Finite Group Databasebeta

← #13079452

Subgroups — #13079452

Order 1408.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623137C212yesmaximal, complemented
2C11×#469C211yesmaximal, characteristic, complemented
3#10622771C212yesmaximal, complemented
4#10622750C211yesmaximal, characteristic, complemented
5#10622739C211yesmaximal, characteristic, complemented
6#10622655C212yesmaximal, complemented
7#10622480C212yesmaximal, complemented
8#10622396C212yesmaximal, complemented
9#10622392C212yesmaximal, complemented
10C2×#4341C2212yes—
11C22×C4×D11C2211yescharacteristic
12C2×C11×D8C2211yescharacteristic, complemented
13C2×C11×M16C2211yescharacteristic
14C11×#121C2212yes—
15#66991C2212yes—
16#66990—22no—
17D4×Dic11—22no—
18C2×#4324C2212yescomplemented
19#66977C2212yes—
20C2×#4318C2211yescharacteristic
21C2×Dic44C2211yescharacteristic, complemented
22#66950C2212yes—
23#66945C2212yes—
24#66936—22no—
25(C22⋊D11)⋊C4—22no—
26C11×#106C2211yescharacteristic, complemented
27C11×#102C2212yescomplemented
28#66896C2212yescomplemented
29(C2×D11)⋊C8C2212yes—
30(C2×D11)⋊C8C2212yes—
31#66881C2211yescharacteristic, complemented
32#66880C2212yescomplemented
33#66874C2212yescomplemented
34#66871C2212yescomplemented
35C23×D11D411yescharacteristic
36C2×D4×C11—22no—
37C2×D4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C2×C22⋊D11—22no—
40C2×C22⋊D11—22no—
41C22×Dic11—22no—
42C22×Dic11D411yescharacteristic
43#4341—42no—
44#4341—42no—
45C2×C4×D11—41no—
46C2×C4×D11—41no—
47C2×C4×D11D412yes—
48C2×C4×D11C2312yes—
49C2×Dic22C2312yes—
50C11×D8—41no—
51C11×M16—41no—
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—22no—
56C22⋊Dic11—22no—
57C22⋊Dic11—22no—
58#4324—42no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64C4×Dic11—22no—
65#4318—41no—
66C2×C11⋊C8C2312yes—
67Dic44—41no—
68#3197—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11C2×D411yescharacteristic
71C22×D11—41no—
72C22×D11—42no—
73C22×D11C2×D412yes—
74D4×C11—22no—
75D4×C11—22no—
76D4×C11—44no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2411yescharacteristic
82C22⋊D11—44no—
83C22⋊D11—44no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—41no—
87C2×Dic11—44no—
88C2×Dic11C2×D412yes—
89C4×D11—22no—
90C4×D11—22no—
91C4×D11—42no—
92Dic22—22no—
93Dic22—22no—
94C8×C11—21no—
95C8×C11—21no—
96C11⋊C8—22no—
97#525—112no—
98#485—112no—
99#482—112no—
100#470—111no—
101#469D1111yescharacteristic, complemented
102#468—112no—
103#452—112no—
104#449—112no—
105#407—111no—
106C22×C11—21no—
107C22×C11—22no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11C22×D411yescharacteristic
112C2×D11—22no—
113C2×D11—22no—
114C2×D11—22no—
115C2×D11—44no—
116C4×C11—21no—
117C4×C11—42no—
118C4×C11H(5,𝔽2)11yescharacteristic
119C4×C11H(5,𝔽2)11yescharacteristic
120Dic11—22no—
121Dic11—42no—
122Dic11—42no—
123C2×#41—112no—
124C23×C4—111no—
125C2×Q16—111no—
126C2×SD16—112no—
127C2×D8C2×D1111yescharacteristic, complemented
128C2×M16—111no—
129C2×M16C2×D1111yescharacteristic
130#123—222no—
131C22⋊Q8—112no—
132C22⋊Q8—112no—
133#121—112no—
134#121C2×D1112yes—
135#120—222no—
136C4×D4—222no—
137C4×D4—222no—
138#117—112no—
139#107—112no—
140#106—111no—
141#106C2×D1111yescharacteristic, complemented
142#103—112no—
143#103—112no—
144#102—112no—
145#102C2×D1112yescomplemented
146C22⋊C8—112no—
147C22⋊C8—112no—
148C2×C11—41no—
149C2×C11—82no—
150C2×C11#53411yescharacteristic
151C2×C11#57512yes—
152D11—42no—
153C24—111no—
154#41—442no—
155#41—442no—
156C2×Q8—112no—
157C2×D4—22no—
158C2×D4—222no—
159C2×D4—222no—
160C2×D4C22×D1112yes—
161C22×C4—111no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4—222no—
165C22×C4—441no—
166C22×C4—441no—
167C22×C4C22×D1111yescharacteristic
168Q16—441no—
169SD16—442no—
170D8—41no—
171M16—41no—
172M16—441no—
173C2×C8—112no—
174C2×C8C22×D1111yescharacteristic
175C2×C8C22×D1111yescharacteristic
176C4⋊C4—112no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4C22×D1112yes—
180C22⋊C4—22no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C42—222no—
186C11#319711yescharacteristic, complemented, Sylow
187C23—22no—
188C23—112no—
189C23—441no—
190C23—442no—
191C23D4×D1111yescharacteristic
192Q8—222no—
193Q8—222no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—444no—
198D4—444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—112no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—442no—
208C2×C4—441no—
209C2×C4—444no—
210C2×C4D4×D1111yescharacteristic
211C2×C4C23×D1111yescharacteristic
212C8—21no—
213C8—21no—
214C8—222no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—222no—
221C22—222no—
222C22—222no—
223C22—444no—
224C22C2×D4×D1111yescharacteristic
225C4—21no—
226C4—42no—
227C4—222no—
228C4—442no—
229C4—442no—
230C4#6703711yescharacteristic
231C4#6704211yescharacteristic
232C2—41no—
233C2—82no—
234C2—442no—
235C2#1062313611yescharacteristic
236C2#1062330412yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#469C2
socleC22×C11C22×D4
hypercenter#469D11
hypocenterC11#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #10623137C2semidirect
2. C11×#469C2semidirect
3. #10622771C2semidirect
4. #10622750C2semidirect
5. #10622739C2semidirect
6. #10622655C2semidirect
7. #10622480C2semidirect
8. #10622396C2semidirect
9. #10622392C2semidirect
12. C2×C11×D8C22semidirect
18. C2×#4324C22semidirect
21. C2×Dic44C22semidirect
26. C11×#106C22semidirect
27. C11×#102C22semidirect
28. #66896C22semidirect
31. #66881C22semidirect
32. #66880C22semidirect
33. #66874C22semidirect
34. #66871C22semidirect
101. #469D11semidirect
127. C2×D8C2×D11semidirect
141. #106C2×D11semidirect
145. #102C2×D11semidirect
186. C11#3197semidirect

Maximal subgroups

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

subgroupindex
#106231372
C11×#4692
#106227712
#106227502
#106227392
#106226552
#106224802
#106223962
#106223922
#319711