Finite Group Databasebeta

← #13074197

Subgroups — #13074197

Order 1408.

604 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 141 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×D4×Dic11C212yesmaximal, complemented
2C11×#392C211yesmaximal, characteristic
3#10622835C212yesmaximal, complemented
4#10622833C212yesmaximal, complemented
5#10622566C211yesmaximal, characteristic, complemented
6#10622563C212yesmaximal, complemented
7#10622558C212yesmaximal, complemented
8#10622556C211yesmaximal, characteristic, complemented
9#10622268C212yesmaximal, complemented
10C22×D4×C11C2212yes—
11C22×D4×C11C2211yescharacteristic
12C23×Dic11C2212yes—
13C23×Dic11C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
21D4×Dic11—28no—
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2212yes—
26C11×#95C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C24×C11C2311yescharacteristic
33C24×C11C2312yes—
34C2×D4×C11—24no—
35C2×D4×C11—24no—
36C2×D4×C11—24no—
37C2×D4×C11—24no—
38C2×D4×C11—41no—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×Dic11—24no—
43C22×Dic11—41no—
44C22×Dic11—42no—
45C22×Dic11—41no—
46C22×Dic11—42no—
47C22×Dic11D414yescomplemented
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C11×C22⋊C4—24no—
53C11×C22⋊C4—41no—
54C22⋊Dic11—24no—
55C22⋊Dic11—24no—
56C22⋊Dic11—24no—
57C22⋊Dic11—41no—
58C22⋊Dic11—42no—
59C4⋊Dic11—24no—
60C4⋊Dic11—41no—
61Dic11⋊C4—24no—
62C4×Dic11—24no—
63#2600—111nomaximal, Sylow
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—21no—
71C23×C11—22no—
72C23×C11—21no—
73C23×C11—22no—
74C23×C11C2×D412yes—
75C23×C11#4114yes—
76C23×C11C2411yescharacteristic
77D4×C11—216no—
78D4×C11—44no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11#4114yes—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—44no—
98C2×Dic11—48no—
99C2×Dic11C2×D414yes—
100C2×C4×D4—112no—
101#397—111no—
102#394—112no—
103#392D1111yescharacteristic
104#388—112no—
105#387—112no—
106#386—112no—
107#385—112no—
108#381—111no—
109C22×C11—24no—
110C22×C11—24no—
111C22×C11—22no—
112C22×C11—24no—
113C22×C11—24no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—41no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—41no—
121C22×C11C22×D411yescharacteristic
122C22×C11C2×#4112yes—
123C22×C11C2×#4112yes—
124C22×C11H(5,𝔽2)11yescharacteristic
125C22×C11H(5,𝔽2)11yescharacteristic
126C4×C11—24no—
127C4×C11—41no—
128C4×C11—41no—
129Dic11—24no—
130Dic11—42no—
131Dic11—42no—
132Dic11—42no—
133C22×D4C2×D1112yes—
134C22×D4C2×D1111yescharacteristic
135C23×C4—111no—
136C23×C4—112no—
137C4×D4—228no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—111no—
141C2×C22⋊C4—112no—
142C2×C22⋊C4—112no—
143C2×C22⋊C4—112no—
144C2×C22⋊C4—111no—
145C2×C22⋊C4—112no—
146C2×C22⋊C4C2×D1112yes—
147C2×C22⋊C4C2×D1111yescharacteristic
148C2×C42—112no—
149#95—112no—
150#95—112no—
151#95—112no—
152#95—112no—
153#95—111no—
154#95C2×D1111yescharacteristic
155C2×C11—42no—
156C2×C11—44no—
157C2×C11#52512yes—
158C2×C11#53411yescharacteristic
159C2×C11#55111yescharacteristic
160C2×C11#55312yes—
161C2×C11#55911yescharacteristic
162C24C22×D1111yescharacteristic
163C24C22×D1112yes—
164C2×D4—24no—
165C2×D4—24no—
166C2×D4—24no—
167C2×D4—24no—
168C2×D4—41no—
169C22×C4—112no—
170C22×C4—114no—
171C22×C4—112no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—224no—
175C22×C4—441no—
176C22×C4—442no—
177C22×C4—441no—
178C22×C4—442no—
179C22×C4C22×D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C4⋊C4—224no—
183C4⋊C4—224no—
184C4⋊C4—441no—
185C22⋊C4—24no—
186C22⋊C4—41no—
187C22⋊C4—224no—
188C22⋊C4—224no—
189C22⋊C4—224no—
190C22⋊C4—441no—
191C22⋊C4—442no—
192C42—224no—
193C11#260011yescharacteristic, complemented, Sylow
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23—21no—
203C23—22no—
204C23D4×D1112yes—
205C23#434114yes—
206C23C23×D1111yescharacteristic
207D4—216no—
208D4—44no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—114no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—444no—
228C2×C4—448no—
229C2×C4#434114yes—
230C22—24no—
231C22—24no—
232C22—24no—
233C22—22no—
234C22—24no—
235C22—42no—
236C22—41no—
237C22—42no—
238C22—41no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22C2×D4×D1111yescharacteristic
243C22C2×#434112yes—
244C22C2×#434112yes—
245C22#6703711yescharacteristic
246C22#6704211yescharacteristic
247C4—24no—
248C4—41no—
249C4—41no—
250C4—224no—
251C4—442no—
252C4—442no—
253C4—442no—
254C2—42no—
255C2—44no—
256C2#1062311712yes—
257C2#1062311811yescharacteristic
258C2#1062313611yescharacteristic
259C2#1062314912yes—
260C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC11×#392C2
hypercenter#392D11
hypocenterC11#2600
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic11C2semidirect
3. #10622835C2semidirect
4. #10622833C2semidirect
5. #10622566C2semidirect
6. #10622563C2semidirect
7. #10622558C2semidirect
8. #10622556C2semidirect
9. #10622268C2semidirect
47. C22×Dic11D4semidirect
193. C11#2600semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C11×#3922
#106228352
#106228332
#106225662
#106225632
#106225582
#106225562
#106222682
#260011