Finite Group Databasebeta

← #13076445

Subgroups — #13076445

Order 1408.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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×#384C211yesmaximal, characteristic, complemented
2#10622607C212yesmaximal, complemented
3#10622604C211yesmaximal, characteristic
4#10622604C212yesmaximal
5#10622603C212yesmaximal, complemented
6#10622603C212yesmaximal, complemented
7#10622599C211yesmaximal, characteristic, complemented
8#10622591C212yesmaximal, complemented
9#10622553C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C2×C11×C4⋊C4C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C23×D11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—41no—
41C2×D44—42no—
42C11×C4⋊C4—42no—
43C11×C4⋊C4—41no—
44C11×C4⋊C4—41no—
45C11×C4⋊C4—42no—
46C42×C11—22no—
47(C2×D11)⋊C4—24no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—24no—
50(C2×D11)⋊C4—42no—
51(C2×D11)⋊C4—42no—
52(C2×D11)⋊C4—42no—
53C4⋊Dic11—41no—
54Dic11⋊C4—24no—
55C4×Dic11—42no—
56#2795—111nomaximal, Sylow
57C23×C11C2411yescharacteristic
58C22×D11—22no—
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11#4112yes—
77C2×C4×C11#4114yes—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87D44—44no—
88#400—111no—
89#396—112no—
90#394—111no—
91#394—112no—
92#388—112no—
93#388—112no—
94#388—112no—
95#387—112no—
96#384D1111yescharacteristic, complemented
97C22×C11C2×#4111yescharacteristic
98C22×C11C2×#4112yes—
99C22×C11H(5,𝔽2)11yescharacteristic
100C22×C11H(5,𝔽2)12yes—
101C22×C112−1+411yescharacteristic
102C2×D11—42no—
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C4×C11—22no—
110C4×C11—24no—
111C4×C11—42no—
112C4×C11—41no—
113C4×C11—41no—
114Dic11—42no—
115Dic11—42no—
116Dic11—42no—
117C22×D4—111no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—111no—
120C2×C4⋊C4C2×D1112yes—
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C4⋊C4C2×D1112yes—
123C2×C4⋊C4C2×D1111yescharacteristic
124C2×C22⋊C4—112no—
125C2×C22⋊C4—112no—
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C22⋊C4—112no—
130C2×C42—112no—
131C2×C42C2×D1111yescharacteristic
132#95—111no—
133#95—112no—
134#95—112no—
135#95—112no—
136#95—111no—
137#95—112no—
138C2×C11#53911yescharacteristic
139C2×C11#54212yes—
140C2×C11#55312yes—
141C2×C11#55511yescharacteristic
142C2×C11#56011yescharacteristic
143D11—82no—
144C24—112no—
145C2×D4—442no—
146C2×D4—441no—
147C22×C4—112no—
148C22×C4—112no—
149C22×C4—112no—
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1112yes—
152C22×C4C22×D1111yescharacteristic
153C22×C4C22×D1111yescharacteristic
154C22×C4C22×D1112yes—
155C4⋊C4—42no—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—41no—
159C4⋊C4—224no—
160C4⋊C4—441no—
161C22⋊C4—224no—
162C22⋊C4—224no—
163C22⋊C4—224no—
164C22⋊C4—442no—
165C22⋊C4—442no—
166C22⋊C4—442no—
167C42—22no—
168C42—442no—
169C11#279511yescharacteristic, complemented, Sylow
170C23—222no—
171C23—222no—
172C23—222no—
173C23—222no—
174C23—222no—
175C23—222no—
176C23—222no—
177C23C23×D1111yescharacteristic
178D4—444no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4#433912yes—
200C2×C4#434314yes—
201C22—442no—
202C22—442no—
203C22—442no—
204C22—442no—
205C22—442no—
206C22—442no—
207C22—442no—
208C22C2×#433911yescharacteristic
209C22#6703712yes—
210C22#6703711yescharacteristic
211C22C2×#434312yes—
212C22#6704011yescharacteristic
213C4—24no—
214C4—22no—
215C4—41no—
216C4—42no—
217C4—41no—
218C4—442no—
219C4—442no—
220C4—442no—
221C2—882no—
222C2#1062304512yes—
223C2#1062304611yescharacteristic
224C2#1062325111yescharacteristic
225C2#1062326412yes—
226C2#1062326511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#384C2
prime radicalC22×D44C22
hypercenter#384D11
hypocenterC11#2795
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C11×#384C2semidirect
2. #10622607C2semidirect
5. #10622603C2semidirect
6. #10622603C2semidirect
7. #10622599C2semidirect
8. #10622591C2semidirect
9. #10622553C2semidirect
96. #384D11semidirect
169. C11#2795semidirect

Maximal subgroups

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

subgroupindex
C11×#3842
#106226072
#106226042
#106226032
#106225992
#106225912
#106225532
#279511