Finite Group Databasebeta

← #13073588

Subgroups — #13073588

Order 1408.

704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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×C11×#124C211yesmaximal, characteristic, complemented
2C2×#67000C211yesmaximal, characteristic, complemented
3C2×#66993C211yesmaximal, characteristic
4C2×C4×D44C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622834C211yesmaximal, characteristic, complemented
7#10622574C214yesmaximal, complemented
8#10622569C214yesmaximal, complemented
9C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C22×C22⋊D11C2214yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2212yes—
15C11×#124—24no—
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2214yes—
20#67000—24no—
21#66993—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2214yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28C4×D44—24no—
29C11⋊#95C2212yes—
30C11⋊#95C2214yes—
31C24×C11C2312yes—
32C23×D11C2312yes—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C2×Q8×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11—22no—
38C2×D4×C11—22no—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11—28no—
44C2×C22⋊D11—28no—
45C2×C22⋊D11—44no—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C2×D44—22no—
50C2×D44—22no—
51C2×D44D414yes—
52C2×C4×D11—24no—
53C2×C4×D11—44no—
54C11×C22⋊C4—24no—
55C11×C22⋊C4—24no—
56C42×C11D414yescomplemented
57C22⋊Dic11—44no—
58(C2×D11)⋊C4—28no—
59(C2×D11)⋊C4—24no—
60C4⋊Dic11—24no—
61C4⋊Dic11—22no—
62C4×Dic11—22no—
63C4×Dic11—22no—
64#2544—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—24no—
68C23×C11—22no—
69C23×C11—24no—
70C23×C11C2411yescharacteristic
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—24no—
74C22×D11—24no—
75C22×D11C2×D414yes—
76Q8×C11—44no—
77D4×C11—44no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2×D412yes—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D412yes—
87C2×C4×C11#4112yes—
88C22⋊D11—416no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—24no—
96C2×Dic11#4114yes—
97D44—28no—
98C4×D11—48no—
99C2×#127—111no—
100C2×#124—111no—
101C2×#124D1111yescharacteristic, complemented
102C2×C4×D4—111no—
103#394—114no—
104#391—111no—
105#390—111no—
106#386—114no—
107C4×C4⋊C4—111no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11—44no—
112C22×C11—44no—
113C22×C11C22×D411yescharacteristic
114C22×C11C22×D411yescharacteristic
115C22×C11C2×#4111yescharacteristic
116C22×C11C2×#4112yes—
117C22×C11H(5,𝔽2)12yes—
118C2×D11—24no—
119C2×D11—28no—
120C2×D11—42no—
121C2×D11—42no—
122C2×D11—44no—
123C4×C11—22no—
124C4×C11—22no—
125C4×C11—42no—
126C4×C11#12114yes—
127Dic11—24no—
128Dic11—42no—
129Dic11—42no—
130C22×Q8C2×D1111yescharacteristic
131C22×D4—114no—
132C22×D4—111no—
133C22×D4C2×D1111yescharacteristic
134C23×C4—112no—
135#127—224no—
136#124—24no—
137#124—224no—
138C4×D4—224no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—112no—
141C2×C22⋊C4—112no—
142C2×C22⋊C4—114no—
143C2×C22⋊C4—114no—
144C2×C22⋊C4C2×D1112yes—
145C2×C22⋊C4C2×D1112yes—
146C2×C42—111no—
147C2×C42—111no—
148C2×C42C2×D1111yescharacteristic
149#95—112no—
150#95—114no—
151C2×C11—82no—
152C2×C11C2×#12111yescharacteristic
153C2×C11#53211yescharacteristic
154C2×C11#53511yescharacteristic
155C2×C11#54612yes—
156C2×C11#55912yes—
157D11—44no—
158C24—112no—
159C24C22×D1112yes—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—22no—
166C2×D4—114no—
167C2×D4—228no—
168C2×D4—228no—
169C2×D4—222no—
170C2×D4—222no—
171C2×D4—444no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—112no—
175C22×C4—224no—
176C22×C4—444no—
177C22×C4C22×D1112yes—
178C22×C4C22×D1111yescharacteristic
179C22×C4C22×D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C4⋊C4—224no—
182C4⋊C4—222no—
183C22⋊C4—24no—
184C22⋊C4—24no—
185C22⋊C4—228no—
186C22⋊C4—224no—
187C22⋊C4—444no—
188C42—222no—
189C42—222no—
190C42C22⋊D1114yescomplemented
191C11#254411yescharacteristic, complemented, Sylow
192C23—22no—
193C23—22no—
194C23—24no—
195C23—24no—
196C23—22no—
197C23—114no—
198C23—222no—
199C23—224no—
200C23—224no—
201C23—222no—
202C23C23×D1111yescharacteristic
203Q8—44no—
204D4—44no—
205D4—228no—
206D4—4416no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—114no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—224no—
219C2×C4—222no—
220C2×C4—448no—
221C2×C4D4×D1112yes—
222C2×C4#434112yes—
223C2×C4C2×C22⋊D1112yes—
224C2×C4C2×C22⋊D1112yes—
225C2×C4C2×C22⋊D1112yes—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—44no—
230C22—44no—
231C22—224no—
232C22—228no—
233C22—442no—
234C22—442no—
235C22—444no—
236C22C2×D4×D1111yescharacteristic
237C22C2×#434111yescharacteristic
238C22#41×D1112yes—
239C22#6704212yes—
240C22C22×C22⋊D1111yescharacteristic
241C4—22no—
242C4—22no—
243C4—42no—
244C4—224no—
245C4—442no—
246C4—442no—
247C4#6699114yes—
248C2—82no—
249C2—444no—
250C2#1062320712yes—
251C2#1062321212yes—
252C2C2×#6699111yescharacteristic
253C2#1062336111yescharacteristic
254C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC2×#66993C2
hypercenterC2×#124D11
hypocenterC11#2544
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#67000C2semidirect
4. C2×C4×D44C2semidirect
5. #10622843C2semidirect
6. #10622834C2semidirect
7. #10622574C2semidirect
8. #10622569C2semidirect
9. C4×C4⋊Dic11C2semidirect
56. C42×C11D4semidirect
101. C2×#124D11semidirect
190. C42C22⋊D11semidirect
191. C11#2544semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#670002
C2×#669932
C2×C4×D442
#106228432
#106228342
#106225742
#106225692
C4×C4⋊Dic112
#254411