Finite Group Databasebeta

← #13079668

Subgroups — #13079668

Order 1408.

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

normal subgroups only

This group has 420 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#10623066C211yesmaximal, characteristic, complemented
2#10623056C211yesmaximal, characteristic, complemented
3C11×#433C211yesmaximal, characteristic, complemented
4#10622457C212yesmaximal, complemented
5#10622456C212yesmaximal, complemented
6#10622347C212yesmaximal, complemented
7#10622345C212yesmaximal, complemented
8#10622326C211yesmaximal, characteristic, complemented
9#10622325C211yesmaximal, characteristic, complemented
10#10622310C211yesmaximal, characteristic, complemented
11#10622308C211yesmaximal, characteristic, complemented
12C2×#4339C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#66983C2212yes—
16C2×D88C2212yes—
17C2×D88C2212yes—
18C2×D88C2212yescomplemented
19C2×#4314C2212yescomplemented
20#66948—22no—
21#66947—22no—
22#66937—22no—
23#66935—22no—
24#66928C2211yescharacteristic
25#66928C2211yescharacteristic
26#66927C2211yescharacteristic
27#66927C2211yescharacteristic
28#66927C2211yescharacteristic, complemented
29C4×D44C2212yescomplemented
30#66923C2211yescharacteristic, complemented
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—
42C2×C22⋊D11—22no—
43#4339—42no—
44C2×D44—21no—
45C2×D44—22no—
46C2×D44—22no—
47C2×D44—22no—
48C2×D44—42no—
49C2×D44C2311yescharacteristic
50C2×D44C2311yescharacteristic
51C2×D44C2311yescharacteristic
52C2×D44C2312yes—
53C2×C4×D11—21no—
54C2×C4×D11—22no—
55C2×Dic22C2311yescharacteristic
56C2×C8×C11C2312yes—
57C2×C8×C11C2312yes—
58C11×C4⋊C4D412yes—
59C11×C22⋊C4D412yes—
60C42×C11C2311yescharacteristic
61C42×C11C2311yescharacteristic
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66C4⋊Dic11C2312yes—
67Dic11⋊C4—22no—
68D88—42no—
69D88—42no—
70D88—42no—
71#4314—42no—
72#3220—111nomaximal, Sylow
73C23×C11C2×D411yescharacteristic
74C22×D11—22no—
75C22×D11—21no—
76C22×D11—21no—
77C22×D11—21no—
78C22×D11—42no—
79C22×D11—82no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D412yes—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C22⋊D11—42no—
86C22⋊D11—82no—
87C2×Dic11—22no—
88C2×Dic11—21no—
89D44—22no—
90D44—22no—
91D44—22no—
92D44—22no—
93D44—22no—
94D44—42no—
95D44—82no—
96D44—82no—
97D44—82no—
98C4×D11—42no—
99C4×D11—82no—
100Dic22—22no—
101C8×C11—22no—
102C8×C11—22no—
103#540—111no—
104#535—111no—
105#496—111no—
106#493—111no—
107#490—111no—
108#488—111no—
109#463—112no—
110#459—112no—
111#449—112no—
112#447—112no—
113#433D1111yescharacteristic, complemented
114C22×C11—21no—
115C22×C11—22no—
116C22×C11C22×D411yescharacteristic
117C2×D11—41no—
118C2×D11—41no—
119C2×D11—41no—
120C2×D11—42no—
121C2×D11—42no—
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—84no—
127C4×C11—21no—
128C4×C11—22no—
129C4×C11—22no—
130C4×C11H(5,𝔽2)12yes—
131Dic11—41no—
132Dic11—42no—
133C2×#41—111no—
134C22×D4—111no—
135C2×SD16—112no—
136C2×D8—112no—
137C2×D8—112no—
138C2×D8—112no—
139#127—111no—
140#127—111no—
141#127—111no—
142#125—111no—
143#124—111no—
144#124—111no—
145#123—222no—
146#121—112no—
147#121—222no—
148#121—222no—
149#120—222no—
150C4×D4—112no—
151#117C2×D1111yescharacteristic
152C4⋊C8C2×D1112yescomplemented
153#103—112no—
154#102—112no—
155#102—112no—
156#102—112no—
157C22⋊C8C2×D1112yes—
158#97C2×D1111yescharacteristic, complemented
159C4×C8C2×D1111yescharacteristic, complemented
160C2×C11—41no—
161C2×C11#53511yescharacteristic
162C2×C11#57612yes—
163D11—81no—
164D11—82no—
165D11—81no—
166D11—81no—
167C24—221no—
168#41—442no—
169C2×Q8—111no—
170C2×D4—111no—
171C2×D4—111no—
172C2×D4—111no—
173C2×D4—112no—
174C2×D4—221no—
175C2×D4—222no—
176C2×D4—221no—
177C2×D4—222no—
178C2×D4—222no—
179C2×D4—222no—
180C2×D4—442no—
181C22×C4—221no—
182C22×C4—222no—
183C22×C4C22×D1111yescharacteristic
184SD16—442no—
185D8—442no—
186D8—442no—
187D8—442no—
188C2×C8C22×D1112yes—
189C2×C8C22×D1112yes—
190C4⋊C4—112no—
191C4⋊C4—222no—
192C4⋊C4D4412yes—
193C22⋊C4—222no—
194C22⋊C4—222no—
195C22⋊C4—222no—
196C22⋊C4—222no—
197C22⋊C4D4412yes—
198C42C22×D1111yescharacteristic
199C42C22×D1111yescharacteristic
200C11#322011yescharacteristic, complemented, Sylow
201C23—222no—
202C23—221no—
203C23—221no—
204C23—221no—
205C23—442no—
206C23—882no—
207C23C2×D4411yescharacteristic
208Q8—222no—
209D4—222no—
210D4—222no—
211D4—222no—
212D4—222no—
213D4—222no—
214D4—442no—
215D4—442no—
216D4—882no—
217D4—882no—
218D4—882no—
219D4—882no—
220C2×C4—22no—
221C2×C4—221no—
222C2×C4—222no—
223C2×C4—442no—
224C2×C4—882no—
225C2×C4C2×D4412yes—
226C2×C4C2×D4412yes—
227C2×C4C2×D4411yescharacteristic
228C2×C4C23×D1111yescharacteristic
229C8—22no—
230C8—22no—
231C22—22no—
232C22—21no—
233C22—442no—
234C22—442no—
235C22—442no—
236C22—442no—
237C22—442no—
238C22—441no—
239C22—441no—
240C22—441no—
241C22—442no—
242C22—884no—
243C22C22×D4411yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—442no—
248C4—441no—
249C4#6704212yes—
250C2—41no—
251C2—881no—
252C2—881no—
253C2—882no—
254C2—881no—
255C2#1062305611yescharacteristic
256C2#1062328312yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
hypercenter#433D11
hypocenterC11#3220
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
1. #10623066C2semidirect
2. #10623056C2semidirect
3. C11×#433C2semidirect
4. #10622457C2semidirect
5. #10622456C2semidirect
6. #10622347C2semidirect
7. #10622345C2semidirect
8. #10622326C2semidirect
9. #10622325C2semidirect
10. #10622310C2semidirect
11. #10622308C2semidirect
18. C2×D88C22semidirect
19. C2×#4314C22semidirect
28. #66927C22semidirect
29. C4×D44C22semidirect
30. #66923C22semidirect
31. C11×C4⋊C8C22semidirect
33. C11×#97C22semidirect
34. C4×C8×C11C22semidirect
37. #66885C22semidirect
38. #66880C22semidirect
113. #433D11semidirect
152. C4⋊C8C2×D11semidirect
158. #97C2×D11semidirect
159. C4×C8C2×D11semidirect
200. C11#3220semidirect

Maximal subgroups

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

subgroupindex
#106230662
#106230562
C11×#4332
#106224572
#106224562
#106223472
#106223452
#106223262
#106223252
#106223102
#106223082
#322011