Finite Group Databasebeta

← #13074293

Subgroups — #13074293

Order 1408.

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

normal subgroups only

This group has 540 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×#66925C212yesmaximal, complemented
2C11×#382C211yesmaximal, characteristic, complemented
3#10622607C212yesmaximal, complemented
4#10622604C211yesmaximal, characteristic
5#10622596C211yesmaximal, characteristic, complemented
6#10622283C212yesmaximal, complemented
7#10622281C212yesmaximal, complemented
8#10622278C212yesmaximal
9#10622266C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25#66925—28no—
26C11×#95C2212yes—
27C11×#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C23×D11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×D44—24no—
42C2×D44—41no—
43C2×C4×D11—24no—
44C2×C4×D11—24no—
45C2×C4×D11—24no—
46C11×C4⋊C4—41no—
47C11×C4⋊C4—41no—
48C42×C11D414yescomplemented
49(C2×D11)⋊C4—24no—
50(C2×D11)⋊C4—24no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—42no—
54C4⋊Dic11—24no—
55C4⋊Dic11—41no—
56Dic11⋊C4—24no—
57Dic11⋊C4—24no—
58C4×Dic11—24no—
59#2609—111nomaximal, Sylow
60C23×C11C2411yescharacteristic
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—22no—
67C22×D11#4114yes—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11C2×D414yes—
80C2×C4×C11C2×D412yes—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11#4114yes—
90D44—44no—
91C4×D11—216no—
92C2×#117—112no—
93#398—111no—
94#396—112no—
95#394—111no—
96#388—112no—
97#387—112no—
98#386—112no—
99#385—112no—
100#382D1111yescharacteristic, complemented
101C22×C11C22×D411yescharacteristic
102C22×C11C2×#4112yes—
103C22×C11C2×#4112yes—
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C112−1+411yescharacteristic
106C2×D11—24no—
107C2×D11—24no—
108C2×D11—24no—
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—42no—
113C4×C11—24no—
114C4×C11—22no—
115C4×C11—41no—
116C4×C11—41no—
117C4×C11—42no—
118Dic11—24no—
119Dic11—42no—
120Dic11—42no—
121C22×D4—111no—
122C23×C4—112no—
123#117—228no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4C2×D1111yescharacteristic
129C2×C4⋊C4C2×D1111yescharacteristic
130C2×C22⋊C4—112no—
131C2×C22⋊C4—112no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—112no—
134C2×C22⋊C4—112no—
135C2×C42—112no—
136C2×C42C2×D1111yescharacteristic
137#95—111no—
138#95—112no—
139#95—111no—
140#95—112no—
141#95C2×D1112yes—
142#95C2×D1112yes—
143C2×C11#52512yes—
144C2×C11#53711yescharacteristic
145C2×C11#55111yescharacteristic
146C2×C11#55212yes—
147C2×C11#55511yescharacteristic
148D11—44no—
149C24—112no—
150C2×D4—224no—
151C2×D4—441no—
152C22×C4—112no—
153C22×C4—112no—
154C22×C4—112no—
155C22×C4—224no—
156C22×C4—224no—
157C22×C4—224no—
158C22×C4C22×D1111yescharacteristic
159C22×C4C22×D1112yes—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1112yes—
162C22×C4C22×D1111yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—224no—
166C4⋊C4—224no—
167C4⋊C4—224no—
168C4⋊C4—441no—
169C22⋊C4—224no—
170C22⋊C4—224no—
171C22⋊C4—224no—
172C22⋊C4—224no—
173C22⋊C4—442no—
174C42—224no—
175C42D4414yescomplemented
176C11#260911yescharacteristic, complemented, Sylow
177C23—114no—
178C23—222no—
179C23—222no—
180C23—222no—
181C23—222no—
182C23—222no—
183C23—222no—
184C23C23×D1111yescharacteristic
185D4—444no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—114no—
198C2×C4—2216no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4C2×D4414yes—
208C2×C4C2×D4412yes—
209C22—224no—
210C22—224no—
211C22—224no—
212C22—442no—
213C22—442no—
214C22—442no—
215C22—442no—
216C22C22×D4411yescharacteristic
217C22#6703711yescharacteristic
218C22#6704011yescharacteristic
219C22#41×D1112yes—
220C22#41×D1112yes—
221C4—22no—
222C4—24no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—224no—
227C4—442no—
228C4—442no—
229C2—444no—
230C2#1062304111yescharacteristic
231C2#1062305512yes—
232C2#1062320111yescharacteristic
233C2#1062321011yescharacteristic
234C2#1062322412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC22×D44C22
hypercenter#382D11
hypocenterC11#2609
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#66925C2semidirect
2. C11×#382C2semidirect
3. #10622607C2semidirect
5. #10622596C2semidirect
6. #10622283C2semidirect
7. #10622281C2semidirect
9. #10622266C2semidirect
48. C42×C11D4semidirect
100. #382D11semidirect
175. C42D44semidirect
176. C11#2609semidirect

Maximal subgroups

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

subgroupindex
C2×#669252
C11×#3822
#106226072
#106226042
#106225962
#106222832
#106222812
#106222782
#106222662
#260911