Finite Group Databasebeta

← #13079477

Subgroups — #13079477

Order 1408.

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

normal subgroups only

This group has 442 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
1C11×#535C211yesmaximal, characteristic, complemented
2#10623361C211yesmaximal, characteristic, complemented
3#10622847C211yesmaximal, characteristic, complemented
4#10622830C212yesmaximal, complemented
5#10622652C212yesmaximal, complemented
6#10622651C212yesmaximal, complemented
7#10622649C212yesmaximal, complemented
8#10622648C212yesmaximal, complemented
9#10622616C212yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic, complemented
12C22×D44C2211yescharacteristic, complemented
13C11×#127—21no—
14C11×#124—21no—
15C11×#121C2212yes—
16C11×#121C2212yescomplemented
17C11×#120—21no—
18C11×#120—21no—
19C11×#117C2211yescharacteristic, complemented
20#67000—21no—
21#66993—21no—
22#66990—21no—
23#66990—21no—
24C2×#4323C2212yes—
25C2×#4323C2212yes—
26#66983C2212yes—
27#66983C2212yescomplemented
28#66979C2211yescharacteristic, complemented
29C2×#4318C2211yescharacteristic, complemented
30C22×C11⋊C8C2211yescharacteristic, complemented
31#66896C2212yescomplemented
32#66896C2212yescomplemented
33C22⋊(C11⋊C8)C2212yescomplemented
34C22⋊(C11⋊C8)C2212yescomplemented
35#66873C2212yescomplemented
36#66873C2212yescomplemented
37#66872C2212yescomplemented
38#66871C2212yescomplemented
39C24×C11—21no—
40C23×D11—21no—
41C11×#41—41no—
42C11×#41—41no—
43C2×Q8×C11D411yescharacteristic
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—21no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11D411yescharacteristic
50C2×D4×C11D411yescharacteristic
51C2×D4×C11D411yescharacteristic
52C2×D4×C11C2312yes—
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C2×C22⋊D11—22no—
57C2×C22⋊D11—22no—
58C2×D44—21no—
59C2×D44—41no—
60C2×D44—41no—
61C2×D44C2312yes—
62C11×C4⋊C4C2312yes—
63C11×C22⋊C4—21no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4—22no—
66C42×C11—21no—
67C22⋊Dic11—21no—
68#4323—42no—
69#4323—42no—
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—22no—
72C4⋊Dic11C2312yes—
73C4×Dic11—21no—
74#4318—41no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3199—111nomaximal, Sylow
79C23×C11—22no—
80C23×C11—42no—
81C23×C11—82no—
82C23×C11C2×D411yescharacteristic
83C23×C11C2×D411yescharacteristic
84C23×C11C2×D411yescharacteristic
85C22×D11—22no—
86C22×D11—42no—
87C22×D11—82no—
88Q8×C11—41no—
89D4×C11—22no—
90D4×C11—22no—
91D4×C11—41no—
92D4×C11—41no—
93D4×C11—41no—
94D4×C11—42no—
95D4×C11—82no—
96D4×C11—82no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11C2×D411yescharacteristic
105C2×C4×C11C2×D411yescharacteristic
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11C2411yescharacteristic
108C22⋊D11—82no—
109C22⋊D11—82no—
110C2×Dic11—22no—
111D44—22no—
112D44—22no—
113D44—42no—
114C11⋊C8—22no—
115C11⋊C8—22no—
116#535—111no—
117#535D1111yescharacteristic, complemented
118#482—112no—
119#482—112no—
120#469—112no—
121#466—112no—
122#447—112no—
123#447—112no—
124#408—111no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—84no—
135C22×C11C22×D411yescharacteristic
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—84no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—42no—
144C4×C11H(5,𝔽2)11yescharacteristic
145C4×C11H(5,𝔽2)11yescharacteristic
146Dic11—42no—
147C2×#41C2×D1111yescharacteristic
148C22×D4—111no—
149C22×D4C2×D1111yescharacteristic, complemented
150C2×D8—112no—
151C2×D8—112no—
152C2×M16—111no—
153C22×C8—111no—
154#127—21no—
155#127—221no—
156#124—21no—
157#124—221no—
158#121—112no—
159#121—112no—
160#121C2×D1112yes—
161#121C2×D1112yescomplemented
162#120—21no—
163#120—21no—
164#120—221no—
165#120—221no—
166#117—111no—
167#117C2×D1111yescharacteristic, complemented
168#107—112no—
169#106—112no—
170#102—112no—
171#102—112no—
172#102—112no—
173#102—112no—
174C22⋊C8—112no—
175C22⋊C8—112no—
176C2×C11—41no—
177C2×C11—41no—
178C2×C11—41no—
179C2×C11—82no—
180C2×C11#53411yescharacteristic
181C2×C11#57612yes—
182D11—82no—
183C24—21no—
184C24—221no—
185#41—41no—
186#41—41no—
187C2×Q8C22⋊D1111yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—112no—
194C2×D4—222no—
195C2×D4—222no—
196C2×D4—221no—
197C2×D4—441no—
198C2×D4—441no—
199C2×D4C22⋊D1111yescharacteristic
200C2×D4C22⋊D1111yescharacteristic
201C2×D4C22⋊D1111yescharacteristic
202C2×D4C22×D1112yes—
203C22×C4C22×D1111yescharacteristic
204C22×C4C22×D1111yescharacteristic
205C22×C4C22×D1111yescharacteristic
206D8—442no—
207D8—442no—
208M16—441no—
209C2×C8—112no—
210C2×C8—112no—
211C2×C8—441no—
212C4⋊C4—112no—
213C4⋊C4C22×D1112yes—
214C22⋊C4—21no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—221no—
218C22⋊C4—222no—
219C22⋊C4—222no—
220C42—21no—
221C42—221no—
222C11#319911yescharacteristic, complemented, Sylow
223C23—22no—
224C23—42no—
225C23—82no—
226C23—222no—
227C23—442no—
228C23—882no—
229C23C2×C22⋊D1111yescharacteristic
230C23C2×C22⋊D1111yescharacteristic
231C23C2×C22⋊D1111yescharacteristic
232Q8—41no—
233D4—22no—
234D4—22no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—42no—
239D4—82no—
240D4—82no—
241D4—222no—
242D4—222no—
243D4—442no—
244D4—882no—
245D4—882no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—222no—
254C2×C4C2×C22⋊D1111yescharacteristic
255C2×C4C2×C22⋊D1111yescharacteristic
256C2×C4C2×C22⋊D1111yescharacteristic
257C2×C4C23×D1111yescharacteristic
258C8—222no—
259C8—222no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—84no—
270C22—442no—
271C22—442no—
272C22—442no—
273C22—884no—
274C22C22×C22⋊D1111yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—42no—
279C4—442no—
280C4#6703711yescharacteristic
281C4#6703711yescharacteristic
282C2—41no—
283C2—41no—
284C2—41no—
285C2—82no—
286C2—882no—
287C2#1062333511yescharacteristic
288C2#1062336612yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3199
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C11×#535C2semidirect
2. #10623361C2semidirect
3. #10622847C2semidirect
4. #10622830C2semidirect
5. #10622652C2semidirect
6. #10622651C2semidirect
7. #10622649C2semidirect
8. #10622648C2semidirect
9. #10622616C2semidirect
11. C22×D4×C11C22semidirect
12. C22×D44C22semidirect
16. C11×#121C22semidirect
19. C11×#117C22semidirect
27. #66983C22semidirect
28. #66979C22semidirect
29. C2×#4318C22semidirect
30. C22×C11⋊C8C22semidirect
31. #66896C22semidirect
32. #66896C22semidirect
33. C22⋊(C11⋊C8)C22semidirect
34. C22⋊(C11⋊C8)C22semidirect
35. #66873C22semidirect
36. #66873C22semidirect
37. #66872C22semidirect
38. #66871C22semidirect
117. #535D11semidirect
149. C22×D4C2×D11semidirect
161. #121C2×D11semidirect
167. #117C2×D11semidirect
222. C11#3199semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106233612
#106228472
#106228302
#106226522
#106226512
#106226492
#106226482
#106226162
#319911