Finite Group Databasebeta

← #13074203

Subgroups — #13074203

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×C4×C22⋊D11C212yesmaximal, complemented
2C11×#381C211yesmaximal, characteristic, complemented
3#10622574C212yesmaximal, complemented
4#10622573C211yesmaximal, characteristic
5#10622566C211yesmaximal, characteristic, complemented
6#10622283C212yesmaximal, complemented
7#10622281C212yesmaximal, complemented
8#10622278C212yesmaximal, complemented
9#10622266C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C4×C22⋊D11—28no—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2212yes—
26C11×#95C2212yes—
27C11×#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C24×C11C2311yescharacteristic
33C23×D11C2312yes—
34C22×C4×C11—41no—
35C22×C4×C11—41no—
36C22×C4×C11D414yescomplemented
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C2×C22⋊D11—24no—
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×D44—24no—
48C2×D44—41no—
49C2×C4×D11—24no—
50C2×C4×D11—42no—
51C2×C4×D11—42no—
52C11×C22⋊C4—41no—
53C11×C22⋊C4—41no—
54C22⋊Dic11—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—24no—
58(C2×D11)⋊C4—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—21no—
67C23×C11—21no—
68C23×C11C2×D412yes—
69C23×C11C2411yescharacteristic
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11#4114yes—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—44no—
87C2×C4×C11C2×D414yes—
88C22⋊D11—216no—
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#4114yes—
98D44—44no—
99C4×D11—48no—
100C2×C4×D4—112no—
101#397—111no—
102#394—112no—
103#392—111no—
104#388—112no—
105#387—112no—
106#386—112no—
107#385—112no—
108#381D1111yescharacteristic, complemented
109C22×C11—24no—
110C22×C11—22no—
111C22×C11—41no—
112C22×C11—42no—
113C22×C11—41no—
114C22×C11C22×D411yescharacteristic
115C22×C11C2×#4112yes—
116C22×C11C2×#4112yes—
117C22×C11H(5,𝔽2)11yescharacteristic
118C22×C11H(5,𝔽2)11yescharacteristic
119C2×D11—24no—
120C2×D11—24no—
121C2×D11—24no—
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C4×C11—24no—
127C4×C11—41no—
128C4×C11—42no—
129C4×C11—41no—
130Dic11—24no—
131Dic11—42no—
132Dic11—42no—
133C22×D4—112no—
134C22×D4—111no—
135C23×C4—112no—
136C23×C4C2×D1111yescharacteristic
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—112no—
145C2×C22⋊C4—112no—
146C2×C22⋊C4C2×D1111yescharacteristic
147C2×C22⋊C4C2×D1111yescharacteristic
148C2×C42—112no—
149#95—112no—
150#95—112no—
151#95—111no—
152#95—111no—
153#95C2×D1112yes—
154#95C2×D1112yes—
155C2×C11—42no—
156C2×C11#52512yes—
157C2×C11#53411yescharacteristic
158C2×C11#55111yescharacteristic
159C2×C11#55312yes—
160C2×C11#55911yescharacteristic
161D11—44no—
162C24—112no—
163C24C22×D1111yescharacteristic
164C2×D4—224no—
165C2×D4—224no—
166C2×D4—224no—
167C2×D4—224no—
168C2×D4—441no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—112no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—224no—
175C22×C4—442no—
176C22×C4—442no—
177C22×C4D4414yescomplemented
178C22×C4C22×D1111yescharacteristic
179C22×C4C22×D1112yes—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C4⋊C4—224no—
183C4⋊C4—224no—
184C4⋊C4—441no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—224no—
188C22⋊C4—224no—
189C22⋊C4—224no—
190C22⋊C4—224no—
191C22⋊C4—442no—
192C42—224no—
193C11#260011yescharacteristic, complemented, Sylow
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—114no—
199C23—222no—
200C23—222no—
201C23—222no—
202C23—222no—
203C23—222no—
204C23—222no—
205C23C2×D4412yes—
206C23C23×D1111yescharacteristic
207D4—2216no—
208D4—444no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—114no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—448no—
229C2×C4C2×D4414yes—
230C22—22no—
231C22—24no—
232C22—41no—
233C22—42no—
234C22—41no—
235C22—224no—
236C22—224no—
237C22—224no—
238C22—442no—
239C22—442no—
240C22—442no—
241C22—442no—
242C22C22×D4411yescharacteristic
243C22#6703711yescharacteristic
244C22#6703711yescharacteristic
245C22#41×D1112yes—
246C22#41×D1112yes—
247C4—24no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—224no—
252C4—442no—
253C4—442no—
254C2—42no—
255C2—444no—
256C2#1062302411yescharacteristic
257C2#1062305512yes—
258C2#1062319011yescharacteristic
259C2#1062319212yes—
260C2#1062319511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radical#10622573C2
hypercenter#381D11
hypocenterC11#2600
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D11C2semidirect
2. C11×#381C2semidirect
3. #10622574C2semidirect
5. #10622566C2semidirect
6. #10622283C2semidirect
7. #10622281C2semidirect
8. #10622278C2semidirect
9. #10622266C2semidirect
36. C22×C4×C11D4semidirect
108. #381D11semidirect
177. C22×C4D44semidirect
193. C11#2600semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C11×#3812
#106225742
#106225732
#106225662
#106222832
#106222812
#106222782
#106222662
#260011