Finite Group Databasebeta

← #13069632

Subgroups — #13069632

Order 1408.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#66993C211yesmaximal, characteristic, complemented
2C2×#66985C211yesmaximal, characteristic, complemented
3#10623056C211yesmaximal, characteristic, complemented
4C11×#418C211yesmaximal, characteristic, complemented
5C2×#66889C211yesmaximal, characteristic, complemented
6C2×#66887C211yesmaximal, characteristic, complemented
7#10622170C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×C22⋊D11—22no—
10C2×#4339C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C2×C11×M16C2211yescharacteristic
13C11×#117C2211yescharacteristic
14#66993—22no—
15#66993—22no—
16C2×#4324—21no—
17#66985—22no—
18#66985—22no—
19C2×#4323—21no—
20C2×C4×Dic11C2211yescharacteristic
21C2×#4318C2211yescharacteristic
22#66948—22no—
23#66935—22no—
24#66928—21no—
25#66927—21no—
26C11×#102—22no—
27#66889—22no—
28#66887—22no—
29C24×C11—21no—
30C23×D11D412yes—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11D412yescomplemented
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—28no—
39C2×C22⋊D11—21no—
40C2×C22⋊D11—48no—
41C22×Dic11—21no—
42#4339—21no—
43#4339—21no—
44#4339—21no—
45#4339—21no—
46C2×D44—24no—
47C2×D44—21no—
48C2×D44—21no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44—21no—
52C2×D44—21no—
53C2×D44D411yescharacteristic, complemented
54C2×C4×D11—21no—
55C2×Dic22D411yescharacteristic, complemented
56C11×M16—21no—
57C11×M16—21no—
58C2×C8×C11—21no—
59C11×C4⋊C4D412yescomplemented
60C11×C22⋊C4—21no—
61C42×C11—21no—
62#4324—24no—
63#4323—24no—
64(C2×D11)⋊C4—24no—
65C4×Dic11—21no—
66C4×Dic11D412yescomplemented
67#4318—21no—
68#4318D412yescomplemented
69C2×C11⋊C8—21no—
70#2002—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—44no—
73C23×C11—41no—
74C23×C11—41no—
75C23×C11C2×D411yescharacteristic
76C22×D11—22no—
77C22×D11—21no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—44no—
81D4×C11—22no—
82D4×C11—22no—
83D4×C11—41no—
84D4×C11—41no—
85C2×C4×C11—22no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11#4111yescharacteristic
92C22⋊D11—416no—
93C22⋊D11—41no—
94C22⋊D11—41no—
95C2×Dic11—24no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98D44—21no—
99D44—21no—
100D44—41no—
101D44—41no—
102D44—41no—
103D44—41no—
104D44—84no—
105C4×D11—41no—
106C4×D11—41no—
107Dic22—21no—
108Dic22—21no—
109C8×C11—41no—
110C11⋊C8—22no—
111C2×AGL(1,ℤ/8)—111no—
112#535—111no—
113C2×#127—111no—
114C2×#104—111no—
115#418D1111yescharacteristic, complemented
116C2×#100—111no—
117#339—111no—
118C22×C11—22no—
119C22×C11—44no—
120C22×C11—42no—
121C22×C11—82no—
122C22×C11—82no—
123C22×C11#12011yescharacteristic
124C22×C11#12011yescharacteristic
125C22×C11#12111yescharacteristic
126C2×D11—44no—
127C2×D11—42no—
128C2×D11—41no—
129C2×D11—44no—
130C2×D11—42no—
131C2×D11—82no—
132C4×C11—42no—
133C4×C11#12011yescharacteristic
134C4×C11#12111yescharacteristic
135C4×C11#12111yescharacteristic
136C4×C11#12711yescharacteristic
137Dic11—24no—
138Dic11—41no—
139C2×#41—111no—
140C22×D4—111no—
141C22×D4—222no—
142C22×D4C2×D1111yescharacteristic
143AGL(1,ℤ/8)—222no—
144AGL(1,ℤ/8)—222no—
145C2×SD16—221no—
146C2×D8—221no—
147C2×M16—111no—
148C2×M16C2×D1111yescharacteristic
149#127—221no—
150#127—222no—
151#127—222no—
152#124—221no—
153#121—222no—
154#120—222no—
155#117C2×D1111yescharacteristic
156C2×C42—111no—
157#104—222no—
158#102—22no—
159#100—222no—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11—82no—
163C2×C11#39211yescharacteristic
164C2×C11#45312yes—
165D11—81no—
166D11—82no—
167C24—21no—
168C24—112no—
169#41—221no—
170#41—221no—
171#41—221no—
172#41—221no—
173C2×Q8—111no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—111no—
180C2×D4—224no—
181C2×D4—228no—
182C2×D4—221no—
183C2×D4—221no—
184C2×D4—221no—
185C2×D4—221no—
186C2×D4—221no—
187C2×D4—221no—
188C2×D4—221no—
189C2×D4—448no—
190C2×D4D4412yescomplemented
191C22×C4—221no—
192C22×C4—221no—
193C22×C4C22×D1111yescharacteristic
194SD16—224no—
195D8—224no—
196M16—21no—
197M16—21no—
198M16—112no—
199M16—221no—
200C2×C8—21no—
201C2×C8—221no—
202C4⋊C4C22⋊D1112yescomplemented
203C22⋊C4—21no—
204C22⋊C4—224no—
205C42—21no—
206C42—112no—
207C42—221no—
208C11#200211yescharacteristic, complemented, Sylow
209C23—22no—
210C23—44no—
211C23—41no—
212C23—41no—
213C23—222no—
214C23—222no—
215C23—221no—
216C23—222no—
217C23—444no—
218C23D4×D1111yescharacteristic
219Q8—221no—
220Q8—221no—
221D4—22no—
222D4—22no—
223D4—41no—
224D4—41no—
225D4—221no—
226D4—221no—
227D4—4416no—
228D4—441no—
229D4—441no—
230D4—441no—
231D4—441no—
232D4—441no—
233D4—441no—
234D4—884no—
235C2×C4—22no—
236C2×C4—224no—
237C2×C4—222no—
238C2×C4—221no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4C2×D4411yescharacteristic
242C2×C4#433911yescharacteristic
243C2×C4D4×D1111yescharacteristic
244C2×C4D4×D1111yescharacteristic
245C2×C4D4×D1111yescharacteristic
246C2×C4C2×C22⋊D1111yescharacteristic
247C8—41no—
248C8—222no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—82no—
253C22—82no—
254C22—444no—
255C22—442no—
256C22—444no—
257C22—441no—
258C22—442no—
259C22—882no—
260C22#6693511yescharacteristic
261C22#6693711yescharacteristic
262C22#6699011yescharacteristic
263C4—42no—
264C4—224no—
265C4—441no—
266C4#6693511yescharacteristic
267C4#6693711yescharacteristic
268C4#6698311yescharacteristic
269C4#6699311yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—882no—
274C2—881no—
275C2#1062257311yescharacteristic
276C2#1062281112yes—
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#418C2
socleC22×C11#120
hypercenter#418D11
hypocenterC11#2002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66985C2semidirect
3. #10623056C2semidirect
4. C11×#418C2semidirect
5. C2×#66889C2semidirect
6. C2×#66887C2semidirect
7. #10622170C2semidirect
36. C2×D4×C11D4semidirect
53. C2×D44D4semidirect
55. C2×Dic22D4semidirect
59. C11×C4⋊C4D4semidirect
66. C4×Dic11D4semidirect
68. #4318D4semidirect
115. #418D11semidirect
190. C2×D4D44semidirect
202. C4⋊C4C22⋊D11semidirect
208. C11#2002semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669852
#106230562
C11×#4182
C2×#668892
C2×#668872
#106221702
#200211