Finite Group Databasebeta

← #13078128

Subgroups — #13078128

Order 1408.

494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C11×#518C211yesmaximal, characteristic, complemented
2C22×#4324C211yesmaximal, characteristic, complemented
3C2×#66985C211yesmaximal, characteristic
4#10623057C211yesmaximal, characteristic, complemented
5#10622632C214yesmaximal, complemented
6#10622629C214yesmaximal, complemented
7#10622617C211yesmaximal, characteristic, complemented
8#10622615C211yesmaximal, characteristic, complemented
9#10622612C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C2×#4339C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C4×D4×C11—22no—
14C4×D4×C11C2214yes—
15C11×#117C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C11×C22⋊C4—22no—
18C2×#4324—24no—
19C2×#4324C2212yes—
20C2×#4324C2214yes—
21#66985—24no—
22C2×#4323C2212yes—
23C2×#4318C2211yescharacteristic
24C22×C11⋊C8C2211yescharacteristic
25#66950—22no—
26#66939—22no—
27#66928C2212yescomplemented
28#66922C2212yescomplemented
29#66874C2212yescomplemented
30#66874C2214yescomplemented
31#66873C2212yescomplemented
32C4⋊(C11⋊C8)C2214yescomplemented
33C24×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—22no—
36C2×D4×C11D414yes—
37C2×D4×C11C2312yes—
38C22×C4×C11—24no—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—21no—
41C22×Dic11—21no—
42#4339—22no—
43#4339—22no—
44C2×D44C2311yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22—22no—
47C2×Dic22—21no—
48C2×Dic22—22no—
49C2×Dic22C2311yescharacteristic
50C2×Dic22C2312yes—
51C11×C4⋊C4D412yes—
52C11×C4⋊C4C2312yes—
53C11×C22⋊C4—21no—
54C11×C22⋊C4—24no—
55C11×C22⋊C4D412yes—
56C42×C11—21no—
57C42×C11C2312yes—
58#4324—24no—
59#4324—28no—
60#4323—24no—
61(C2×D11)⋊C4—24no—
62C4⋊Dic11—24no—
63#4318—22no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8C2312yes—
66C2×C11⋊C8C2312yes—
67#3042—111nomaximal, Sylow
68C23×C11—22no—
69C23×C11—24no—
70C23×C11—82no—
71C23×C11C2×D411yescharacteristic
72C22×D11—21no—
73D4×C11—24no—
74D4×C11—22no—
75D4×C11C2×D414yes—
76C2×C4×C11—22no—
77C2×C4×C11—84no—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×D414yes—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11#4112yes—
82C2×C4×C11C2411yescharacteristic
83C22⋊D11—42no—
84C2×Dic11—21no—
85C2×Dic11—22no—
86C2×Dic11—42no—
87D44—21no—
88D44—21no—
89C4×D11—42no—
90Dic22—22no—
91Dic22—21no—
92Dic22—22no—
93Dic22—21no—
94Dic22—42no—
95C11⋊C8—22no—
96C11⋊C8—22no—
97C2×AGL(1,ℤ/8)—111no—
98C22×SD16—111no—
99#536—111no—
100#518D1111yescharacteristic, complemented
101#463—114no—
102#461—114no—
103#424—111no—
104#419—111no—
105#416—111no—
106C22×C11—22no—
107C22×C11—24no—
108C22×C11—44no—
109C22×C11—84no—
110C22×C11#12112yes—
111C22×C11C22×D411yescharacteristic
112C2×D11—41no—
113C2×D11—42no—
114C4×C11—24no—
115C4×C11—42no—
116C4×C11#12112yes—
117C4×C11C22×D411yescharacteristic
118C4×C11C2×#4111yescharacteristic
119Dic11—42no—
120Dic11—41no—
121C2×#41—111no—
122C22×Q8—111no—
123C22×D4C2×D1111yescharacteristic
124AGL(1,ℤ/8)—224no—
125C2×SD16—114no—
126C2×SD16—112no—
127C2×SD16—224no—
128C2×D8—112no—
129C2×M16—111no—
130C22×C8—111no—
131C4⋊Q8—112no—
132#124—112no—
133#123—222no—
134C22⋊Q8—222no—
135C4×D4—22no—
136C4×D4C2×D1114yes—
137#117C2×D1111yescharacteristic
138#117C2×D1111yescharacteristic
139C2×C22⋊C4—22no—
140C4⋊C8—114no—
141#103—112no—
142#103—114no—
143#102—112no—
144C2×C11—22no—
145C2×C11—44no—
146C2×C11C2×#12111yescharacteristic
147C2×C11#57712yes—
148D11—81no—
149C24—21no—
150#41—222no—
151#41—222no—
152C2×Q8—112no—
153C2×Q8—111no—
154C2×Q8—221no—
155C2×Q8—222no—
156C2×Q8—222no—
157C2×D4—22no—
158C2×D4—21no—
159C2×D4—111no—
160C2×D4—221no—
161C2×D4D4414yes—
162C2×D4C22×D1112yes—
163C22×C4—24no—
164C22×C4—221no—
165C22×C4—221no—
166C22×C4C22×D1111yescharacteristic
167SD16—228no—
168SD16—224no—
169D8—224no—
170M16—222no—
171C2×C8—112no—
172C2×C8—112no—
173C2×C8—222no—
174C4⋊C4—224no—
175C4⋊C4C22⋊D1112yes—
176C4⋊C4C22×D1112yes—
177C22⋊C4—21no—
178C22⋊C4—24no—
179C22⋊C4—224no—
180C22⋊C4C22⋊D1112yes—
181C42—21no—
182C42C22×D1112yes—
183C11#304211yescharacteristic, complemented, Sylow
184C23—22no—
185C23—24no—
186C23—82no—
187C23—221no—
188C23C2×C22⋊D1111yescharacteristic
189Q8—222no—
190Q8—221no—
191Q8—222no—
192Q8—221no—
193Q8—442no—
194D4—24no—
195D4—22no—
196D4—221no—
197D4—221no—
198D4—442no—
199D4C2×D4414yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—222no—
203C2×C4—221no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4C2×D4412yes—
207C2×C4#433912yes—
208C2×C4C2×C22⋊D1114yes—
209C2×C4C2×C22⋊D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—222no—
212C8—222no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—441no—
218C22—442no—
219C22#6698312yes—
220C22C22×C22⋊D1111yescharacteristic
221C4—24no—
222C4—42no—
223C4—441no—
224C4—442no—
225C4#6698312yes—
226C4C22×D4411yescharacteristic
227C4C2×#433911yescharacteristic
228C2—22no—
229C2—44no—
230C2—881no—
231C2C2×#6698311yescharacteristic
232C2#1062336712yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#518C2
socleC22×C11C22×D4
prime radicalC2×#66985C2
hypercenter#518D11
hypocenterC11#3042
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C11×#518C2semidirect
2. C22×#4324C2semidirect
4. #10623057C2semidirect
5. #10622632C2semidirect
6. #10622629C2semidirect
7. #10622617C2semidirect
8. #10622615C2semidirect
9. #10622612C2semidirect
27. #66928C22semidirect
28. #66922C22semidirect
29. #66874C22semidirect
30. #66874C22semidirect
31. #66873C22semidirect
32. C4⋊(C11⋊C8)C22semidirect
100. #518D11semidirect
183. C11#3042semidirect

Maximal subgroups

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

subgroupindex
C11×#5182
C22×#43242
C2×#669852
#106230572
#106226322
#106226292
#106226172
#106226152
#106226122
#304211