Finite Group Databasebeta

← #14781176

Subgroups — #14781176

Order 2816.

1378 conjugacy classes of subgroups; only the 275 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 275 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
1#13070995C213yesmaximal
2#13069782C214yesmaximal, complemented
3#13069779C214yesmaximal
4#13068349C213yesmaximal, complemented
5C11×#3458C211yesmaximal, characteristic, complemented
6C23×C4×D11C2211yescharacteristic
7C11×#544—26no—
8C11×#543C2214yes—
9C11×#533—26no—
10C2×C11×#117C2213yes—
11C2×#66979C2213yes—
12#10622600—26no—
13#10622568C2216yes—
14#10622556C2216yes—
15C4×(C2×D11)⋊C4—26no—
16#10622164C22112yes—
17C24×D11C2311yescharacteristic
18C23×C4×C11C2311yescharacteristic
19C23×Dic11C2311yescharacteristic
20C22×C4×D11—23no—
21C22×C4×D11—23no—
22C22×C4×D11—26no—
23C22×C4×D11Q814yescomplemented
24C11×C4⋊Q8—212no—
25C11×#125—212no—
26C11×C22⋊Q8—224no—
27C4×Q8×C11—28no—
28C11×#117—26no—
29C11×#117—26no—
30C2×C11×C4⋊C4D416yes—
31C2×C11×C22⋊C4C2316yes—
32C2×C42×C11D416yes—
33C2×C22⋊Dic11C2316yes—
34C2×(C2×D11)⋊C4—212no—
35#66979—212no—
36C2×C4⋊Dic11—23no—
37C2×C4×Dic11—23no—
38C11⋊#95—212no—
39#23467—111nomaximal, Sylow
40C24×C11C2411yescharacteristic
41C23×D11—23no—
42C23×D11—23no—
43C23×D11—44no—
44C23×D11C2×Q812yes—
45C2×Q8×C11—28no—
46C22×C4×C11C2×D4112yes—
47C22×C4×C11C2×D413yes—
48C22×C4×C11C2×D413yes—
49C22×C4×C11C2×Q812yes—
50C22×C4×C11#4116yes—
51C22×Dic11—23no—
52C22×Dic11—26no—
53C22×Dic11—23no—
54C22×Dic11C2×Q812yes—
55C2×C4×D11—212no—
56C2×C4×D11—212no—
57C2×C4×D11—43no—
58C2×C4×D11—41no—
59C2×C4×D11—46no—
60C2×C4×D11—46no—
61C11×C4⋊C4—224no—
62C11×C4⋊C4—212no—
63C11×C22⋊C4—212no—
64C42×C11—26no—
65C42×C11—26no—
66C22⋊Dic11—212no—
67(C2×D11)⋊C4—424no—
68C4⋊Dic11—46no—
69C4×Dic11—46no—
70#3458D1111yescharacteristic, complemented
71#2280—113no—
72#2030—114no—
73#2029—114no—
74#1740—113no—
75C23×C11—42no—
76C23×C11C22×D413yes—
77C23×C11C22×Q811yescharacteristic
78C23×C11C2×#4113yes—
79C22×D11—212no—
80C22×D11—26no—
81C22×D11—44no—
82C22×D11—412no—
83C22×D11—46no—
84C22×D11—41no—
85C22×D11—43no—
86Q8×C11—88no—
87C2×C4×C11—212no—
88C2×C4×C11—412no—
89C2×C4×C11#12013yes—
90C2×C4×C11#12011yescharacteristic
91C2×C4×C11C22⋊Q816yes—
92C2×C4×C11C22⋊Q816yes—
93C2×C4×C11#12416yes—
94C2×C4×C11#12416yes—
95C2×Dic11—26no—
96C2×Dic11—41no—
97C2×Dic11—43no—
98C2×Dic11—412no—
99C2×Dic11—46no—
100C4×D11—412no—
101C4×D11—44no—
102C24×C4—111no—
103#544—26no—
104#543C2×D1114yes—
105#533—26no—
106C2×#117—113no—
107C2×#117C2×D1113yes—
108#381—116no—
109#380—226no—
110#379—116no—
111C4×C22⋊C4—226no—
112#342—1112no—
113C22×C11—26no—
114C22×C11—41no—
115C22×C11—43no—
116C22×C11C2×#12011yescharacteristic
117C22×C11C2×C22⋊Q813yes—
118C22×C11C2×#12413yes—
119C2×D11—212no—
120C2×D11—412no—
121C2×D11—46no—
122C2×D11—42no—
123C2×D11—44no—
124C4×C11—412no—
125C4×C11#39316yes—
126C4×C11#39312yes—
127Dic11—42no—
128Dic11—86no—
129C25—111no—
130C23×C4—111no—
131C23×C4—114no—
132C23×C4—226no—
133C23×C4—223no—
134C23×C4—223no—
135C23×C4C22×D1111yescharacteristic
136C4⋊Q8—212no—
137#125—212no—
138C22⋊Q8—224no—
139C4×Q8—28no—
140#117—26no—
141#117—26no—
142#117—2212no—
143C2×C4⋊C4—223no—
144C2×C4⋊C4C22⋊D1116yes—
145C2×C22⋊C4—116no—
146C2×C22⋊C4—2212no—
147C2×C22⋊C4C22×D1116yes—
148C2×C42—223no—
149C2×C42C22⋊D1116yes—
150#95—2212no—
151C2×C11—23no—
152C2×C11—23no—
153C2×C11C2×#39311yescharacteristic
154C2×C11#302512yes—
155D11—44no—
156C24—112no—
157C24—223no—
158C24—223no—
159C24—444no—
160C24C23×D1111yescharacteristic
161C2×Q8—28no—
162C22×C4—112no—
163C22×C4—223no—
164C22×C4—223no—
165C22×C4—2212no—
166C22×C4—2212no—
167C22×C4—226no—
168C22×C4—446no—
169C22×C4—446no—
170C22×C4—443no—
171C22×C4—441no—
172C22×C4Q8×D1112yes—
173C22×C4#434316yes—
174C22×C4C2×C22⋊D11112yes—
175C22×C4C2×C22⋊D1113yes—
176C22×C4C2×C22⋊D1113yes—
177C4⋊C4—224no—
178C4⋊C4—212no—
179C4⋊C4—446no—
180C22⋊C4—212no—
181C22⋊C4—2212no—
182C22⋊C4—4424no—
183C42—26no—
184C42—26no—
185C42—446no—
186C11#2346711yescharacteristic, complemented, Sylow
187C23—42no—
188C23—2212no—
189C23—226no—
190C23—446no—
191C23—444no—
192C23—4412no—
193C23—443no—
194C23—441no—
195C23C2×Q8×D1111yescharacteristic
196C23C2×#434313yes—
197C23C22×C22⋊D1113yes—
198Q8—88no—
199C2×C4—212no—
200C2×C4—412no—
201C2×C4—226no—
202C2×C4—443no—
203C2×C4—441no—
204C2×C4—4412no—
205C2×C4—444no—
206C2×C4—4412no—
207C2×C4—446no—
208C2×C4#6699916yes—
209C2×C4#6699916yes—
210C2×C4#6700016yes—
211C2×C4#6700016yes—
212C2×C4#6700613yes—
213C2×C4#6700611yescharacteristic
214C22—26no—
215C22—41no—
216C22—43no—
217C22—2212no—
218C22—4412no—
219C22—446no—
220C22—442no—
221C22—444no—
222C22C2×#6699913yes—
223C22C2×#6700013yes—
224C22C2×#6700611yescharacteristic
225C4—412no—
226C4—442no—
227C4—886no—
228C4#1062284416yes—
229C4#1062284412yes—
230C2—23no—
231C2—23no—
232C2—444no—
233C2C2×#1062284411yescharacteristic
234C2#1307800812yes—
subgroupG/H
centerC2×C4#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC24×D11C23
hypercenter#3458D11
hypocenterC11#23467
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
2. #13069782C2semidirect
4. #13068349C2semidirect
5. C11×#3458C2semidirect
23. C22×C4×D11Q8semidirect
70. #3458D11semidirect
186. C11#23467semidirect

Maximal subgroups

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

subgroupindex
#130709952
#130697822
#130697792
#130683492
C11×#34582
#2346711