Finite Group Databasebeta

← #13079535

Subgroups — #13079535

Order 1408.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623256C211yesmaximal, characteristic, complemented
2D11×#127C211yesmaximal, characteristic, complemented
3C11×#486C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5#10622686C211yesmaximal, characteristic, complemented
6#10622399C214yesmaximal, complemented
7#10622386C214yesmaximal, complemented
8#10622308C211yesmaximal, characteristic, complemented
9#10622298C211yesmaximal, characteristic, complemented
10C2×#4343—21no—
11C2×D4×D11—21no—
12C2×D4×D11—21no—
13C2×D4×D11C2212yes—
14C11×C4⋊Q8C2211yescharacteristic, complemented
15C11×#127C2211yescharacteristic
16#67000—21no—
17#66993—21no—
18#66993—21no—
19#66993C2212yes—
20C2×#4323C2214yescomplemented
21C2×D88C2214yescomplemented
22#66948—21no—
23#66948C2212yes—
24#66946—21no—
25#66946C2212yescomplemented
26#66927C2211yescharacteristic
27#66927C2211yescharacteristic, complemented
28C42×D11C2211yescharacteristic
29C11×#102C2214yescomplemented
30C4×C8×C11C2211yescharacteristic, complemented
31(C2×D11)⋊C8C2212yes—
32Dic11⋊C8C2212yescomplemented
33#66873C2214yescomplemented
34C4×C11⋊C8C2211yescharacteristic, complemented
35C23×D11—22no—
36C2×Q8×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11C2312yes—
40C2×C22⋊D11—22no—
41C2×C22⋊D11—22no—
42C2×C22⋊D11—22no—
43#4343—44no—
44D4×D11—44no—
45D4×D11—44no—
46D4×D11—44no—
47C2×D44—22no—
48C2×D44—21no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44—21no—
52C2×D44C2312yes—
53C2×D44C2312yes—
54C2×C4×D11—22no—
55C2×C4×D11D411yescharacteristic
56C2×C4×D11D411yescharacteristic
57C2×C4×D11C2311yescharacteristic
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2312yes—
61C42×C11C2311yescharacteristic
62#4323—44no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65C4×Dic11D411yescharacteristic
66C4×Dic11D411yescharacteristic
67C4×Dic11C2311yescharacteristic
68C2×C11⋊C8C2312yes—
69D88—44no—
70#3205—111nomaximal, Sylow
71C23×C11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—44no—
75C22×D11—44no—
76C22×D11—44no—
77C22×D11C2×D411yescharacteristic
78Q8×C11—42no—
79D4×C11—24no—
80D4×C11—42no—
81D4×C11—42no—
82C2×C4×C11—22no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—44no—
87C22⋊D11—44no—
88C22⋊D11—44no—
89C2×Dic11C2×D411yescharacteristic
90C2×Dic11C2×D411yescharacteristic
91C2×Dic11C2×D411yescharacteristic
92D44—24no—
93D44—24no—
94D44—44no—
95D44—42no—
96D44—42no—
97D44—42no—
98D44—42no—
99C4×D11—22no—
100C4×D11—22no—
101C4×D11—44no—
102C4×D11D814yescomplemented
103C8×C11—22no—
104C11⋊C8—22no—
105#532—111no—
106C2×#127—111no—
107#493—111no—
108#493—111no—
109#486—111no—
110#486D1111yescharacteristic, complemented
111#459—114no—
112#447—114no—
113#431—111no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11C22×D411yescharacteristic
118C2×D11—21no—
119C2×D11—21no—
120C2×D11—42no—
121C2×D11—42no—
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—88no—
127C2×D11C2×D812yes—
128C4×C11—42no—
129C4×C11C2×D812yes—
130C4×C11AGL(1,ℤ/8)12yes—
131C4×C11H(5,𝔽2)12yes—
132Dic11—21no—
133Dic11—21no—
134Dic11C2×D812yes—
135C2×#41—221no—
136C22×D4—112no—
137C22×D4—221no—
138C22×D4—221no—
139C2×D8—114no—
140C2×D8—114no—
141C4⋊Q8C2×D1111yescharacteristic, complemented
142#127—112no—
143#127—111no—
144#127—111no—
145#127—221no—
146#127—221no—
147#127C2×D1111yescharacteristic
148#124—221no—
149#121—112no—
150#121—221no—
151C4×D4—112no—
152C4×D4—221no—
153C2×C42—111no—
154C4⋊C8—112no—
155#102—114no—
156#102C2×D1114yescomplemented
157C22⋊C8—112no—
158C4×C8—111no—
159C4×C8C2×D1111yescharacteristic, complemented
160C2×C11—82no—
161C2×C11#53511yescharacteristic
162C2×C11C22×D811yescharacteristic
163C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
164D11—22no—
165D11—82no—
166D11—82no—
167C24—222no—
168#41—444no—
169C2×Q8—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—112no—
173C2×D4—112no—
174C2×D4—222no—
175C2×D4—222no—
176C2×D4—222no—
177C2×D4—222no—
178C2×D4—221no—
179C2×D4—221no—
180C2×D4—221no—
181C2×D4—221no—
182C2×D4—444no—
183C2×D4—444no—
184C2×D4—444no—
185C2×D4C22×D1112yes—
186C22×C4—111no—
187C22×C4—111no—
188C22×C4—111no—
189C22×C4—222no—
190D8—444no—
191D8—444no—
192C2×C8—112no—
193C2×C8C22×D1112yes—
194C4⋊C4—21no—
195C4⋊C4C22×D1112yes—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C42—111no—
199C42—111no—
200C42—111no—
201C42C22×D1111yescharacteristic
202C11#320511yescharacteristic, complemented, Sylow
203C23—22no—
204C23—111no—
205C23—222no—
206C23—222no—
207C23—444no—
208C23—444no—
209C23—444no—
210Q8—42no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—224no—
215D4—224no—
216D4—444no—
217D4—444no—
218D4—444no—
219D4—444no—
220D4—442no—
221D4—442no—
222D4—442no—
223D4—442no—
224C2×C4—22no—
225C2×C4—111no—
226C2×C4—114no—
227C2×C4—111no—
228C2×C4—111no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—444no—
232C2×C4D4×D1111yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4C23×D1111yescharacteristic
235C8—22no—
236C8—222no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—112no—
241C22—221no—
242C22—221no—
243C22—442no—
244C22—442no—
245C22—442no—
246C22—442no—
247C22—442no—
248C22—442no—
249C22—888no—
250C22C2×D4×D1111yescharacteristic
251C4—42no—
252C4—112no—
253C4—221no—
254C4—221no—
255C4D8×D1112yes—
256C4#6696712yes—
257C4#6704212yes—
258C2—82no—
259C2—222no—
260C2—882no—
261C2—882no—
262C2#1062320511yescharacteristic
263C2C2×D8×D1111yescharacteristic
264C2C2×#6696711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
hypercenter#486D11
hypocenterC11#3205
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10623256C2semidirect
2. D11×#127C2semidirect
3. C11×#486C2semidirect
4. #10622701C2semidirect
5. #10622686C2semidirect
6. #10622399C2semidirect
7. #10622386C2semidirect
8. #10622308C2semidirect
9. #10622298C2semidirect
14. C11×C4⋊Q8C22semidirect
20. C2×#4323C22semidirect
21. C2×D88C22semidirect
25. #66946C22semidirect
27. #66927C22semidirect
29. C11×#102C22semidirect
30. C4×C8×C11C22semidirect
32. Dic11⋊C8C22semidirect
33. #66873C22semidirect
34. C4×C11⋊C8C22semidirect
102. C4×D11D8semidirect
110. #486D11semidirect
141. C4⋊Q8C2×D11semidirect
156. #102C2×D11semidirect
159. C4×C8C2×D11semidirect
202. C11#3205semidirect

Maximal subgroups

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

subgroupindex
#106232562
D11×#1272
C11×#4862
#106227012
#106226862
#106223992
#106223862
#106223082
#106222982
#320511