Finite Group Databasebeta

← #13079459

Subgroups — #13079459

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#10623158C212yesmaximal, complemented
2C11×#470C211yesmaximal, characteristic, complemented
3#10622800C212yesmaximal, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622739C211yesmaximal, characteristic, complemented
6#10622662C212yesmaximal, complemented
7#10622479C212yesmaximal, complemented
8#10622428C212yesmaximal, complemented
9#10622424C212yesmaximal, complemented
10C2×#4343C2212yes—
11C22×C4×D11C2211yescharacteristic
12C2×C11×Q16C2211yescharacteristic, complemented
13C2×C11×M16C2211yescharacteristic
14C11×C22⋊Q8C2212yes—
15#66999C2212yes—
16C2×#4325C2212yescomplemented
17#66983C2212yes—
18C2×#4318C2211yescharacteristic
19C2×D88C2211yescharacteristic, complemented
20#66948C2212yes—
21#66947—22no—
22#66946—22no—
23#66945C2212yes—
24#66935—22no—
25(C22⋊D11)⋊C4—22no—
26C11×#106C2211yescharacteristic, complemented
27C11×#103C2212yescomplemented
28#66899C2212yescomplemented
29#66885C2212yescomplemented
30(C2×D11)⋊C8C2212yes—
31(C2×D11)⋊C8C2212yes—
32#66881C2211yescharacteristic, complemented
33#66873C2212yescomplemented
34#66871C2212yescomplemented
35C23×D11D411yescharacteristic
36C2×Q8×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39C22×Dic11D411yescharacteristic
40#4343—42no—
41#4343—42no—
42C2×D44—22no—
43C2×D44—22no—
44C2×D44C2312yes—
45C2×C4×D11—22no—
46C2×C4×D11—41no—
47C2×C4×D11—41no—
48C2×C4×D11D412yes—
49C2×C4×D11C2312yes—
50C11×Q16—41no—
51C11×M16—41no—
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4—22no—
55C11×C4⋊C4C2312yes—
56C11×C22⋊C4—22no—
57#4325—42no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64C4×Dic11—22no—
65#4318—41no—
66C2×C11⋊C8C2312yes—
67D88—41no—
68#3197—111nomaximal, Sylow
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11—41no—
72C22×D11—42no—
73C22×D11C2×D412yes—
74Q8×C11—22no—
75Q8×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2411yescharacteristic
82C22⋊D11—44no—
83C2×Dic11—22no—
84C2×Dic11—41no—
85C2×Dic11C2×D412yes—
86D44—22no—
87D44—22no—
88D44—44no—
89D44—44no—
90C4×D11—22no—
91C4×D11—22no—
92C4×D11—42no—
93C4×D11—44no—
94C8×C11—21no—
95C8×C11—21no—
96C11⋊C8—22no—
97#525—112no—
98#485—112no—
99#482—112no—
100#470D1111yescharacteristic, complemented
101#469—111no—
102#468—112no—
103#452—112no—
104#449—112no—
105#407—111no—
106C22×C11—21no—
107C22×C11—22no—
108C22×C11C22×D411yescharacteristic
109C2×D11—22no—
110C2×D11—22no—
111C2×D11—22no—
112C2×D11—44no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C4×C11—21no—
117C4×C11—42no—
118C4×C11—42no—
119C4×C11H(5,𝔽2)11yescharacteristic
120C4×C11H(5,𝔽2)11yescharacteristic
121Dic11—22no—
122Dic11—42no—
123C2×#41—112no—
124C23×C4—111no—
125C2×Q16C2×D1111yescharacteristic, complemented
126C2×SD16—112no—
127C2×D8—111no—
128C2×M16—111no—
129C2×M16C2×D1111yescharacteristic
130#123—222no—
131C22⋊Q8—112no—
132C22⋊Q8C2×D1112yes—
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#106C2×D1111yescharacteristic, complemented
142#103—112no—
143#103C2×D1112yescomplemented
144#102—112no—
145#102—112no—
146C22⋊C8—112no—
147C22⋊C8—112no—
148C2×C11—41no—
149C2×C11#53411yescharacteristic
150C2×C11#57512yes—
151D11—42no—
152D11—82no—
153C24—111no—
154#41—442no—
155#41—442no—
156C2×Q8C22×D1112yes—
157C2×D4—112no—
158C2×D4—222no—
159C2×D4—222no—
160C2×D4—222no—
161C22×C4—111no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4—222no—
165C22×C4—441no—
166C22×C4—441no—
167C22×C4C22×D1111yescharacteristic
168Q16—41no—
169SD16—442no—
170D8—441no—
171M16—41no—
172M16—441no—
173C2×C8—112no—
174C2×C8C22×D1111yescharacteristic
175C2×C8C22×D1111yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—112no—
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—112no—
188C23—222no—
189C23—441no—
190C23—442no—
191C23D4×D1111yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—222no—
195D4—222no—
196D4—444no—
197D4—444no—
198D4—444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—112no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—442no—
208C2×C4—444no—
209C2×C4—441no—
210C2×C4D4×D1111yescharacteristic
211C2×C4C23×D1111yescharacteristic
212C8—21no—
213C8—21no—
214C8—222no—
215C22—22no—
216C22—21no—
217C22—222no—
218C22—222no—
219C22—222no—
220C22—444no—
221C22—442no—
222C22—442no—
223C22—442no—
224C22C2×D4×D1111yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—222no—
229C4—442no—
230C4#6703711yescharacteristic
231C4#6704211yescharacteristic
232C2—41no—
233C2—442no—
234C2—882no—
235C2#1062313611yescharacteristic
236C2#1062330812yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#470C2
socleC22×C11C22×D4
hypercenter#470D11
hypocenterC11#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #10623158C2semidirect
2. C11×#470C2semidirect
3. #10622800C2semidirect
4. #10622748C2semidirect
5. #10622739C2semidirect
6. #10622662C2semidirect
7. #10622479C2semidirect
8. #10622428C2semidirect
9. #10622424C2semidirect
12. C2×C11×Q16C22semidirect
16. C2×#4325C22semidirect
19. C2×D88C22semidirect
26. C11×#106C22semidirect
27. C11×#103C22semidirect
28. #66899C22semidirect
29. #66885C22semidirect
32. #66881C22semidirect
33. #66873C22semidirect
34. #66871C22semidirect
100. #470D11semidirect
125. C2×Q16C2×D11semidirect
141. #106C2×D11semidirect
143. #103C2×D11semidirect
186. C11#3197semidirect

Maximal subgroups

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

subgroupindex
#106231582
C11×#4702
#106228002
#106227482
#106227392
#106226622
#106224792
#106224282
#106224242
#319711