Finite Group Databasebeta

← #13079690

Subgroups — #13079690

Order 1408.

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

normal subgroups only

This group has 396 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#10623056C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic, complemented
3C11×#433C211yesmaximal, characteristic, complemented
4#10622461C212yesmaximal, complemented
5#10622458C212yesmaximal, complemented
6#10622346C212yesmaximal, complemented
7#10622344C212yesmaximal, complemented
8#10622328C211yesmaximal, characteristic, complemented
9#10622326C211yesmaximal, characteristic, complemented
10#10622310C211yesmaximal, characteristic, complemented
11#10622306C211yesmaximal, characteristic, complemented
12C2×#4339C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#66977C2212yes—
16C2×Dic44C2212yescomplemented
17C2×#4314C2212yes—
18C2×#4314C2212yes—
19C2×#4314C2212yescomplemented
20#66948—22no—
21#66942—22no—
22#66935—22no—
23#66932—22no—
24#66928C2211yescharacteristic
25#66928C2211yescharacteristic
26#66927C2211yescharacteristic
27#66927C2211yescharacteristic
28#66923C2211yescharacteristic, complemented
29#66922C2211yescharacteristic, complemented
30C4×Dic22C2212yescomplemented
31C11×C4⋊C8C2212yescomplemented
32C11×C22⋊C8C2212yes—
33C11×#97C2211yescharacteristic, complemented
34C4×C8×C11C2211yescharacteristic, complemented
35#66885C2212yes—
36#66885C2212yes—
37#66885C2212yescomplemented
38#66880C2212yescomplemented
39C23×D11—21no—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—21no—
42#4339—42no—
43C2×D44—21no—
44C2×D44—22no—
45C2×D44—22no—
46C2×D44—42no—
47C2×D44C2311yescharacteristic
48C2×D44C2311yescharacteristic
49C2×D44C2311yescharacteristic
50C2×C4×D11—21no—
51C2×Dic22C2311yescharacteristic
52C2×Dic22C2312yes—
53C2×C8×C11C2312yes—
54C2×C8×C11C2312yes—
55C11×C4⋊C4D412yes—
56C11×C22⋊C4D412yes—
57C42×C11C2311yescharacteristic
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11C2312yes—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67C4×Dic11—22no—
68Dic44—42no—
69#4314—42no—
70#4314—42no—
71#4314—42no—
72#3222—111nomaximal, Sylow
73C23×C11C2×D411yescharacteristic
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—21no—
77C22×D11—42no—
78C22×D11—82no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2411yescharacteristic
84C22⋊D11—42no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—21no—
88D44—22no—
89D44—22no—
90D44—22no—
91D44—42no—
92D44—82no—
93D44—82no—
94C4×D11—42no—
95Dic22—22no—
96Dic22—22no—
97Dic22—22no—
98C8×C11—22no—
99C8×C11—22no—
100#541—111no—
101#535—111no—
102#497—111no—
103#492—111no—
104#490—111no—
105#488—111no—
106#464—112no—
107#460—112no—
108#452—112no—
109#450—112no—
110#433D1111yescharacteristic, complemented
111C22×C11—21no—
112C22×C11—22no—
113C22×C11C22×D411yescharacteristic
114C2×D11—41no—
115C2×D11—41no—
116C2×D11—41no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—84no—
121C4×C11—21no—
122C4×C11—22no—
123C4×C11—22no—
124C4×C11H(5,𝔽2)12yes—
125Dic11—41no—
126Dic11—42no—
127Dic11—42no—
128C2×#41—111no—
129C22×D4—111no—
130C2×Q16—112no—
131C2×SD16—112no—
132C2×SD16—112no—
133C2×SD16—112no—
134C4⋊Q8—111no—
135#127—111no—
136#127—111no—
137#126—222no—
138#125—111no—
139#125—222no—
140#124—111no—
141#124—111no—
142C22⋊Q8—112no—
143#121—222no—
144#120—222no—
145C4×Q8—112no—
146#117C2×D1111yescharacteristic
147C4⋊C8C2×D1112yescomplemented
148#103—112no—
149#102—112no—
150#102—112no—
151#102—112no—
152C22⋊C8C2×D1112yes—
153#97C2×D1111yescharacteristic, complemented
154C4×C8C2×D1111yescharacteristic, complemented
155C2×C11—41no—
156C2×C11#53511yescharacteristic
157C2×C11#57712yes—
158D11—81no—
159D11—81no—
160D11—81no—
161C24—221no—
162#41—442no—
163C2×Q8—111no—
164C2×Q8—112no—
165C2×D4—111no—
166C2×D4—111no—
167C2×D4—111no—
168C2×D4—221no—
169C2×D4—221no—
170C2×D4—222no—
171C2×D4—222no—
172C2×D4—442no—
173C22×C4—221no—
174C22×C4C22×D1111yescharacteristic
175Q16—442no—
176SD16—442no—
177SD16—442no—
178SD16—442no—
179C2×C8C22×D1112yes—
180C2×C8C22×D1112yes—
181C4⋊C4—112no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4D4412yes—
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4D4412yes—
191C42—222no—
192C42C22×D1111yescharacteristic
193C42C22×D1111yescharacteristic
194C11#322211yescharacteristic, complemented, Sylow
195C23—221no—
196C23—221no—
197C23—221no—
198C23—442no—
199C23—882no—
200C23C2×D4411yescharacteristic
201Q8—222no—
202Q8—222no—
203Q8—222no—
204D4—222no—
205D4—222no—
206D4—222no—
207D4—442no—
208D4—442no—
209D4—882no—
210D4—882no—
211C2×C4—22no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—442no—
216C2×C4C2×D4412yes—
217C2×C4C2×D4412yes—
218C2×C4C2×D4411yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—442no—
225C22—442no—
226C22—442no—
227C22—441no—
228C22—441no—
229C22—441no—
230C22—884no—
231C22C22×D4411yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—442no—
236C4—441no—
237C4—442no—
238C4#6704212yes—
239C2—41no—
240C2—881no—
241C2—881no—
242C2—881no—
243C2#1062305611yescharacteristic
244C2#1062328212yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
prime radical#10623056C2
hypercenter#433D11
hypocenterC11#3222
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #10623049C2semidirect
3. C11×#433C2semidirect
4. #10622461C2semidirect
5. #10622458C2semidirect
6. #10622346C2semidirect
7. #10622344C2semidirect
8. #10622328C2semidirect
9. #10622326C2semidirect
10. #10622310C2semidirect
11. #10622306C2semidirect
16. C2×Dic44C22semidirect
19. C2×#4314C22semidirect
28. #66923C22semidirect
29. #66922C22semidirect
30. C4×Dic22C22semidirect
31. C11×C4⋊C8C22semidirect
33. C11×#97C22semidirect
34. C4×C8×C11C22semidirect
37. #66885C22semidirect
38. #66880C22semidirect
110. #433D11semidirect
147. C4⋊C8C2×D11semidirect
153. #97C2×D11semidirect
154. C4×C8C2×D11semidirect
194. C11#3222semidirect

Maximal subgroups

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

subgroupindex
#106230562
#106230492
C11×#4332
#106224612
#106224582
#106223462
#106223442
#106223282
#106223262
#106223102
#106223062
#322211