Finite Group Databasebeta

← #13078999

Subgroups — #13078999

Order 1408.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623219C211yesmaximal, characteristic, complemented
2D11×#124C211yesmaximal, characteristic
3C11×#488C211yesmaximal, characteristic, complemented
4#10622681C211yesmaximal, characteristic, complemented
5#10622669C211yesmaximal, characteristic, complemented
6#10622415C212yesmaximal, complemented
7#10622408C212yesmaximal, complemented
8#10622383C212yesmaximal
9#10622378C212yesmaximal, complemented
10#10622310C211yesmaximal, characteristic, complemented
11C4×#4313C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C2×D4×D11C2211yescharacteristic
14C11×#125C2211yescharacteristic, complemented
15C11×#124C2211yescharacteristic
16#67000C2211yescharacteristic
17#66989C2211yescharacteristic
18C2×#4313C2212yes—
19#66949—22no—
20#66945C2212yes—
21#66941C2212yescomplemented
22#66940—22no—
23#66938—22no—
24C22⋊C4×D11—22no—
25#66928C2211yescharacteristic
26C42×D11C2211yescharacteristic
27#66923C2211yescharacteristic, complemented
28C11×#103C2212yescomplemented
29C11×#102C2212yes—
30C4×C8×C11C2211yescharacteristic, complemented
31#66899C2212yescomplemented
32#66896C2212yes—
33#66885C2212yes—
34#66880C2212yescomplemented
35#66879C2212yescomplemented
36#66874C2212yescomplemented
37#66873C2212yes—
38C4×C11⋊C8C2211yescharacteristic, complemented
39C23×D11—21no—
40C2×Q8×C11C2311yescharacteristic
41C2×D4×C11C2311yescharacteristic
42C2×C22⋊D11—21no—
43Q8×D11—24no—
44D4×D11—24no—
45C2×D44C2311yescharacteristic
46C2×C4×D11—21no—
47C2×C4×D11D412yes—
48C2×C4×D11C2311yescharacteristic
49C2×Dic22—21no—
50C2×Dic22—22no—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2312yes—
53C11×C4⋊C4—22no—
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—22no—
56C42×C11C2311yescharacteristic
57C22⋊Dic11—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64C4×Dic11—22no—
65C4×Dic11D412yes—
66C4×Dic11C2311yescharacteristic
67C2×C11⋊C8C2312yes—
68#4313—24no—
69#3140—111nomaximal, Sylow
70C23×C11—21no—
71C22×D11—21no—
72C22×D11—44no—
73C22×D11—42no—
74C22×D11C2×D411yescharacteristic
75Q8×C11—22no—
76D4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2411yescharacteristic
81C22⋊D11—42no—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11C2×D412yes—
85C2×Dic11C2×D411yescharacteristic
86D44—22no—
87C4×D11—42no—
88C4×D11—42no—
89C4×D11#4114yes—
90Dic22—22no—
91Dic22—44no—
92Dic22—42no—
93C8×C11—22no—
94C11⋊C8—22no—
95#533—111no—
96C2×#124—111no—
97#489—112no—
98#489—112no—
99#488—111no—
100#488—111no—
101#488—111no—
102#488D1111yescharacteristic, complemented
103#419—112no—
104#418—112no—
105C4×M16—111no—
106C22×C11—41no—
107C22×C11—42no—
108C22×C11C22×D411yescharacteristic
109C2×D11—22no—
110C2×D11—41no—
111C2×D11—42no—
112C2×D11—84no—
113C2×D11#12412yes—
114C4×C11—22no—
115C4×C11—41no—
116C4×C11—42no—
117C4×C11C2×#4112yes—
118Dic11—22no—
119Dic11—41no—
120Dic11—42no—
121Dic11#12412yes—
122C22×Q8—111no—
123C22×D4—111no—
124C2×M16—112no—
125C4⋊Q8—112no—
126#125—111no—
127#125C2×D1111yescharacteristic, complemented
128#124—111no—
129#124—111no—
130#124—111no—
131#124—222no—
132#124C2×D1111yescharacteristic
133C22⋊Q8—222no—
134C4×Q8—222no—
135#117—112no—
136C2×C22⋊C4—222no—
137C2×C42—111no—
138#103—112no—
139#103—112no—
140#103—112no—
141#103C2×D1112yescomplemented
142#102—112no—
143#102—112no—
144#102—112no—
145#102C2×D1112yes—
146#97—112no—
147C4×C8—111no—
148C4×C8C2×D1111yescharacteristic, complemented
149C2×C11—81no—
150C2×C11C2×#12411yescharacteristic
151C2×C11#57512yes—
152D11—22no—
153D11—81no—
154C24—221no—
155C2×Q8—111no—
156C2×Q8—222no—
157C2×Q8—221no—
158C2×Q8—224no—
159C2×Q8C22×D1111yescharacteristic
160C2×D4—111no—
161C2×D4—224no—
162C2×D4—221no—
163C2×D4C22×D1111yescharacteristic
164C22×C4—111no—
165C22×C4—112no—
166C22×C4—221no—
167M16—224no—
168C2×C8—112no—
169C2×C8C22×D1112yes—
170C4⋊C4—22no—
171C4⋊C4—112no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4C22×D1112yes—
175C22⋊C4—22no—
176C22⋊C4—222no—
177C22⋊C4—222no—
178C22⋊C4—222no—
179C22⋊C4—222no—
180C42—112no—
181C42—111no—
182C42—222no—
183C42C22×D1111yescharacteristic
184C11#314011yescharacteristic, complemented, Sylow
185C23—21no—
186C23—111no—
187C23—221no—
188C23—442no—
189C23—444no—
190Q8—22no—
191Q8—222no—
192Q8—442no—
193Q8—444no—
194D4—22no—
195D4—222no—
196D4—442no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—111no—
200C2×C4—114no—
201C2×C4—112no—
202C2×C4—222no—
203C2×C4—221no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4D4×D1112yes—
207C2×C4C23×D1111yescharacteristic
208C8—22no—
209C8—222no—
210C22—42no—
211C22—41no—
212C22—112no—
213C22—222no—
214C22—442no—
215C22—441no—
216C22—884no—
217C22C2×D4×D1111yescharacteristic
218C4—22no—
219C4—42no—
220C4—41no—
221C4—112no—
222C4—222no—
223C4—442no—
224C4—441no—
225C4#41×D1112yes—
226C2—81no—
227C2—222no—
228C2—881no—
229C2D11×#12411yescharacteristic
230C2#1062329912yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#488D11
hypocenterC11#3140
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623219C2semidirect
3. C11×#488C2semidirect
4. #10622681C2semidirect
5. #10622669C2semidirect
6. #10622415C2semidirect
7. #10622408C2semidirect
9. #10622378C2semidirect
10. #10622310C2semidirect
11. C4×#4313C2semidirect
14. C11×#125C22semidirect
21. #66941C22semidirect
27. #66923C22semidirect
28. C11×#103C22semidirect
30. C4×C8×C11C22semidirect
31. #66899C22semidirect
34. #66880C22semidirect
35. #66879C22semidirect
36. #66874C22semidirect
38. C4×C11⋊C8C22semidirect
102. #488D11semidirect
127. #125C2×D11semidirect
141. #103C2×D11semidirect
148. C4×C8C2×D11semidirect
184. C11#3140semidirect

Maximal subgroups

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

subgroupindex
#106232192
D11×#1242
C11×#4882
#106226812
#106226692
#106224152
#106224082
#106223832
#106223782
#106223102
C4×#43132
#314011