Finite Group Databasebeta

← #13079001

Subgroups — #13079001

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#10623259C211yesmaximal, characteristic, complemented
2D11×#124C211yesmaximal, characteristic
3C11×#489C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic, complemented
5#10622668C211yesmaximal, characteristic, complemented
6#10622415C212yesmaximal, complemented
7#10622413C212yesmaximal, complemented
8#10622383C212yesmaximal
9#10622381C212yesmaximal, complemented
10#10622327C211yesmaximal, characteristic, complemented
11#10622320C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C2×D4×D11C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic, complemented
15C11×#124C2211yescharacteristic
16#67000C2211yescharacteristic
17#66999—21no—
18Q8×Dic11—21no—
19#66989C2211yescharacteristic
20C2×#4313C2212yes—
21#66950—21no—
22#66945C2212yes—
23#66943C2212yescomplemented
24#66940—21no—
25#66938—21no—
26#66938—21no—
27C22⋊C4×D11—21no—
28C22⋊C4×D11—21no—
29#66928C2211yescharacteristic
30C42×D11C2211yescharacteristic
31#66922C2211yescharacteristic, complemented
32C11×#103C2212yescomplemented
33C11×#102C2212yes—
34C11×#97C2211yescharacteristic, complemented
35#66899C2212yescomplemented
36#66896C2212yes—
37#66885C2212yes—
38#66880C2212yescomplemented
39C8×Dic11C2212yescomplemented
40#66874C2212yescomplemented
41#66873C2212yes—
42#66867C2211yescharacteristic, complemented
43C23×D11—21no—
44C2×Q8×C11—21no—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48Q8×D11—24no—
49D4×D11—24no—
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×C4×D11D411yescharacteristic
53C2×C4×D11D411yescharacteristic
54C2×C4×D11C2311yescharacteristic
55C2×Dic22—21no—
56C2×Dic22—21no—
57C2×Dic22C2311yescharacteristic
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2312yes—
61C11×C22⋊C4—21no—
62C11×C22⋊C4—21no—
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65C22⋊Dic11—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71C4⋊Dic11—22no—
72C4⋊Dic11—21no—
73C4⋊Dic11C2312yes—
74Dic11⋊C4—22no—
75C4×Dic11—22no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C2×C11⋊C8C2312yes—
80#4313—24no—
81#3140—111nomaximal, Sylow
82C23×C11—21no—
83C22×D11—21no—
84C22×D11—42no—
85C22×D11—42no—
86C22×D11—42no—
87C22×D11C2×D411yescharacteristic
88Q8×C11—22no—
89Q8×C11—42no—
90D4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—42no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11C2×D411yescharacteristic
100C2×Dic11C2×D411yescharacteristic
101C2×Dic11C2×D411yescharacteristic
102D44—22no—
103C4×D11—41no—
104C4×D11—41no—
105C4×D11—42no—
106C4×D11#4114yes—
107Dic22—22no—
108Dic22—42no—
109Dic22—42no—
110C8×C11—22no—
111C11⋊C8—22no—
112#533—111no—
113C2×#124—111no—
114#489—111no—
115#489—111no—
116#489—111no—
117#489D1111yescharacteristic, complemented
118#488—112no—
119#488—112no—
120#419—112no—
121#418—112no—
122C4×M16—111no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11C22×D411yescharacteristic
127C2×D11—21no—
128C2×D11—21no—
129C2×D11—41no—
130C2×D11—41no—
131C2×D11—41no—
132C2×D11—84no—
133C2×D11#12412yes—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—41no—
137C4×C11—42no—
138C4×C11C2×#4112yes—
139Dic11—21no—
140Dic11—21no—
141Dic11—41no—
142Dic11—42no—
143Dic11#12412yes—
144C22×Q8—111no—
145C22×D4—111no—
146C2×M16—112no—
147C4⋊Q8—111no—
148C4⋊Q8C2×D1111yescharacteristic, complemented
149#125—112no—
150#124—111no—
151#124—111no—
152#124—111no—
153#124—221no—
154#124—221no—
155#124C2×D1111yescharacteristic
156C22⋊Q8—221no—
157C22⋊Q8—221no—
158C4×Q8—221no—
159C4×Q8—221no—
160#117—112no—
161C2×C22⋊C4—221no—
162C2×C22⋊C4—221no—
163C2×C42—111no—
164#103—112no—
165#103—112no—
166#103—112no—
167#103C2×D1112yescomplemented
168#102—112no—
169#102—112no—
170#102—112no—
171#102C2×D1112yes—
172#97—111no—
173#97C2×D1111yescharacteristic, complemented
174C4×C8—112no—
175C2×C11—81no—
176C2×C11C2×#12411yescharacteristic
177C2×C11#57511yescharacteristic
178C2×C11#57511yescharacteristic
179D11—22no—
180D11—81no—
181C24—221no—
182C2×Q8—21no—
183C2×Q8—111no—
184C2×Q8—221no—
185C2×Q8—224no—
186C2×Q8—221no—
187C2×Q8C22×D1111yescharacteristic
188C2×D4—111no—
189C2×D4—224no—
190C2×D4—221no—
191C2×D4C22×D1111yescharacteristic
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—111no—
195C22×C4—221no—
196M16—224no—
197C2×C8—112no—
198C2×C8C22×D1112yes—
199C4⋊C4—21no—
200C4⋊C4—112no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—221no—
204C4⋊C4C22×D1112yes—
205C22⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—221no—
208C22⋊C4—221no—
209C22⋊C4—222no—
210C22⋊C4—221no—
211C22⋊C4—221no—
212C22⋊C4—221no—
213C22⋊C4—221no—
214C42—111no—
215C42—111no—
216C42—111no—
217C42—222no—
218C42C22×D1111yescharacteristic
219C11#314011yescharacteristic, complemented, Sylow
220C23—21no—
221C23—111no—
222C23—221no—
223C23—442no—
224C23—442no—
225C23—442no—
226Q8—22no—
227Q8—42no—
228Q8—222no—
229Q8—442no—
230Q8—442no—
231D4—22no—
232D4—222no—
233D4—442no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—111no—
237C2×C4—114no—
238C2×C4—111no—
239C2×C4—111no—
240C2×C4—222no—
241C2×C4—221no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—442no—
245C2×C4D4×D1111yescharacteristic
246C2×C4D4×D1111yescharacteristic
247C2×C4C23×D1111yescharacteristic
248C8—22no—
249C8—222no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—112no—
254C22—221no—
255C22—221no—
256C22—441no—
257C22—441no—
258C22—441no—
259C22—884no—
260C22C2×D4×D1111yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—112no—
266C4—221no—
267C4—221no—
268C4—442no—
269C4—441no—
270C4#41×D1112yes—
271C2—81no—
272C2—222no—
273C2—881no—
274C2D11×#12411yescharacteristic
275C2#1062330411yescharacteristic
276C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#489C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#489D11
hypocenterC11#3140
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#489C2semidirect
4. #10622702C2semidirect
5. #10622668C2semidirect
6. #10622415C2semidirect
7. #10622413C2semidirect
9. #10622381C2semidirect
10. #10622327C2semidirect
11. #10622320C2semidirect
14. C11×C4⋊Q8C22semidirect
23. #66943C22semidirect
31. #66922C22semidirect
32. C11×#103C22semidirect
34. C11×#97C22semidirect
35. #66899C22semidirect
38. #66880C22semidirect
39. C8×Dic11C22semidirect
40. #66874C22semidirect
42. #66867C22semidirect
117. #489D11semidirect
148. C4⋊Q8C2×D11semidirect
167. #103C2×D11semidirect
173. #97C2×D11semidirect
219. C11#3140semidirect

Maximal subgroups

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

subgroupindex
#106232592
D11×#1242
C11×#4892
#106227022
#106226682
#106224152
#106224132
#106223832
#106223812
#106223272
#106223202
#314011