Finite Group Databasebeta

← #13076740

Subgroups — #13076740

Order 1408.

508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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×#400C211yesmaximal, characteristic, complemented
2#10622604C212yesmaximal, complemented
3#10622604C211yesmaximal, characteristic, complemented
4#10622601C211yesmaximal, characteristic, complemented
5#10622288C212yesmaximal, complemented
6#10622285C212yesmaximal, complemented
7#10622284C212yesmaximal, complemented
8#10622284C212yesmaximal, complemented
9#10622282C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×D44C2212yes—
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C11×#95C2212yes—
27C11×#95C2212yes—
28C11×#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C23×D11C2312yes—
32C23×D11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—22no—
41C2×D44—41no—
42C2×D44—41no—
43C2×D44—42no—
44C2×D44—42no—
45C2×D44—42no—
46C2×D44—42no—
47C2×D44—42no—
48C2×D44—42no—
49C2×D44—41no—
50C2×D44—42no—
51C11×C4⋊C4—41no—
52C11×C4⋊C4—41no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—42no—
55(C2×D11)⋊C4—42no—
56(C2×D11)⋊C4—42no—
57(C2×D11)⋊C4—42no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60(C2×D11)⋊C4—42no—
61Dic11⋊C4—42no—
62C4×Dic11—41no—
63#2828—111nomaximal, Sylow
64C23×C11C2411yescharacteristic
65C22×D11—22no—
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11#4112yes—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98D44—44no—
99D44—48no—
100D44—44no—
101D44—48no—
102#400D1111yescharacteristic, complemented
103#397—112no—
104#394—112no—
105#394—111no—
106#394—112no—
107#392—112no—
108#392—112no—
109#390—111no—
110#388—112no—
111C22×C11C2×#4111yescharacteristic
112C22×C11H(5,𝔽2)11yescharacteristic
113C22×C11H(5,𝔽2)11yescharacteristic
114C22×C11H(5,𝔽2)12yes—
115C22×C11H(5,𝔽2)12yes—
116C2×D11—42no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—42no—
121C2×D11—42no—
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C4×C11—22no—
131C4×C11—41no—
132C4×C11—42no—
133C4×C11—41no—
134C4×C11—42no—
135Dic11—42no—
136Dic11—42no—
137C22×D4—111no—
138C22×D4—112no—
139C22×D4—111no—
140C22×D4—112no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4C2×D1111yescharacteristic
143C2×C4⋊C4C2×D1111yescharacteristic
144C2×C22⋊C4—112no—
145C2×C22⋊C4—112no—
146C2×C22⋊C4—112no—
147C2×C22⋊C4—112no—
148C2×C22⋊C4—112no—
149C2×C22⋊C4—112no—
150C2×C22⋊C4—112no—
151C2×C22⋊C4—112no—
152C2×C42—111no—
153#95—112no—
154#95—111no—
155#95C2×D1112yes—
156#95C2×D1112yes—
157#95C2×D1111yescharacteristic
158C2×C11#53811yescharacteristic
159C2×C11#54012yes—
160C2×C11#56012yes—
161C2×C11#56011yescharacteristic
162C2×C11H(3,𝔽4)11yescharacteristic
163D11—82no—
164D11—82no—
165C24—112no—
166C24—112no—
167C2×D4—222no—
168C2×D4—441no—
169C2×D4—441no—
170C2×D4—441no—
171C2×D4—442no—
172C2×D4—442no—
173C2×D4—442no—
174C2×D4—442no—
175C2×D4—442no—
176C2×D4—442no—
177C2×D4—442no—
178C22×C4—112no—
179C22×C4—112no—
180C22×C4C22×D1112yes—
181C22×C4C22×D1111yescharacteristic
182C22×C4C22×D1112yes—
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1111yescharacteristic
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—442no—
188C22⋊C4—224no—
189C22⋊C4—442no—
190C22⋊C4—442no—
191C22⋊C4—442no—
192C22⋊C4—442no—
193C22⋊C4—442no—
194C22⋊C4—442no—
195C22⋊C4—442no—
196C42—441no—
197C11#282811yescharacteristic, complemented, Sylow
198C23—222no—
199C23—222no—
200C23—222no—
201C23—222no—
202C23—222no—
203C23—222no—
204C23—222no—
205C23—222no—
206C23—222no—
207C23—222no—
208C23—222no—
209C23—222no—
210C23—222no—
211C23—222no—
212C23C23×D1111yescharacteristic
213D4—444no—
214D4—448no—
215D4—444no—
216D4—448no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4#434312yes—
236C22—442no—
237C22—442no—
238C22—442no—
239C22—442no—
240C22—442no—
241C22—442no—
242C22—442no—
243C22—442no—
244C22—442no—
245C22—442no—
246C22—442no—
247C22—442no—
248C22—442no—
249C22—442no—
250C22#6703711yescharacteristic
251C22C2×#434311yescharacteristic
252C22#6704211yescharacteristic
253C22#6704212yes—
254C22#6704212yes—
255C4—22no—
256C4—42no—
257C4—41no—
258C4—41no—
259C4—42no—
260C4—442no—
261C4—442no—
262C2—882no—
263C2—882no—
264C2#1062317511yescharacteristic
265C2#1062319711yescharacteristic
266C2#1062321411yescharacteristic
267C2#1062322912yes—
268C2#1062324212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
hypercenter#400D11
hypocenterC11#2828
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C11×#400C2semidirect
2. #10622604C2semidirect
3. #10622604C2semidirect
4. #10622601C2semidirect
5. #10622288C2semidirect
6. #10622285C2semidirect
7. #10622284C2semidirect
8. #10622284C2semidirect
9. #10622282C2semidirect
102. #400D11semidirect
197. C11#2828semidirect

Maximal subgroups

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

subgroupindex
C11×#4002
#106226042
#106226012
#106222882
#106222852
#106222842
#106222822
#282811