Finite Group Databasebeta

← #13079422

Subgroups — #13079422

Order 1408.

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

normal subgroups only

This group has 462 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
1C2×C11×#121C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3#10622831C212yesmaximal, complemented
4#10622820C211yesmaximal, characteristic, complemented
5#10622655C214yesmaximal, complemented
6#10622653C212yesmaximal, complemented
7#10622646C212yesmaximal, complemented
8#10622583C212yesmaximal, complemented
9C22×D4×C11—21no—
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic, complemented
13C11×#121—21no—
14C11×#121—21no—
15C11×#121C2212yes—
16C11×#121C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4—21no—
19C2×C22⋊Dic11—21no—
20C2×#4324C2214yescomplemented
21C2×C4⋊Dic11C2211yescharacteristic, complemented
22#66977—21no—
23#66977—21no—
24#66977C2212yes—
25#66977C2212yescomplemented
26C2×Dic11⋊C4—21no—
27C2×#4318C2212yescomplemented
28#66896C2214yescomplemented
29C22⋊(C11⋊C8)C2212yes—
30C22⋊(C11⋊C8)C2212yescomplemented
31#66874C2214yescomplemented
32#66871C2214yescomplemented
33C24×C11—21no—
34C24×C11D411yescharacteristic
35C2×D4×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11—21no—
38C2×D4×C11—42no—
39C2×D4×C11—44no—
40C2×D4×C11C2312yes—
41C22×C4×C11—21no—
42C22×C4×C11—42no—
43C22×C4×C11D411yescharacteristic
44C22×C4×C11D411yescharacteristic
45C22×C4×C11D411yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×Dic11—21no—
50C22×Dic11—21no—
51C2×Dic22—21no—
52C2×Dic22—42no—
53C2×Dic22C2312yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4C2312yes—
56C11×C22⋊C4—22no—
57C11×C22⋊C4—22no—
58C22⋊Dic11—22no—
59C22⋊Dic11—22no—
60#4324—44no—
61C4⋊Dic11—21no—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65#4318—42no—
66C2×C11⋊C8C2314yes—
67#3193—111nomaximal, Sylow
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—41no—
72C23×C11—42no—
73C23×C11—42no—
74C23×C11—42no—
75C23×C11C2×D411yescharacteristic
76C23×C11C2×D411yescharacteristic
77C23×C11C2×D411yescharacteristic
78D4×C11—24no—
79D4×C11—42no—
80D4×C11—44no—
81D4×C11—44no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—42no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98Dic22—24no—
99Dic22—42no—
100C11⋊C8—24no—
101C2×C22⋊Q8—111no—
102C2×#121D1111yescharacteristic
103#484—112no—
104#480—112no—
105#468—114no—
106#450—112no—
107#448—112no—
108#407—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—21no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11—21no—
116C22×C11—44no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—84no—
121C22×C11AGL(1,ℤ/8)12yes—
122C22×C11#13712yes—
123C22×C11C22×D411yescharacteristic
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—42no—
128C4×C11H(5,𝔽2)12yes—
129Dic11—42no—
130Dic11—42no—
131C22×Q8—111no—
132C22×D4—21no—
133C22×D4C2×D1111yescharacteristic
134C23×C4C2×D1111yescharacteristic
135C2×SD16—114no—
136C2×M16—112no—
137C22⋊Q8—112no—
138C22⋊Q8—112no—
139C22⋊Q8—221no—
140C22⋊Q8—221no—
141#121—21no—
142#121—21no—
143#121C2×D1112yes—
144#121C2×D1112yes—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4C2×D1111yescharacteristic
148C2×C22⋊C4—21no—
149C2×C22⋊C4—221no—
150#107—114no—
151#103—114no—
152#102—114no—
153C22⋊C8—112no—
154C22⋊C8—112no—
155C2×C11—22no—
156C2×C11—22no—
157C2×C11—41no—
158C2×C11—82no—
159C2×C11#53411yescharacteristic
160C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C11C2×#13711yescharacteristic
162C24—21no—
163C24C22⋊D1111yescharacteristic
164C2×Q8—112no—
165C2×Q8—221no—
166C2×Q8—442no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—42no—
171C2×D4—44no—
172C2×D4C22×D1112yes—
173C22×C4—21no—
174C22×C4—42no—
175C22×C4—221no—
176C22×C4—221no—
177C22×C4C22⋊D1111yescharacteristic
178C22×C4C22⋊D1111yescharacteristic
179C22×C4C22⋊D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1111yescharacteristic
182C22×C4C22×D1111yescharacteristic
183SD16—444no—
184M16—442no—
185C2×C8—114no—
186C4⋊C4—21no—
187C4⋊C4—112no—
188C4⋊C4—221no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4C22×D1112yes—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—222no—
195C22⋊C4—222no—
196C11#319311yescharacteristic, complemented, Sylow
197C23—22no—
198C23—22no—
199C23—22no—
200C23—41no—
201C23—42no—
202C23—42no—
203C23—42no—
204C23C2×C22⋊D1111yescharacteristic
205C23C2×C22⋊D1111yescharacteristic
206C23C2×C22⋊D1111yescharacteristic
207Q8—224no—
208Q8—442no—
209D4—24no—
210D4—42no—
211D4—44no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4C2×C22⋊D1111yescharacteristic
226C2×C4C2×C22⋊D1111yescharacteristic
227C2×C4C2×C22⋊D1111yescharacteristic
228C2×C4C23×D1111yescharacteristic
229C8—224no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—44no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—84no—
242C22#6698512yes—
243C22#6700412yes—
244C22C22×C22⋊D1111yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—442no—
250C4—442no—
251C4#6703712yes—
252C2—22no—
253C2—22no—
254C2—41no—
255C2—82no—
256C2C2×#6698511yescharacteristic
257C2#1062333511yescharacteristic
258C2C2×#6700411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC2×C11×#121C2
socleC22×C11C22×D4
hypercenterC2×#121D11
hypocenterC11#3193
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. #10622831C2semidirect
4. #10622820C2semidirect
5. #10622655C2semidirect
6. #10622653C2semidirect
7. #10622646C2semidirect
8. #10622583C2semidirect
12. C22×Dic22C22semidirect
20. C2×#4324C22semidirect
21. C2×C4⋊Dic11C22semidirect
25. #66977C22semidirect
27. C2×#4318C22semidirect
28. #66896C22semidirect
30. C22⋊(C11⋊C8)C22semidirect
31. #66874C22semidirect
32. #66871C22semidirect
196. C11#3193semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669772
#106228312
#106228202
#106226552
#106226532
#106226462
#106225832
#319311