Finite Group Databasebeta

← #13069646

Subgroups — #13069646

Order 1408.

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

normal subgroups only

This group has 394 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×#67000C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic, complemented
3#10623056C211yesmaximal, characteristic
4C11×#419C211yesmaximal, characteristic, complemented
5C2×#66889C211yesmaximal, characteristic, complemented
6C2×#66887C211yesmaximal, characteristic, complemented
7#10622170C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C22×D44C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C11×#117C2211yescharacteristic
13#67000—22no—
14#67000—22no—
15C2×#4326—21no—
16#66995—22no—
17#66995—22no—
18C2×#4325—21no—
19C2×(C2×D11)⋊C4—22no—
20C2×C4×Dic11C2211yescharacteristic
21C2×#4318C2211yescharacteristic
22#66948—22no—
23#66935—22no—
24#66928—21no—
25#66927—21no—
26C11×#103—22no—
27#66889—22no—
28#66887—22no—
29C23×D11D412yes—
30C2×Q8×C11—21no—
31C2×Q8×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11D412yescomplemented
36C22×C4×C11—21no—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—21no—
39C22×Dic11—21no—
40#4339—21no—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44C2×D44—24no—
45C2×D44—21no—
46C2×D44—21no—
47C2×D44—21no—
48C2×D44—21no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44D411yescharacteristic
52C2×C4×D11—21no—
53C2×Dic22D411yescharacteristic
54C11×M16—21no—
55C11×M16—21no—
56C2×C8×C11—21no—
57C11×C4⋊C4D412yes—
58C11×C22⋊C4—21no—
59C42×C11—21no—
60#4326—24no—
61#4325—24no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—28no—
64C4×Dic11—21no—
65C4×Dic11D412yescomplemented
66#4318—21no—
67#4318D412yescomplemented
68C2×C11⋊C8—21no—
69#2004—111nomaximal, Sylow
70C23×C11C2×D411yescharacteristic
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—21no—
74C22×D11—22no—
75C22×D11—44no—
76Q8×C11—22no—
77Q8×C11—22no—
78Q8×C11—41no—
79Q8×C11—41no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C22⋊D11—41no—
91C22⋊D11—41no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—42no—
95D44—21no—
96D44—21no—
97D44—41no—
98D44—41no—
99D44—41no—
100D44—41no—
101D44—84no—
102C4×D11—41no—
103C4×D11—41no—
104Dic22—21no—
105Dic22—21no—
106C8×C11—41no—
107C11⋊C8—22no—
108C2×#137—111no—
109#535—111no—
110C2×#124—111no—
111C2×#104—111no—
112#419D1111yescharacteristic, complemented
113C2×#100—111no—
114#339—111no—
115C22×C11—22no—
116C22×C11#12011yescharacteristic
117C22×C11#12011yescharacteristic
118C22×C11#12111yescharacteristic
119C2×D11—44no—
120C2×D11—42no—
121C2×D11—41no—
122C2×D11—44no—
123C2×D11—42no—
124C2×D11—82no—
125C4×C11—42no—
126C4×C11—42no—
127C4×C11#12011yescharacteristic
128C4×C11#12111yescharacteristic
129C4×C11#12111yescharacteristic
130C4×C11#12711yescharacteristic
131Dic11—42no—
132Dic11—41no—
133C2×#41—111no—
134C22×Q8C2×D1111yescharacteristic
135C22×D4—111no—
136#137—222no—
137#137—222no—
138C2×Q16—221no—
139C2×SD16—221no—
140C2×M16—111no—
141C2×M16C2×D1111yescharacteristic
142#127—221no—
143#124—221no—
144#124—222no—
145#124—222no—
146#121—222no—
147#120—222no—
148#117C2×D1111yescharacteristic
149C2×C22⋊C4—222no—
150C2×C42—111no—
151#104—222no—
152#103—22no—
153#100—222no—
154C2×C11—21no—
155C2×C11—21no—
156C2×C11#39211yescharacteristic
157C2×C11#45512yes—
158D11—81no—
159D11—82no—
160C24—112no—
161#41—221no—
162#41—221no—
163#41—221no—
164#41—221no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—111no—
171C2×Q8D4412yescomplemented
172C2×D4—111no—
173C2×D4—224no—
174C2×D4—221no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—221no—
178C2×D4—221no—
179C2×D4—221no—
180C2×D4—221no—
181C22×C4—21no—
182C22×C4—221no—
183C22×C4—221no—
184C22×C4C22×D1111yescharacteristic
185Q16—224no—
186SD16—224no—
187M16—21no—
188M16—21no—
189M16—112no—
190M16—221no—
191C2×C8—21no—
192C2×C8—221no—
193C4⋊C4C22⋊D1112yes—
194C22⋊C4—21no—
195C22⋊C4—228no—
196C22⋊C4—224no—
197C42—21no—
198C42—112no—
199C42—221no—
200C11#200411yescharacteristic, complemented, Sylow
201C23—222no—
202C23—222no—
203C23—221no—
204C23—222no—
205C23—444no—
206C23D4×D1111yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—221no—
212Q8—221no—
213D4—221no—
214D4—221no—
215D4—441no—
216D4—441no—
217D4—441no—
218D4—441no—
219D4—441no—
220D4—441no—
221D4—884no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—222no—
227C2×C4—221no—
228C2×C4—442no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4C2×D4411yescharacteristic
232C2×C4#433911yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4D4×D1111yescharacteristic
235C2×C4D4×D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C8—41no—
238C8—222no—
239C22—22no—
240C22—444no—
241C22—442no—
242C22—444no—
243C22—441no—
244C22—442no—
245C22—882no—
246C22#6693511yescharacteristic
247C22#6693711yescharacteristic
248C22#6699011yescharacteristic
249C4—42no—
250C4—42no—
251C4—442no—
252C4—441no—
253C4#6693511yescharacteristic
254C4#6693711yescharacteristic
255C4#6698311yescharacteristic
256C4#6699311yescharacteristic
257C2—21no—
258C2—21no—
259C2—882no—
260C2—881no—
261C2#1062257311yescharacteristic
262C2#1062281512yes—
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#419C2
socleC22×C11#120
prime radical#10623056C2
hypercenter#419D11
hypocenterC11#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66995C2semidirect
4. C11×#419C2semidirect
5. C2×#66889C2semidirect
6. C2×#66887C2semidirect
7. #10622170C2semidirect
35. C2×Q8×C11D4semidirect
65. C4×Dic11D4semidirect
67. #4318D4semidirect
112. #419D11semidirect
171. C2×Q8D44semidirect
200. C11#2004semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669952
#106230562
C11×#4192
C2×#668892
C2×#668872
#106221702
#200411