Finite Group Databasebeta

← #13078621

Subgroups — #13078621

Order 1408.

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

normal subgroups only

This group has 448 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#10623153C211yesmaximal, characteristic, complemented
2C2×#66946C211yesmaximal, characteristic
3C11×#483C211yesmaximal, characteristic, complemented
4#10622659C211yesmaximal, characteristic
5#10622584C211yesmaximal, characteristic, complemented
6#10622483C212yesmaximal, complemented
7#10622465C212yesmaximal, complemented
8#10622431C212yesmaximal, complemented
9#10622401C212yesmaximal, complemented
10#10622344C211yesmaximal, characteristic
11#10622331C211yesmaximal, characteristic, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11—21no—
14C11×C22⋊Q8C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16Q8×Dic11C2211yescharacteristic, complemented
17#66997C2211yescharacteristic, complemented
18C2×#4325C2212yes—
19C2×(C2×D11)⋊C4—21no—
20#66977C2211yescharacteristic
21C2×C4×Dic11C2211yescharacteristic
22C2×#4314C2212yes—
23#66946—21no—
24#66946—21no—
25#66946C2212yes—
26#66946C2212yes—
27#66942—21no—
28#66941C2211yescharacteristic, complemented
29#66940—21no—
30#66940C2211yescharacteristic, complemented
31#66931—21no—
32#66930—21no—
33C11×#106C2212yescomplemented
34C11×#103C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66885C2212yes—
38Dic11⋊C8C2212yescomplemented
39C8×Dic11C2212yescomplemented
40#66874C2212yescomplemented
41#66873C2212yes—
42#66872C2212yescomplemented
43C23×D11—21no—
44C2×Q8×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11D411yescharacteristic
48C22×Dic11D411yescharacteristic
49C2×D44—24no—
50C2×D44—21no—
51C2×D44C2312yes—
52C2×C4×D11—22no—
53C2×C4×D11—22no—
54C2×C4×D11—44no—
55C2×Dic22—21no—
56C2×Dic22C2311yescharacteristic
57C2×C8×C11C2312yes—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2312yes—
61C11×C4⋊C4C2311yescharacteristic
62C11×C22⋊C4—21no—
63C22⋊Dic11—21no—
64#4325—24no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—22no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74C4×Dic11—21no—
75C4×Dic11—21no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C4×Dic11C2311yescharacteristic
80C2×C11⋊C8C2312yes—
81#4314—24no—
82#3101—111nomaximal, Sylow
83C23×C11C2×D411yescharacteristic
84C22×D11—24no—
85C22×D11—22no—
86C22×D11—42no—
87C22×D11—42no—
88Q8×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—42no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—41no—
99C2×Dic11SD1614yescomplemented
100C2×Dic11C2×D411yescharacteristic
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104D44—24no—
105D44—22no—
106D44#4114yes—
107C4×D11—44no—
108C4×D11—44no—
109Dic22—22no—
110Dic22—42no—
111C8×C11—22no—
112C11⋊C8—22no—
113#533—111no—
114C2×C4×D4—111no—
115#483—111no—
116#483D1111yescharacteristic, complemented
117#476—112no—
118#461—112no—
119#450—111no—
120#450—111no—
121C4×SD16—112no—
122C4×SD16—112no—
123#431—111no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11C2×SD1612yes—
127C22×C11C22×D411yescharacteristic
128C2×D11—24no—
129C2×D11—48no—
130C2×D11—42no—
131C2×D11—42no—
132C4×C11—21no—
133C4×C11—41no—
134C4×C11—42no—
135C4×C11—41no—
136C4×C11C2×#4112yes—
137Dic11—21no—
138Dic11—21no—
139Dic11—41no—
140Dic11—41no—
141Dic11C2×SD1612yes—
142Dic11C2×SD1612yes—
143C22×D4—111no—
144C23×C4—221no—
145C2×SD16—112no—
146C2×SD16—112no—
147C4⋊Q8—111no—
148C4⋊Q8—111no—
149#125—221no—
150C22⋊Q8—111no—
151C22⋊Q8—221no—
152C22⋊Q8C2×D1111yescharacteristic
153C4×Q8—111no—
154C4×Q8—111no—
155C4×Q8—221no—
156C4×D4—112no—
157C4×D4—112no—
158C4×D4—221no—
159C4×D4—221no—
160#117—221no—
161C2×C4⋊C4C2×D1111yescharacteristic
162C2×C22⋊C4—221no—
163C2×C42—111no—
164#106—112no—
165#106C2×D1112yescomplemented
166C4⋊C8—112no—
167#103—112no—
168#103C2×D1112yescomplemented
169#102—112no—
170#102—112no—
171C22⋊C8—111no—
172C22⋊C8C2×D1111yescharacteristic
173C4×C8—112no—
174C2×C11—22no—
175C2×C11#52511yescharacteristic
176C2×C11C22×SD1611yescharacteristic
177C2×C11#57511yescharacteristic
178D11—44no—
179C24—221no—
180C2×Q8—111no—
181C2×Q8—221no—
182C2×Q8C22×D1111yescharacteristic
183C2×D4—112no—
184C2×D4—224no—
185C2×D4—221no—
186C22×C4—21no—
187C22×C4—111no—
188C22×C4—111no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—444no—
192C22×C4C22×D1111yescharacteristic
193SD16—224no—
194SD16—224no—
195C2×C8—112no—
196C2×C8C22×D1112yes—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—111no—
200C4⋊C4—221no—
201C4⋊C4—221no—
202C4⋊C4—221no—
203C4⋊C4—221no—
204C4⋊C4—221no—
205C4⋊C4—221no—
206C4⋊C4C22×D1111yescharacteristic
207C4⋊C4C22×D1112yes—
208C22⋊C4—21no—
209C22⋊C4—222no—
210C22⋊C4—222no—
211C22⋊C4—221no—
212C42—111no—
213C42—111no—
214C42—111no—
215C42—111no—
216C42—221no—
217C42—221no—
218C11#310111yescharacteristic, complemented, Sylow
219C23—224no—
220C23—222no—
221C23—442no—
222C23—442no—
223C23D4×D1111yescharacteristic
224Q8—22no—
225Q8—222no—
226Q8—442no—
227D4—114no—
228D4—224no—
229D4—222no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—114no—
236C2×C4—111no—
237C2×C4—111no—
238C2×C4—111no—
239C2×C4—111no—
240C2×C4—221no—
241C2×C4—221no—
242C2×C4—444no—
243C2×C4—444no—
244C2×C4—441no—
245C2×C4D4×D1111yescharacteristic
246C2×C4C23×D1111yescharacteristic
247C8—22no—
248C8—222no—
249C22—21no—
250C22—21no—
251C22—224no—
252C22—448no—
253C22—442no—
254C22—442no—
255C22SD16×D1112yes—
256C22C2×D4×D1111yescharacteristic
257C4—21no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—112no—
262C4—112no—
263C4—221no—
264C4—221no—
265C4—441no—
266C4—441no—
267C4#41×D1112yes—
268C2—22no—
269C2—444no—
270C2#1062318711yescharacteristic
271C2C2×SD16×D1111yescharacteristic
272C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radicalC22×D44C22
hypercenter#483D11
hypocenterC11#3101
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #10623153C2semidirect
3. C11×#483C2semidirect
5. #10622584C2semidirect
6. #10622483C2semidirect
7. #10622465C2semidirect
8. #10622431C2semidirect
9. #10622401C2semidirect
11. #10622331C2semidirect
16. Q8×Dic11C22semidirect
17. #66997C22semidirect
28. #66941C22semidirect
30. #66940C22semidirect
33. C11×#106C22semidirect
34. C11×#103C22semidirect
38. Dic11⋊C8C22semidirect
39. C8×Dic11C22semidirect
40. #66874C22semidirect
42. #66872C22semidirect
99. C2×Dic11SD16semidirect
116. #483D11semidirect
165. #106C2×D11semidirect
168. #103C2×D11semidirect
218. C11#3101semidirect

Maximal subgroups

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

subgroupindex
#106231532
C2×#669462
C11×#4832
#106226592
#106225842
#106224832
#106224652
#106224312
#106224012
#106223442
#106223312
#310111