Finite Group Databasebeta

← #13079666

Subgroups — #13079666

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
1C11×#535C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic, complemented
3#10622851C212yesmaximal, complemented
4#10622830C212yesmaximal, complemented
5#10622686C211yesmaximal, characteristic, complemented
6#10622685C212yesmaximal, complemented
7#10622684C211yesmaximal, characteristic, complemented
8#10622671C211yesmaximal, characteristic, complemented
9#10622670C212yesmaximal, complemented
10#10622669C211yesmaximal, characteristic, complemented
11#10622613C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C11×#127C2211yescharacteristic
15C11×#127C2211yescharacteristic
16C11×#124C2211yescharacteristic
17C11×#124C2211yescharacteristic
18C11×#121—22no—
19C11×#120—22no—
20C11×#117C2211yescharacteristic
21C2×#4325C2212yescomplemented
22C2×#4323C2212yes—
23C2×#4323C2212yes—
24C2×#4323C2212yescomplemented
25#66983C2212yes—
26#66947—22no—
27#66937—22no—
28#66927C2211yescharacteristic, complemented
29C4×D44C2212yescomplemented
30#66923C2211yescharacteristic, complemented
31#66899C2212yescomplemented
32#66896C2212yes—
33#66896C2212yes—
34#66896C2212yescomplemented
35C22⋊(C11⋊C8)C2212yes—
36C4⋊(C11⋊C8)C2212yescomplemented
37#66867C2211yescharacteristic, complemented
38C4×C11⋊C8C2211yescharacteristic, complemented
39C24×C11—21no—
40C11×#41—42no—
41C2×Q8×C11C2311yescharacteristic
42C2×D4×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—42no—
47C2×D4×C11C2311yescharacteristic
48C2×D4×C11C2311yescharacteristic
49C2×D4×C11C2311yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11C2311yescharacteristic
52C2×C22⋊D11—22no—
53C2×D44—22no—
54C2×D44C2312yes—
55C2×C4×D11—22no—
56C11×C4⋊C4D412yes—
57C11×C22⋊C4—22no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4D412yes—
60C42×C11C2311yescharacteristic
61C42×C11C2311yescharacteristic
62#4325—42no—
63#4323—42no—
64#4323—42no—
65#4323—42no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68C4⋊Dic11C2312yes—
69Dic11⋊C4—22no—
70C2×C11⋊C8C2312yes—
71C2×C11⋊C8C2312yes—
72#3220—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—42no—
77C23×C11—82no—
78C23×C11C2×D411yescharacteristic
79C22×D11—22no—
80Q8×C11—22no—
81D4×C11—22no—
82D4×C11—22no—
83D4×C11—22no—
84D4×C11—42no—
85D4×C11—42no—
86D4×C11—82no—
87D4×C11—82no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—42no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—82no—
96C2×Dic11—22no—
97D44—22no—
98D44—22no—
99D44—82no—
100C4×D11—82no—
101C11⋊C8—22no—
102C11⋊C8—22no—
103#540—111no—
104#535D1111yescharacteristic, complemented
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#433—111no—
114C22×C11—21no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—84no—
123C22×C11C22×D411yescharacteristic
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—42no—
127C4×C11—21no—
128C4×C11—22no—
129C4×C11—22no—
130C4×C11—41no—
131C4×C11H(5,𝔽2)12yes—
132Dic11—42no—
133C2×#41C2×D1111yescharacteristic
134C22×D4C2×D1111yescharacteristic
135C2×SD16—112no—
136C2×D8—112no—
137C2×D8—112no—
138C2×D8—112no—
139#127—111no—
140#127C2×D1111yescharacteristic
141#127C2×D1111yescharacteristic
142#125—111no—
143#124C2×D1111yescharacteristic
144#124C2×D1111yescharacteristic
145#123—222no—
146#121—22no—
147#121—112no—
148#121—222no—
149#120—22no—
150C4×D4—112no—
151#117C2×D1111yescharacteristic
152C4⋊C8—112no—
153#103—112no—
154#102—112no—
155#102—112no—
156#102—112no—
157C22⋊C8—112no—
158#97—111no—
159C4×C8—111no—
160C2×C11—41no—
161C2×C11—81no—
162C2×C11—81no—
163C2×C11—81no—
164C2×C11#53511yescharacteristic
165C2×C11#57612yes—
166D11—82no—
167C24—21no—
168#41—42no—
169C2×Q8C22×D1111yescharacteristic
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—42no—
175C2×D4—112no—
176C2×D4—222no—
177C2×D4—222no—
178C2×D4C22×D1111yescharacteristic
179C2×D4C22×D1111yescharacteristic
180C2×D4C22×D1111yescharacteristic
181C22×C4—21no—
182C22×C4—222no—
183C22×C4C22×D1111yescharacteristic
184SD16—442no—
185D8—442no—
186D8—442no—
187D8—442no—
188C2×C8—112no—
189C2×C8—112no—
190C4⋊C4—112no—
191C4⋊C4—222no—
192C4⋊C4C22⋊D1112yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—222no—
196C22⋊C4—222no—
197C22⋊C4C22⋊D1112yes—
198C42C22×D1111yescharacteristic
199C42C22×D1111yescharacteristic
200C11#322011yescharacteristic, complemented, Sylow
201C23—21no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23—82no—
206C23—222no—
207C23C2×C22⋊D1111yescharacteristic
208Q8—22no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—42no—
213D4—42no—
214D4—82no—
215D4—82no—
216D4—222no—
217D4—222no—
218D4—882no—
219D4—882no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—222no—
224C2×C4—882no—
225C2×C4C2×C22⋊D1112yes—
226C2×C4C2×C22⋊D1112yes—
227C2×C4C2×C22⋊D1111yescharacteristic
228C2×C4C23×D1111yescharacteristic
229C8—222no—
230C8—222no—
231C22—21no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—84no—
240C22—442no—
241C22—442no—
242C22—442no—
243C22C22×C22⋊D1111yescharacteristic
244C4—21no—
245C4—22no—
246C4—22no—
247C4—41no—
248C4—442no—
249C4#6703712yes—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—81no—
254C2—882no—
255C2#1062333611yescharacteristic
256C2#1062336612yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3220
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C11×#535C2semidirect
2. #10623066C2semidirect
3. #10622851C2semidirect
4. #10622830C2semidirect
5. #10622686C2semidirect
6. #10622685C2semidirect
7. #10622684C2semidirect
8. #10622671C2semidirect
9. #10622670C2semidirect
10. #10622669C2semidirect
11. #10622613C2semidirect
21. C2×#4325C22semidirect
24. C2×#4323C22semidirect
28. #66927C22semidirect
29. C4×D44C22semidirect
30. #66923C22semidirect
31. #66899C22semidirect
34. #66896C22semidirect
36. C4⋊(C11⋊C8)C22semidirect
37. #66867C22semidirect
38. C4×C11⋊C8C22semidirect
104. #535D11semidirect
200. C11#3220semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106230662
#106228512
#106228302
#106226862
#106226852
#106226842
#106226712
#106226702
#106226692
#106226132
#322011