C11—82no—
150C2×C11C2×#12111yescharacteristic
151C2×C11#57612yes—
152D11—44no—
153D11—81no—
154C24—21no—
155C24—221no—
156#41—222no—
157#41—222no—
158C2×Q8—111no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—114no—
163C2×D4—112no—
164C2×D4—111no—
165C2×D4—224no—
166C2×D4—221no—
167C2×D4—222no—
168C2×D4—221no—
169C2×D4C22×D1112yes—
170C22×C4—224no—
171C22×C4—221no—
172C22×C4C22×D1111yescharacteristic
173SD16—224no—
174D8—224no—
175D8—228no—
176M16—22no—
177C2×C8—112no—
178C2×C8—222no—
179C2×C8C22×D1112yes—
180C4⋊C4—112no—
181C4⋊C4C22×D1112yes—
182C22⋊C4—21no—
183C22⋊C4—112no—
184C22⋊C4—224no—
185C22⋊C4—224no—
186C42—21no—
187C42—112no—
188C11#304111yescharacteristic, complemented, Sylow
189C23—22no—
190C23—42no—
191C23—82no—
192C23—222no—
193C23—224no—
194C23—221no—
195C23—882no—
196C23D4×D1111yescharacteristic
197Q8—221no—
198Q8—221no—
199D4—22no—
200D4—22no—
201D4—42no—
202D4—114no—
203D4—224no—
204D4—222no—
205D4—221no—
206D4—221no—
207D4—442no—
208D4—884no—
209C2×C4—22no—
210C2×C4—114no—
211C2×C4—221no—
212C2×C4—442no—
213C2×C4—884no—
214C2×C4#433912yes—
215C2×C4D4×D1111yescharacteristic
216C2×C4D4×D1112yes—
217C2×C4C23×D1111yescharacteristic
218C8—22no—
219C8—222no—
220C22—22no—
221C22—42no—
222C22—44no—
223C22—84no—
224C22—224no—
225C22—444no—
226C22—441no—
227C22—442no—
228C22—884no—
229C22#6693712yes—
230C22C2×D4×D1111yescharacteristic
231C4—42no—
232C4—224no—
233C4—441no—
234C4#6693712yes—
235C4C2×#433911yescharacteristic
236C4C2×D4×D1111yescharacteristic
237C2—22no—
238C2—82no—
239C2—444no—
240C2—881no—
241C2C2×#6693711yescharacteristic
242C2#1062330512yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
hypercenter#418D11
hypocenterC11#3041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #10623336C2semidirect
2. C22×#4323C2semidirect
3. C2×#66961C2semidirect
4. #10623052C2semidirect
5. C11×#418C2semidirect
6. #10622732C2semidirect
7. #10622615C2semidirect
8. #10622400C2semidirect
9. #10622399C2semidirect
16. #66993C22semidirect
18. #66989C22semidirect
24. C2×D88C22semidirect
25. C2×#4314C22semidirect
26. #66946C22semidirect
29. C11×#102C22semidirect
30. Dic11⋊C8C22semidirect
31. #66874C22semidirect
32. #66873C22semidirect
46. C2×D44D4semidirect
106. #418D11semidirect
147. #102C2×D11semidirect
188. C11#3041semidirect

Maximal subgroups

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

subgroupindex
#106233362
C22×#43232
C2×#669612
#106230522
C11×#4182
#106227322
#106226152
#106224002
#106223992
#304111