Finite Group Databasebeta

← #14781181

Subgroups — #14781181

Order 2816.

1506 conjugacy classes of subgroups; only the 275 normal subgroups are shown.

normal subgroups only

This group has 1506 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#13071191C213yesmaximal
2#13069782C214yesmaximal, complemented
3#13069779C214yesmaximal, complemented
4C2×#10622164C213yesmaximal, complemented
5C2×C11×#543C211yesmaximal, characteristic, complemented
6C23×C22⋊D11C2211yescharacteristic
7C11×#543—26no—
8C11×#543C2214yes—
9C2×C11×C22⋊Q8—26no—
10C22×C11×C22⋊C4C2213yes—
11C22×C22⋊Dic11C2213yes—
12#10622826—26no—
13#10622571—26no—
14#10622568C2216yes—
15#10622556C2216yes—
16#10622164C22112yes—
17C25×C11C2311yescharacteristic
18C24×D11C2311yescharacteristic
19C22×Q8×C11—22no—
20C23×C4×C11D416yes—
21C22×C22⋊D11—23no—
22C22×C22⋊D11—23no—
23C22×C22⋊D11—26no—
24C22×C22⋊D11Q814yescomplemented
25C23×Dic11—23no—
26C23×Dic11C2311yescharacteristic
27C11×C22⋊Q8—224no—
28C11×C22⋊Q8—224no—
29C2×C11×C4⋊C4—26no—
30C2×C11×C22⋊C4—26no—
31C2×C11×C22⋊C4—26no—
32C2×C11×C22⋊C4D416yes—
33C2×C11×C22⋊C4C2316yes—
34C2×C22⋊Dic11—212no—
35C2×C22⋊Dic11—23no—
36C2×C22⋊Dic11C2316yes—
37C2×(C2×D11)⋊C4—212no—
38C11⋊#95—212no—
39#23468—111nomaximal, Sylow
40C24×C11—82no—
41C24×C11C2×D413yes—
42C24×C11C2×D413yes—
43C24×C11C2×Q812yes—
44C24×C11#4116yes—
45C24×C11C2411yescharacteristic
46C23×D11—23no—
47C23×D11—23no—
48C23×D11—82no—
49C23×D11C2×Q812yescomplemented
50C2×Q8×C11—28no—
51C2×Q8×C11—84no—
52C22×C4×C11—26no—
53C22×C4×C11—26no—
54C22×C4×C11—86no—
55C22×C4×C11C2×D4112yes—
56C2×C22⋊D11—212no—
57C2×C22⋊D11—212no—
58C2×C22⋊D11—43no—
59C2×C22⋊D11—41no—
60C2×C22⋊D11—46no—
61C2×C22⋊D11—46no—
62C22×Dic11—23no—
63C22×Dic11—26no—
64C22×Dic11—23no—
65C22×Dic11—46no—
66C22×Dic11—86no—
67C22×Dic11C2×Q812yescomplemented
68C11×C4⋊C4—224no—
69C11×C22⋊C4—212no—
70C11×C22⋊C4—212no—
71C22⋊Dic11—212no—
72C22⋊Dic11—46no—
73(C2×D11)⋊C4—812no—
74C2×#543D1111yescharacteristic, complemented
75#2308—113no—
76#2030—114no—
77#2029—114no—
78C2×#342—113no—
79C23×C11—46no—
80C23×C11—46no—
81C23×C11—42no—
82C23×C11—82no—
83C23×C11—86no—
84C23×C11#12013yes—
85C23×C11#12011yescharacteristic
86C23×C11C22⋊Q816yes—
87C23×C11C22⋊Q816yes—
88C23×C11#12416yes—
89C23×C11#12416yes—
90C23×C11C22×D413yes—
91C23×C11C22×Q811yescharacteristic
92C23×C11C2×#4113yes—
93C22×D11—26no—
94C22×D11—412no—
95C22×D11—41no—
96C22×D11—43no—
97C22×D11—82no—
98C22×D11—86no—
99Q8×C11—88no—
100C2×C4×C11—212no—
101C2×C4×C11—412no—
102C2×C4×C11—412no—
103C2×C4×C11—86no—
104C22⋊D11—412no—
105C22⋊D11—44no—
106C2×Dic11—26no—
107C2×Dic11—41no—
108C2×Dic11—43no—
109C2×Dic11—412no—
110C2×Dic11—46no—
111C2×Dic11—812no—
112C23×D4—111no—
113#543—26no—
114#543C2×D1114yes—
115C2×C22⋊Q8—26no—
116C22×C22⋊C4—113no—
117C22×C22⋊C4C2×D1113yes—
118#386—226no—
119#386—226no—
120#381—116no—
121#379—116no—
122#342—1112no—
123C22×C11—22no—
124C22×C11—26no—
125C22×C11—26no—
126C22×C11—41no—
127C22×C11—43no—
128C22×C11—46no—
129C22×C11—46no—
130C22×C11—46no—
131C22×C11—46no—
132C22×C11#39316yes—
133C22×C11#39312yes—
134C22×C11C2×#12011yescharacteristic
135C22×C11C2×C22⋊Q813yes—
136C22×C11C2×#12413yes—
137C2×D11—412no—
138C2×D11—42no—
139C2×D11—86no—
140C2×D11—82no—
141C4×C11—412no—
142Dic11—42no—
143Dic11—86no—
144C25—111no—
145C25C22×D1111yescharacteristic
146C22×Q8—22no—
147C22×D4—114no—
148C22×D4—226no—
149C22×D4—223no—
150C22×D4—223no—
151C23×C4—111no—
152C23×C4—223no—
153C23×C4C22⋊D1116yes—
154C22⋊Q8—224no—
155C22⋊Q8—224no—
156C2×C4⋊C4—26no—
157C2×C22⋊C4—26no—
158C2×C22⋊C4—26no—
159C2×C22⋊C4—116no—
160C2×C22⋊C4—2212no—
161C2×C22⋊C4—223no—
162C2×C22⋊C4—2212no—
163C2×C22⋊C4C22⋊D1116yes—
164C2×C22⋊C4C22×D1116yes—
165#95—2212no—
166C2×C11—23no—
167C2×C11—23no—
168C2×C11—22no—
169C2×C11—26no—
170C2×C11C2×#39311yescharacteristic
171C2×C11#302612yes—
172D11—82no—
173C24—82no—
174C24—112no—
175C24—223no—
176C24—223no—
177C24—882no—
178C24Q8×D1112yes—
179C24#434316yes—
180C24C2×C22⋊D1113yes—
181C24C2×C22⋊D1113yes—
182C24C23×D1111yescharacteristic
183C2×Q8—28no—
184C2×Q8—84no—
185C2×D4—2212no—
186C2×D4—2212no—
187C2×D4—446no—
188C2×D4—446no—
189C2×D4—443no—
190C2×D4—441no—
191C22×C4—26no—
192C22×C4—26no—
193C22×C4—86no—
194C22×C4—112no—
195C22×C4—223no—
196C22×C4—223no—
197C22×C4—226no—
198C22×C4—446no—
199C22×C4—886no—
200C22×C4C2×C22⋊D11112yes—
201C4⋊C4—224no—
202C22⋊C4—212no—
203C22⋊C4—212no—
204C22⋊C4—2212no—
205C22⋊C4—446no—
206C22⋊C4—8812no—
207C11#2346811yescharacteristic, complemented, Sylow
208C23—46no—
209C23—46no—
210C23—42no—
211C23—82no—
212C23—86no—
213C23—226no—
214C23—4412no—
215C23—443no—
216C23—441no—
217C23—882no—
218C23—886no—
219C23#6699916yes—
220C23#6699916yes—
221C23#6700016yes—
222C23#6700016yes—
223C23#6700613yes—
224C23#6700611yescharacteristic
225C23C2×Q8×D1111yescharacteristic
226C23C2×#434313yes—
227C23C22×C22⋊D1113yes—
228Q8—88no—
229D4—444no—
230D4—4412no—
231C2×C4—212no—
232C2×C4—412no—
233C2×C4—412no—
234C2×C4—86no—
235C2×C4—226no—
236C2×C4—443no—
237C2×C4—441no—
238C2×C4—4412no—
239C2×C4—446no—
240C2×C4—8812no—
241C22—22no—
242C22—26no—
243C22—26no—
244C22—46no—
245C22—41no—
246C22—43no—
247C22—46no—
248C22—46no—
249C22—46no—
250C22—4412no—
251C22—442no—
252C22—886no—
253C22—882no—
254C22#1062284412yes—
255C22#1062284416yes—
256C22C2×#6699913yes—
257C22C2×#6700013yes—
258C22C2×#6700611yescharacteristic
259C4—412no—
260C4—442no—
261C4—886no—
262C2—23no—
263C2—23no—
264C2—22no—
265C2—26no—
266C2—882no—
267C2C2×#1062284411yescharacteristic
268C2#1307801312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#543C2
socleC22×C11C2×#120
prime radicalC23×C22⋊D11C22
hypercenterC2×#543D11
hypocenterC11#23468
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
2. #13069782C2semidirect
3. #13069779C2semidirect
4. C2×#10622164C2semidirect
5. C2×C11×#543C2semidirect
24. C22×C22⋊D11Q8semidirect
49. C23×D11C2×Q8semidirect
67. C22×Dic11C2×Q8semidirect
74. C2×#543D11semidirect
207. C11#23468semidirect

Maximal subgroups

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

subgroupindex
#130711912
#130697822
#130697792
C2×#106221642
C2×C11×#5432
#2346811