Finite Group Databasebeta

← D11×#2030 #14781171

Subgroups — D11×#2030 #14781171

Order 2816.

1482 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 217 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
1D11×#543C211yesmaximal, characteristic
2D11×#381C213yesmaximal
3#13069784C213yesmaximal, complemented
4#13069783C213yesmaximal, complemented
5#13069782C211yesmaximal, characteristic, complemented
6D11×#342C213yesmaximal
7C11×#2030C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C11×#543C2211yescharacteristic
10#10623165—26no—
11D11×C22⋊Q8—26no—
12C2×C22⋊C4×D11C2213yes—
13C2×C22⋊C4×D11C2213yes—
14#10623014C2213yes—
15C11×#381C2213yes—
16#10622824C2213yes—
17#10622556C2213yes—
18#10622556C2213yes—
19#10622277—26no—
20D11×#95—26no—
21C11×#342C2213yes—
22#10622165C2216yes—
23#10622164C2213yes—
24C24×D11C2311yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11C2311yescharacteristic
27C2×Q8×D11—22no—
28C22×C4×D11—23no—
29C22×C4×D11—23no—
30C22×C4×D11—26no—
31C22×C4×D11—23no—
32C22×C4×D11D416yes—
33C22×C4×D11Q814yescomplemented
34C11×C22⋊Q8—26no—
35C2×C11×C22⋊C4C2313yes—
36C2×C11×C22⋊C4C2313yes—
37C2×C22⋊Dic11C2313yes—
38C2×C22⋊Dic11C2313yes—
39#66999—26no—
40C2×(C2×D11)⋊C4—23no—
41C2×(C2×D11)⋊C4D416yes—
42#66977—26no—
43#66950—26no—
44#66949—212no—
45C4⋊C4×D11—26no—
46C22⋊C4×D11—26no—
47C22⋊C4×D11—26no—
48C22⋊C4×D11—212no—
49#66931—212no—
50C11×#95—26no—
51C11⋊#95—26no—
52C11⋊#95—26no—
53C11⋊#95—26no—
54C2×#2030—111nomaximal, Sylow
55C24×C11C2411yescharacteristic
56C23×D11—44no—
57C23×D11C2×D413yes—
58C23×D11C2×D413yes—
59C23×D11C2×Q812yes—
60C23×D11#4116yes—
61C2×Q8×C11—22no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11C2×D416yes—
66C22×C4×C11C2×Q812yescomplemented
67C22×Dic11—23no—
68C22×Dic11—23no—
69C22×Dic11—23no—
70C22×Dic11C2×D416yes—
71C22×Dic11C2×Q812yescomplemented
72Q8×D11—84no—
73C2×C4×D11—26no—
74C2×C4×D11—26no—
75C2×C4×D11—212no—
76C2×C4×D11—212no—
77C2×C4×D11—412no—
78C2×C4×D11—412no—
79C2×C4×D11—43no—
80C2×C4×D11—41no—
81C2×C4×D11—46no—
82C2×C4×D11—46no—
83C2×C4×D11—46no—
84C2×Dic22—26no—
85C11×C4⋊C4—26no—
86C11×C22⋊C4—26no—
87C11×C22⋊C4—26no—
88C22⋊Dic11—26no—
89C22⋊Dic11—26no—
90(C2×D11)⋊C4—212no—
91(C2×D11)⋊C4—46no—
92C4⋊Dic11—26no—
93Dic11⋊C4—212no—
94C2×#543—111no—
95C2×#381—113no—
96#2030—113no—
97#2030—113no—
98#2030—111no—
99#2030D1111yescharacteristic, direct product factor
100C2×#342—113no—
101C23×C11—42no—
102C23×C11C22×D413yes—
103C23×C11C22×Q811yescharacteristic
104C23×C11C2×#4113yes—
105C22×D11—212no—
106C22×D11—44no—
107C22×D11—412no—
108C22×D11—46no—
109C22×D11#12013yes—
110C22×D11#12011yescharacteristic
111C22×D11C22⋊Q816yes—
112C22×D11C22⋊Q816yes—
113C22×D11#12416yes—
114C22×D11#12416yes—
115Q8×C11—82no—
116C2×C4×C11—26no—
117C2×C4×C11—26no—
118C2×C4×C11—41no—
119C2×C4×C11—43no—
120C2×C4×C11—46no—
121C2×C4×C11—46no—
122C2×C4×C11—43no—
123C2×Dic11—26no—
124C2×Dic11—26no—
125C2×Dic11—41no—
126C2×Dic11—43no—
127C2×Dic11—46no—
128C2×Dic11—46no—
129C2×Dic11—43no—
130C4×D11—412no—
131C4×D11—44no—
132C4×D11—412no—
133C4×D11—86no—
134C4×D11—812no—
135Dic22—86no—
136C24×C4—111no—
137#543—113no—
138#543—226no—
139#543C2×D1111yescharacteristic
140C2×C22⋊Q8—226no—
141C22×C22⋊C4—113no—
142C22×C22⋊C4—113no—
143#381—113no—
144#381—113no—
145#381—113no—
146#381—226no—
147#381C2×D1113yes—
148C2×#95—226no—
149#342—113no—
150#342—116no—
151#342C2×D1113yes—
152C22×C11—26no—
153C22×C11—41no—
154C22×C11—43no—
155C22×C11C2×#12011yescharacteristic
156C22×C11C2×C22⋊Q813yes—
157C22×C11C2×#12413yes—
158C2×D11—26no—
159C2×D11—212no—
160C2×D11—212no—
161C2×D11—46no—
162C2×D11—46no—
163C2×D11#39316yes—
164C2×D11#39312yes—
165C2×D11#45814yes—
166C4×C11—42no—
167C4×C11—46no—
168C4×C11—83no—
169Dic11—42no—
170Dic11—46no—
171Dic11—83no—
172C25—111no—
173C22×Q8—222no—
174C23×C4—111no—
175C23×C4—114no—
176C23×C4—116no—
177C23×C4—223no—
178C23×C4—223no—
179C23×C4—226no—
180C23×C4—223no—
181C23×C4C22×D1111yescharacteristic
182C22⋊Q8—26no—
183C22⋊Q8—2212no—
184C22⋊Q8—2212no—
185C22⋊Q8—226no—
186C22⋊Q8—226no—
187C22⋊Q8—226no—
188C2×C4⋊C4—226no—
189C2×C22⋊C4—113no—
190C2×C22⋊C4—116no—
191C2×C22⋊C4—113no—
192C2×C22⋊C4—226no—
193C2×C22⋊C4—226no—
194C2×C22⋊C4—2212no—
195C2×C22⋊C4—223no—
196C2×C22⋊C4C22×D1113yes—
197C2×C22⋊C4C22×D1113yes—
198#95—26no—
199#95—226no—
200#95—226no—
201#95—226no—
202C2×C11—23no—
203C2×C11—23no—
204C2×C11C2×#39311yescharacteristic
205C2×C11C2×#45812yes—
206D11—26no—
207D11#203014yesdirect product factor
208C24—113no—
209C24—113no—
210C24—112no—
211C24—116no—
212C24—444no—
213C24C23×D1111yescharacteristic
214C2×Q8—22no—
215C2×Q8—226no—
216C2×Q8—884no—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—112no—
221C22×C4—116no—
222C22×C4—226no—
223C22×C4—2212no—
224C22×C4—2212no—
225C22×C4—226no—
226C22×C4—223no—
227C22×C4—223no—
228C22×C4—223no—
229C22×C4—441no—
230C22×C4—443no—
231C22×C4—446no—
232C22×C4—446no—
233C22×C4—4412no—
234C22×C4—446no—
235C22×C4—4412no—
236C22×C4D4×D1116yes—
237C22×C4Q8×D1112yescomplemented
238C4⋊C4—26no—
239C4⋊C4—2212no—
240C4⋊C4—226no—
241C22⋊C4—26no—
242C22⋊C4—26no—
243C22⋊C4—2212no—
244C22⋊C4—226no—
245C22⋊C4—226no—
246C22⋊C4—446no—
247C11C2×#203011yescharacteristic, complemented, Sylow
248C23—42no—
249C23—111no—
250C23—113no—
251C23—116no—
252C23—116no—
253C23—116no—
254C23—116no—
255C23—2212no—
256C23—446no—
257C23—444no—
258C23—4412no—
259C23C2×D4×D1113yes—
260C23C2×Q8×D1111yescharacteristic
261C23#41×D1113yes—
262Q8—82no—
263Q8—886no—
264C2×C4—26no—
265C2×C4—26no—
266C2×C4—41no—
267C2×C4—43no—
268C2×C4—46no—
269C2×C4—46no—
270C2×C4—43no—
271C2×C4—226no—
272C2×C4—226no—
273C2×C4—444no—
274C2×C4—4412no—
275C2×C4—4412no—
276C2×C4—441no—
277C2×C4—443no—
278C2×C4—446no—
279C2×C4—446no—
280C2×C4—443no—
281C2×C4—886no—
282C2×C4—8812no—
283C22—26no—
284C22—41no—
285C22—43no—
286C22—112no—
287C22—114no—
288C22—116no—
289C22—2212no—
290C22—2212no—
291C22—226no—
292C22—446no—
293C22—446no—
294C22D11×#12011yescharacteristic
295C22D11×C22⋊Q813yes—
296C22D11×#12413yes—
297C4—42no—
298C4—46no—
299C4—83no—
300C4—442no—
301C4—446no—
302C4—883no—
303C2—23no—
304C2—23no—
305C2—114no—
306C2—226no—
307C2D11×#39311yescharacteristic
308C2D11×#45812yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2030C2
socleC22×C11C2×#120
prime radicalC24×D11C23
hypercenter#2030D11
hypocenterC11C2×#2030
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
3. #13069784C2semidirect
4. #13069783C2semidirect
5. #13069782C2semidirect
7. C11×#2030C2semidirect
33. C22×C4×D11Q8semidirect
66. C22×C4×C11C2×Q8semidirect
71. C22×Dic11C2×Q8semidirect
99. #2030D11direct (N × H)
207. D11#2030direct (N × H)
237. C22×C4Q8×D11semidirect
247. C11C2×#2030semidirect

Maximal subgroups

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

subgroupindex
D11×#5432
D11×#3812
#130697842
#130697832
#130697822
D11×#3422
C11×#20302
C2×#203011