Finite Group Databasebeta

← #13069633

Subgroups — #13069633

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
1#10623336C211yesmaximal, characteristic, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66961C211yesmaximal, characteristic, complemented
4C2×C11×#100C211yesmaximal, characteristic, complemented
5C2×#66889C211yesmaximal, characteristic, complemented
6#10622744C211yesmaximal, characteristic, complemented
7#10622193C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×C22⋊D11—22no—
10C2×#4339C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C2×C11×M16C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14#67006—22no—
15#66993—22no—
16#66993—21no—
17#66993—22no—
18#66991—22no—
19#66989—21no—
20#66979C2211yescharacteristic
21C2×C4×Dic11C2211yescharacteristic
22#66961—22no—
23#66961—22no—
24C2×D88—21no—
25C2×#4314—21no—
26C11×#100—22no—
27#66889—22no—
28#66885—22no—
29C24×C11D412yes—
30C23×D11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—28no—
39C2×C22⋊D11—24no—
40C2×C22⋊D11—21no—
41C2×C22⋊D11—48no—
42C22×Dic11—21no—
43#4339—21no—
44#4339—21no—
45#4339—21no—
46#4339—21no—
47C2×D44—21no—
48C2×D44—21no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44—21no—
52C2×D44D411yescharacteristic, complemented
53C2×D44D412yescomplemented
54C2×C4×D11—21no—
55C2×Dic22D411yescharacteristic, complemented
56C11×M16—21no—
57C11×M16—21no—
58C11×M16—21no—
59C11×M16D412yescomplemented
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C22⋊Dic11—24no—
63C22⋊Dic11—21no—
64C4⋊Dic11D412yescomplemented
65C4×Dic11—21no—
66C4×Dic11—21no—
67C4×Dic11D412yescomplemented
68D88—24no—
69#4314—24no—
70#2002—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—44no—
75C23×C11C2×D411yescharacteristic
76C22×D11—21no—
77C22×D11—22no—
78C22×D11—44no—
79C22×D11—41no—
80C22×D11—41no—
81D4×C11—41no—
82D4×C11—41no—
83D4×C11—41no—
84D4×C11—41no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11#4111yescharacteristic
91C22⋊D11—416no—
92C22⋊D11—41no—
93C22⋊D11—41no—
94C22⋊D11—84no—
95C2×Dic11—24no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99D44—22no—
100D44—21no—
101D44—22no—
102D44—21no—
103D44—41no—
104D44—41no—
105C4×D11—41no—
106C4×D11—41no—
107Dic22—21no—
108Dic22—21no—
109C8×C11—22no—
110C8×C11—41no—
111C2×AGL(1,ℤ/8)—111no—
112#535—111no—
113C2×#127—111no—
114C2×#104—111no—
115#418—111no—
116C2×#100D1111yescharacteristic, complemented
117#339—111no—
118C22×C11—22no—
119C22×C11—44no—
120C22×C11—42no—
121C22×C11—44no—
122C22×C11—82no—
123C22×C11#12011yescharacteristic
124C22×C11#12011yescharacteristic
125C22×C11#12111yescharacteristic
126C2×D11—44no—
127C2×D11—42no—
128C2×D11—41no—
129C2×D11—42no—
130C2×D11—82no—
131C2×D11—82no—
132C4×C11#12011yescharacteristic
133C4×C11#12111yescharacteristic
134C4×C11#12111yescharacteristic
135C4×C11#12711yescharacteristic
136Dic11—24no—
137Dic11—41no—
138Dic11—42no—
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×M16C2×D1111yescharacteristic
148C2×M16C2×D1111yescharacteristic
149#127—222no—
150#127—222no—
151#127—221no—
152#124—221no—
153#121—222no—
154#120—222no—
155#117—111no—
156C2×C42—111no—
157#104—222no—
158#102—222no—
159#100—22no—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11—82no—
163C2×C11#39211yescharacteristic
164C2×C11#45312yes—
165D11—81no—
166D11—82no—
167C24—221no—
168C24D4412yes—
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—21no—
180C2×D4—111no—
181C2×D4—112no—
182C2×D4—228no—
183C2×D4—221no—
184C2×D4—224no—
185C2×D4—221no—
186C2×D4—221no—
187C2×D4—221no—
188C2×D4—221no—
189C2×D4—221no—
190C2×D4—448no—
191C22×C4—221no—
192C22×C4—221no—
193C22×C4C22×D1111yescharacteristic
194SD16—224no—
195D8—224no—
196M16—21no—
197M16—21no—
198M16—21no—
199M16C22⋊D1112yescomplemented
200C2×C8—21no—
201C2×C8—21no—
202C4⋊C4—112no—
203C22⋊C4—224no—
204C22⋊C4—221no—
205C42—112no—
206C42—221no—
207C42—221no—
208C11#200211yescharacteristic, complemented, Sylow
209C23—22no—
210C23—22no—
211C23—22no—
212C23—44no—
213C23—222no—
214C23—221no—
215C23—444no—
216C23—441no—
217C23—441no—
218C23C2×D4411yescharacteristic
219Q8—221no—
220Q8—221no—
221D4—41no—
222D4—41no—
223D4—41no—
224D4—41no—
225D4—222no—
226D4—221no—
227D4—221no—
228D4—222no—
229D4—4416no—
230D4—441no—
231D4—441no—
232D4—441no—
233D4—441no—
234D4—884no—
235C2×C4—224no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—221no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4#433911yescharacteristic
242C2×C4D4×D1111yescharacteristic
243C2×C4D4×D1111yescharacteristic
244C2×C4D4×D1111yescharacteristic
245C2×C4D4×D1111yescharacteristic
246C2×C4C2×C22⋊D1111yescharacteristic
247C8—22no—
248C8—41no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—44no—
253C22—82no—
254C22—444no—
255C22—441no—
256C22—442no—
257C22—442no—
258C22—882no—
259C22—882no—
260C22#6693511yescharacteristic
261C22#6693511yescharacteristic
262C22#6698311yescharacteristic
263C4—224no—
264C4—441no—
265C4—442no—
266C4#6693711yescharacteristic
267C4#6693711yescharacteristic
268C4#6699011yescharacteristic
269C4#6699311yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—882no—
274C2—881no—
275C2#1062236012yes—
276C2#1062257311yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#100C2
socleC22×C11#120
hypercenterC2×#100D11
hypocenterC11#2002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. #10623336C2semidirect
2. C2×#66993C2semidirect
3. C2×#66961C2semidirect
4. C2×C11×#100C2semidirect
5. C2×#66889C2semidirect
6. #10622744C2semidirect
7. #10622193C2semidirect
52. C2×D44D4semidirect
53. C2×D44D4semidirect
55. C2×Dic22D4semidirect
59. C11×M16D4semidirect
64. C4⋊Dic11D4semidirect
67. C4×Dic11D4semidirect
116. C2×#100D11semidirect
199. M16C22⋊D11semidirect
208. C11#2002semidirect

Maximal subgroups

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

subgroupindex
#106233362
C2×#669932
C2×#669612
C2×C11×#1002
C2×#668892
#106227442
#106221932
#200211