Finite Group Databasebeta

← #13073019

Subgroups — #13073019

Order 1408.

412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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×#382C211yesmaximal, characteristic, complemented
2#10622600C211yesmaximal, characteristic
3#10622600C211yesmaximal, characteristic
4#10622598C211yesmaximal, characteristic, complemented
5C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic, complemented
8#10622288C212yesmaximal
9#10622283C212yesmaximal
10C11⋊#401C212yesmaximal, complemented
11#10622267C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16C2×(C2×D11)⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2212yes—
26C11×#95C2212yes—
27C11×#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C23×D11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11—22no—
48C2×C4×D11—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C42×C11—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—42no—
56C4⋊Dic11—24no—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59Dic11⋊C4—42no—
60C4×Dic11—22no—
61C4×Dic11—42no—
62#2494—111nomaximal, Sylow
63C23×C11C2411yescharacteristic
64C22×D11—21no—
65C22×D11—21no—
66C22×D11—21no—
67C22×D11—21no—
68C22×D11—21no—
69C22×D11—21no—
70C22×D11#4112yes—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11#4112yes—
84C2×C4×C11#4112yes—
85C2×C4×C11#4112yes—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11#4112yes—
101C4×D11—44no—
102#401—112no—
103#397—112no—
104#389—111no—
105#389—111no—
106#388—112no—
107#387—112no—
108#382D1111yescharacteristic, complemented
109#380—111no—
110#380—111no—
111C4×C4⋊C4—111no—
112C4×C22⋊C4—111no—
113C22×C11C2×#4111yescharacteristic
114C22×C11C2×#4111yescharacteristic
115C22×C11C2×#4111yescharacteristic
116C22×C11C2×#4111yescharacteristic
117C22×C11C2×#4111yescharacteristic
118C22×C11H(5,𝔽2)11yescharacteristic
119C22×C112−1+411yescharacteristic
120C2×D11—22no—
121C2×D11—22no—
122C2×D11—22no—
123C2×D11—41no—
124C2×D11—41no—
125C2×D11—41no—
126C2×D11—41no—
127C4×C11—42no—
128C4×C11—42no—
129C4×C11—41no—
130C4×C11—41no—
131C4×C11#12614yes—
132Dic11—22no—
133Dic11—41no—
134Dic11—41no—
135Dic11—42no—
136Dic11—42no—
137C23×C4—111no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4C2×D1111yescharacteristic
143C2×C4⋊C4C2×D1111yescharacteristic
144C2×C22⋊C4—111no—
145C2×C22⋊C4—111no—
146C2×C22⋊C4—112no—
147C2×C22⋊C4—112no—
148C2×C42—111no—
149C2×C42—112no—
150C2×C42C2×D1111yescharacteristic
151#95—111no—
152#95—111no—
153#95—112no—
154#95—112no—
155#95—112no—
156#95—112no—
157#95—112no—
158#95C2×D1112yes—
159#95C2×D1112yes—
160C2×C11C2×#12611yescharacteristic
161C2×C11#52911yescharacteristic
162C2×C11#54211yescharacteristic
163C2×C11#55211yescharacteristic
164C2×C11#55311yescharacteristic
165C2×C11#55311yescharacteristic
166C2×C11#55611yescharacteristic
167D11—42no—
168C24—111no—
169C22×C4—111no—
170C22×C4—111no—
171C22×C4—111no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—222no—
175C22×C4—222no—
176C22×C4—222no—
177C22×C4C22×D1111yescharacteristic
178C22×C4C22×D1112yes—
179C22×C4C22×D1112yes—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1111yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—224no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—442no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4—224no—
191C22⋊C4—442no—
192C42—22no—
193C42—222no—
194C42—442no—
195C11#249411yescharacteristic, complemented, Sylow
196C23—112no—
197C23—221no—
198C23—221no—
199C23—221no—
200C23—221no—
201C23—221no—
202C23—221no—
203C23C23×D1111yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—112no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—222no—
220C2×C4—221no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—222no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—444no—
232C2×C4#433912yes—
233C2×C4#434112yes—
234C2×C4#434312yes—
235C22—222no—
236C22—222no—
237C22—222no—
238C22—441no—
239C22—441no—
240C22—441no—
241C22—441no—
242C22C2×#433911yescharacteristic
243C22C2×#434111yescharacteristic
244C22C2×#434311yescharacteristic
245C22#41×D1111yescharacteristic
246C22#41×D1111yescharacteristic
247C22#6704211yescharacteristic
248C22#6704311yescharacteristic
249C4—41no—
250C4—41no—
251C4—42no—
252C4—42no—
253C4—222no—
254C4—441no—
255C4—442no—
256C4—441no—
257C4—442no—
258C4#6695114yes—
259C2—442no—
260C2C2×#6695111yescharacteristic
261C2#1062306111yescharacteristic
262C2#1062306411yescharacteristic
263C2#1062321111yescharacteristic
264C2#1062321311yescharacteristic
265C2#1062322511yescharacteristic
266C2#1062322611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC23×D11C23
hypercenter#382D11
hypocenterC11#2494
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C11×#382C2semidirect
4. #10622598C2semidirect
5. C4⋊C4×Dic11C2semidirect
7. #10622541C2semidirect
10. C11⋊#401C2semidirect
11. #10622267C2semidirect
108. #382D11semidirect
195. C11#2494semidirect

Maximal subgroups

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

subgroupindex
C11×#3822
#106226002
#106225982
C4⋊C4×Dic112
C4×(C2×D11)⋊C42
#106225412
#106222882
#106222832
C11⋊#4012
#106222672
#249411