Finite Group Databasebeta

← #13071751

Subgroups — #13071751

Order 1408.

552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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×#66988C211yesmaximal, characteristic
2C11×#390C211yesmaximal, characteristic
3#10622833C211yesmaximal, characteristic
4#10622591C212yesmaximal, complemented
5#10622558C212yesmaximal, complemented
6#10622558C212yesmaximal, complemented
7C22⋊C4×Dic11C212yesmaximal, complemented
8C22⋊C4×Dic11C212yesmaximal, complemented
9C4×Dic11⋊C4C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21#66988C418yescomplemented
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25C2×C4×Dic11C2212yes—
26C2×C4×Dic11C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C24×C11C2311yescharacteristic
33C24×C11C2311yescharacteristic
34C2×D4×C11—41no—
35C2×D4×C11—41no—
36C2×D4×C11C2×C414yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×Dic11—24no—
41C22×Dic11—41no—
42C22×Dic11—41no—
43C22×Dic11—41no—
44C22×Dic11C2×C414yescomplemented
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C11×C4⋊C4—41no—
50C11×C22⋊C4—24no—
51C11×C22⋊C4—24no—
52C42×C11—41no—
53C22⋊Dic11—24no—
54C22⋊Dic11—41no—
55C22⋊Dic11C2×C418yes—
56C22⋊Dic11C2×C414yescomplemented
57Dic11⋊C4—24no—
58Dic11⋊C4C2×C418yescomplemented
59C4×Dic11—24no—
60C4×Dic11—42no—
61C4×Dic11—42no—
62#2374—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—21no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—21no—
71C23×C11C22×C412yes—
72C23×C11C22×C412yes—
73C23×C11C2411yescharacteristic
74D4×C11—44no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11C22×C412yes—
83C2×C4×C11#4114yes—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—44no—
94C2×Dic11—44no—
95C2×Dic11C22×C414yes—
96C2×Dic11C22×C414yes—
97C2×Dic11#4114yes—
98C2×#123—111no—
99#390D1111yescharacteristic
100#388—112no—
101#388—112no—
102#387—112no—
103#386—111no—
104C4×C4⋊C4—112no—
105C4×C22⋊C4—112no—
106C4×C22⋊C4—112no—
107C22×C11—24no—
108C22×C11—24no—
109C22×C11—22no—
110C22×C11—22no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—41no—
116C22×C11—41no—
117C22×C11C23×C411yescharacteristic
118C22×C11C2×#4112yes—
119C22×C11C2×#4112yes—
120C22×C11H(5,𝔽2)11yescharacteristic
121C22×C11H(5,𝔽2)11yescharacteristic
122C4×C11—22no—
123C4×C11—24no—
124C4×C11—42no—
125Dic11—24no—
126Dic11—24no—
127Dic11—24no—
128Dic11—42no—
129C22×D4C2×D1111yescharacteristic
130C23×C4—111no—
131C23×C4—111no—
132#123—118no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4C2×D1111yescharacteristic
136C2×C22⋊C4—112no—
137C2×C22⋊C4—111no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—111no—
140C2×C22⋊C4C2×D1112yes—
141C2×C22⋊C4C2×D1112yes—
142C2×C42—112no—
143C2×C42—112no—
144C2×C42—112no—
145C2×C42C2×D1111yescharacteristic
146#95—112no—
147#95—112no—
148#95—112no—
149#95—112no—
150#95—112no—
151C2×C11—42no—
152C2×C11—42no—
153C2×C11C4×#4112yes—
154C2×C11#51811yescharacteristic
155C2×C11#55111yescharacteristic
156C2×C11#55312yes—
157C2×C11#55911yescharacteristic
158C24C22×D1111yescharacteristic
159C24C22×D1111yescharacteristic
160C2×D4—41no—
161C2×D4—41no—
162C2×D4C4×D1114yes—
163C22×C4—112no—
164C22×C4—112no—
165C22×C4—112no—
166C22×C4—114no—
167C22×C4—112no—
168C22×C4—224no—
169C22×C4—441no—
170C22×C4—441no—
171C22×C4—441no—
172C22×C4C22×D1112yes—
173C22×C4C22×D1111yescharacteristic
174C22×C4C22×D1112yes—
175C4⋊C4—41no—
176C4⋊C4—118no—
177C4⋊C4—224no—
178C22⋊C4—24no—
179C22⋊C4—24no—
180C22⋊C4—118no—
181C22⋊C4—114no—
182C22⋊C4—224no—
183C22⋊C4—441no—
184C42—41no—
185C42—224no—
186C42—442no—
187C42—442no—
188C11#237411yescharacteristic, complemented, Sylow
189C23—22no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23C2×C4×D1112yes—
198C23C2×C4×D1112yes—
199C23C23×D1111yescharacteristic
200D4—44no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—114no—
209C2×C4—114no—
210C2×C4—114no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—444no—
221C2×C4—444no—
222C2×C4C2×C4×D1112yes—
223C2×C4#434114yes—
224C22—22no—
225C22—22no—
226C22—24no—
227C22—24no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22C22×C4×D1111yescharacteristic
235C22C2×#434112yes—
236C22#6703711yescharacteristic
237C22#6703711yescharacteristic
238C22#41×D1112yes—
239C4—22no—
240C4—24no—
241C4—42no—
242C4—224no—
243C4—224no—
244C4—224no—
245C4—442no—
246C2—42no—
247C2—42no—
248C2#1062301711yescharacteristic
249C2C4×#434112yes—
250C2#1062313212yes—
251C2#1062321011yescharacteristic
252C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#390C2
socle, cosocleC23×C11C24
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2374
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #10622591C2semidirect
5. #10622558C2semidirect
6. #10622558C2semidirect
7. C22⋊C4×Dic11C2semidirect
8. C22⋊C4×Dic11C2semidirect
9. C4×Dic11⋊C4C2semidirect
21. #66988C4semidirect
44. C22×Dic11C2×C4semidirect
56. C22⋊Dic11C2×C4semidirect
58. Dic11⋊C4C2×C4semidirect
188. C11#2374semidirect

Maximal subgroups

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

subgroupindex
C2×#669882
C11×#3902
#106228332
#106225912
#106225582
C22⋊C4×Dic112
C4×Dic11⋊C42
#237411