Finite Group Databasebeta

← #13079458

Subgroups — #13079458

Order 1408.

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

normal subgroups only

This group has 418 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#10623322C212yesmaximal, complemented
2C11×#407C211yesmaximal, characteristic, complemented
3#10622750C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622747C212yesmaximal, complemented
6#10622350C212yesmaximal, complemented
7#10622347C212yesmaximal, complemented
8#10622346C212yesmaximal, complemented
9#10622336C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C2×#4339C2212yes—
12C2×C11×M16C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14#67006—22no—
15#66983C2212yes—
16#66983C2212yes—
17#66982—22no—
18C4×C22⋊D11—22no—
19C4×C22⋊D11—22no—
20#66979C2212yes—
21#66977C2212yes—
22#66977C2212yes—
23C2×Dic44C2211yescharacteristic, complemented
24C2×D88C2211yescharacteristic, complemented
25C2×#4314C2212yescomplemented
26C11×C22⋊C8C2212yes—
27C11×C22⋊C8C2212yes—
28#66885C2212yescomplemented
29#66885C2212yescomplemented
30#66882C2212yescomplemented
31#66881C2211yescharacteristic, complemented
32#66881C2211yescharacteristic, complemented
33#66880C2212yescomplemented
34#66880C2212yescomplemented
35C24×C11D411yescharacteristic
36C22×C4×C11—41no—
37C22×C4×C11—41no—
38C22×C4×C11D411yescharacteristic
39C22×C4×C11D412yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—22no—
43C2×C22⋊D11—22no—
44C2×C22⋊D11—22no—
45#4339—42no—
46#4339—42no—
47C2×D44C2312yes—
48C2×C4×D11—22no—
49C2×Dic22C2312yes—
50C11×M16—41no—
51C11×M16—41no—
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2312yes—
54C2×C8×C11C2311yescharacteristic
55C22⋊Dic11—22no—
56C22⋊Dic11—22no—
57C22⋊Dic11—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60C4⋊Dic11C2312yes—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64C4×Dic11—22no—
65Dic44—41no—
66D88—41no—
67#4314—42no—
68#3197—111nomaximal, Sylow
69C23×C11—41no—
70C23×C11—42no—
71C23×C11C2×D411yescharacteristic
72C23×C11C2×D412yes—
73C22×D11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11—41no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2411yescharacteristic
83C22⋊D11—44no—
84C22⋊D11—44no—
85C22⋊D11—44no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89D44—22no—
90D44—22no—
91C4×D11—44no—
92Dic22—22no—
93Dic22—22no—
94C8×C11—22no—
95C8×C11—21no—
96C8×C11—21no—
97#525—112no—
98#485—112no—
99#482—112no—
100#470—111no—
101#469—111no—
102#468—112no—
103#452—112no—
104#449—112no—
105#407D1111yescharacteristic, complemented
106C22×C11—21no—
107C22×C11—22no—
108C22×C11—22no—
109C22×C11—22no—
110C22×C11—22no—
111C22×C11—44no—
112C22×C11C22×D411yescharacteristic
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C4×C11—21no—
117C4×C11—22no—
118C4×C11H(5,𝔽2)11yescharacteristic
119C4×C11H(5,𝔽2)11yescharacteristic
120Dic11—42no—
121Dic11—42no—
122Dic11—42no—
123C2×#41—112no—
124C23×C4C2×D1111yescharacteristic
125C2×Q16—111no—
126C2×SD16—112no—
127C2×D8—111no—
128C2×M16C2×D1111yescharacteristic
129C2×M16C2×D1111yescharacteristic
130#123—222no—
131C22⋊Q8—112no—
132C22⋊Q8—112no—
133#121—112no—
134#121—112no—
135#120—222no—
136C4×D4—222no—
137C4×D4—222no—
138#117—112no—
139#107—112no—
140#106—111no—
141#106—111no—
142#103—112no—
143#103—112no—
144#102—112no—
145#102—112no—
146C22⋊C8C2×D1112yes—
147C22⋊C8C2×D1112yes—
148C2×C11—41no—
149C2×C11—42no—
150C2×C11#53411yescharacteristic
151C2×C11#57512yes—
152D11—82no—
153C24D4411yescharacteristic
154#41—442no—
155#41—442no—
156C2×Q8—112no—
157C2×D4—112no—
158C2×D4—222no—
159C2×D4—222no—
160C2×D4—222no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—222no—
164C22×C4D4411yescharacteristic
165C22×C4D4412yes—
166C22×C4C22×D1112yes—
167C22×C4C22×D1111yescharacteristic
168Q16—441no—
169SD16—442no—
170D8—441no—
171M16—41no—
172M16—41no—
173C2×C8C22×D1111yescharacteristic
174C2×C8C22×D1112yes—
175C2×C8C22×D1111yescharacteristic
176C4⋊C4—112no—
177C4⋊C4—112no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C22⋊C4—222no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C42—222no—
186C11#319711yescharacteristic, complemented, Sylow
187C23—41no—
188C23—42no—
189C23—222no—
190C23C2×D4411yescharacteristic
191C23C2×D4412yes—
192Q8—222no—
193Q8—222no—
194D4—222no—
195D4—222no—
196D4—444no—
197D4—444no—
198D4—444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—444no—
209C2×C4C2×D4412yes—
210C2×C4C2×D4411yescharacteristic
211C2×C4C23×D1111yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—442no—
222C22—442no—
223C22—442no—
224C22C22×D4411yescharacteristic
225C4—22no—
226C4—21no—
227C4—442no—
228C4—442no—
229C4—442no—
230C4#6703711yescharacteristic
231C4#6703711yescharacteristic
232C2—41no—
233C2—42no—
234C2—882no—
235C2#1062302411yescharacteristic
236C2#1062327912yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#407C2
socleC22×C11C22×D4
hypercenter#407D11
hypocenterC11#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #10623322C2semidirect
2. C11×#407C2semidirect
3. #10622750C2semidirect
4. #10622748C2semidirect
5. #10622747C2semidirect
6. #10622350C2semidirect
7. #10622347C2semidirect
8. #10622346C2semidirect
9. #10622336C2semidirect
23. C2×Dic44C22semidirect
24. C2×D88C22semidirect
25. C2×#4314C22semidirect
28. #66885C22semidirect
29. #66885C22semidirect
30. #66882C22semidirect
31. #66881C22semidirect
32. #66881C22semidirect
33. #66880C22semidirect
34. #66880C22semidirect
105. #407D11semidirect
186. C11#3197semidirect

Maximal subgroups

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

subgroupindex
#106233222
C11×#4072
#106227502
#106227482
#106227472
#106223502
#106223472
#106223462
#106223362
#319711