Finite Group Databasebeta

← D11×#2091 #14783518

Subgroups — D11×#2091 #14783518

Order 2816.

1102 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 207 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×#430C213yesmaximal, complemented
2D11×#407C213yesmaximal
3#13070133C211yesmaximal, characteristic, complemented
4#13070132C213yesmaximal, complemented
5#13070131C213yesmaximal, complemented
6D11×#338C211yesmaximal, characteristic, complemented
7C11×#2091C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×M16×D11C2213yes—
10C2×M16×D11C2213yes—
11C11×#430C2213yescomplemented
12C11×#407C2213yes—
13#10622820C2213yes—
14#10622739C2213yes—
15#10622739C2213yes—
16#10622738C2213yescomplemented
17#10622737C2216yescomplemented
18#10622506—26no—
19D11×#108—26no—
20#10622339—26no—
21D11×C22⋊C8—26no—
22C11×#338C2211yescharacteristic, complemented
23C11⋊#338C2213yescomplemented
24C24×D11Q811yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11Q811yescharacteristic
27C22×C4×D11—23no—
28C22×C4×D11—23no—
29C22×C4×D11—23no—
30C22×C4×D11—23no—
31C22×C4×D11Q811yescharacteristic
32C22×C4×D11Q811yescharacteristic
33C22×C4×D11C2311yescharacteristic
34C22×C4×D11C2311yescharacteristic
35C2×C11×M16C2313yes—
36C2×C11×M16C2313yes—
37C2×#4318C2313yes—
38C2×#4318C2313yes—
39M16×D11—26no—
40M16×D11—26no—
41M16×D11—26no—
42M16×D11—26no—
43C2×#4313—23no—
44C2×#4313D416yes—
45C2×C8×D11—23no—
46C2×C8×D11D416yes—
47C11×#108—26no—
48C11×C22⋊C8—26no—
49C22⋊(C11⋊C8)—26no—
50#66886—212no—
51(C2×D11)⋊C8—26no—
52(C2×D11)⋊C8—26no—
53#66883—26no—
54C2×#2091—111nomaximal, Sylow
55C24×C11C2×Q811yescharacteristic
56C23×D11—23no—
57C23×D11—23no—
58C23×D11—44no—
59C23×D11C2×Q811yescharacteristic
60C23×D11C2×Q811yescharacteristic
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11C2×Q811yescharacteristic
64C22×C4×C11C2411yescharacteristic
65C22×Dic11—23no—
66C22×Dic11—23no—
67C22×Dic11C2×Q811yescharacteristic
68C22×Dic11C2×Q811yescharacteristic
69C2×C4×D11—23no—
70C2×C4×D11—23no—
71C2×C4×D11—23no—
72C2×C4×D11—23no—
73C2×C4×D11—23no—
74C2×C4×D11—23no—
75C2×C4×D11—43no—
76C2×C4×D11—43no—
77C2×C4×D11—46no—
78C2×C4×D11—41no—
79C2×C4×D11—43no—
80C2×C4×D11C2×D413yes—
81C2×C4×D11C2×D413yes—
82C2×C4×D11#4113yes—
83C2×C4×D11#4113yes—
84C11×M16—26no—
85C11×M16—26no—
86C2×C8×C11—23no—
87C2×C8×C11C2×D416yes—
88#4318—26no—
89#4318—26no—
90C2×C11⋊C8—23no—
91C2×C11⋊C8C2×D416yes—
92#4313—212no—
93#4313—46no—
94C8×D11—26no—
95C8×D11—26no—
96C8×D11—43no—
97C8×D11—43no—
98C2×#430—113no—
99C2×#407—113no—
100#2091—113no—
101#2091—113no—
102#2091—111no—
103#2091D1111yescharacteristic, direct product factor
104C2×#338—111no—
105C23×C11—23no—
106C23×C11—42no—
107C23×C11C22×Q811yescharacteristic
108C22×D11—212no—
109C22×D11—23no—
110C22×D11—42no—
111C22×D11—42no—
112C22×D11—46no—
113C22×D11—46no—
114C22×D11—46no—
115C22×D11—43no—
116C22×D11—41no—
117C22×D11C22⋊Q813yes—
118C22×D11C22⋊Q813yes—
119C2×C4×C11—23no—
120C2×C4×C11—43no—
121C2×C4×C11—41no—
122C2×C4×C11C22×D413yes—
123C2×C4×C11C2×#4113yes—
124C2×Dic11—23no—
125C2×Dic11—41no—
126C2×Dic11—43no—
127C2×Dic11C22⋊Q813yes—
128C2×Dic11C22⋊Q813yes—
129C4×D11—43no—
130C4×D11—41no—
131C4×D11—43no—
132C4×D11—41no—
133C4×D11—41no—
134C4×D11—43no—
135C4×D11#12313yes—
136C4×D11#12313yes—
137C4×D11#12316yes—
138C4×D11#12711yescharacteristic
139C4×D11#12713yes—
140C8×C11—26no—
141C8×C11—43no—
142C11⋊C8—26no—
143C11⋊C8—43no—
144C24×C4—111no—
145C22×M16—113no—
146C22×M16—113no—
147#430—116no—
148#430—113no—
149#430—226no—
150#430C2×D1113yescomplemented
151C2×#108—226no—
152#407—113no—
153#407—113no—
154#407—113no—
155#407—226no—
156#407C2×D1113yes—
157C2×C22⋊C8—226no—
158#338—113no—
159#338C2×D1111yescharacteristic, complemented
160C22×C11—26no—
161C22×C11—41no—
162C22×C11—43no—
163C22×C11—41no—
164C22×C11C2×C22⋊Q813yes—
165C2×D11—26no—
166C2×D11—26no—
167C2×D11—43no—
168C2×D11—412no—
169C2×D11—43no—
170C2×D11—41no—
171C2×D11—44no—
172C2×D11#39913yes—
173C2×D11#39911yescharacteristic
174C4×C11—41no—
175C4×C11C2×#12313yes—
176C4×C11C2×#12711yescharacteristic
177Dic11—41no—
178Dic11#39911yescharacteristic
179Dic11#39913yes—
180C25—111no—
181C23×C4—111no—
182C23×C4—111no—
183C23×C4—111no—
184C23×C4—111no—
185C23×C4—111no—
186C23×C4—223no—
187C23×C4—223no—
188C23×C4—223no—
189C23×C4—223no—
190C23×C4C22×D1111yescharacteristic
191C2×M16—113no—
192C2×M16—116no—
193C2×M16—113no—
194C2×M16—223no—
195C2×M16—226no—
196C2×M16—226no—
197C2×M16—226no—
198C2×M16—226no—
199C2×M16C22×D1113yes—
200C2×M16C22×D1113yes—
201C22×C8—116no—
202C22×C8—223no—
203#108—26no—
204#108—2212no—
205#108—226no—
206C22⋊C8—26no—
207C22⋊C8—226no—
208C22⋊C8—226no—
209C22⋊C8—226no—
210C2×C11—23no—
211C2×C11—42no—
212C2×C11C2×#39911yescharacteristic
213D11—23no—
214D11—42no—
215D11#209112yesdirect product factor
216C24—111no—
217C24—111no—
218C24—223no—
219C24—223no—
220C24—444no—
221C24Q8×D1111yescharacteristic
222C22×C4—23no—
223C22×C4—23no—
224C22×C4—111no—
225C22×C4—113no—
226C22×C4—113no—
227C22×C4—113no—
228C22×C4—113no—
229C22×C4—111no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4—223no—
233C22×C4—223no—
234C22×C4—223no—
235C22×C4—223no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4—441no—
239C22×C4—443no—
240C22×C4—443no—
241C22×C4—443no—
242C22×C4—446no—
243C22×C4Q8×D1111yescharacteristic
244C22×C4C23×D1111yescharacteristic
245M16—26no—
246M16—26no—
247M16—2212no—
248M16—226no—
249M16—226no—
250M16—446no—
251C2×C8—23no—
252C2×C8—116no—
253C2×C8—226no—
254C2×C8—226no—
255C2×C8—223no—
256C2×C8—443no—
257C2×C8—443no—
258C2×C8D4×D1116yes—
259C11C2×#209111yescharacteristic, complemented, Sylow
260C23—23no—
261C23—42no—
262C23—113no—
263C23—113no—
264C23—2212no—
265C23—223no—
266C23—446no—
267C23—441no—
268C23—443no—
269C23—442no—
270C23—442no—
271C23—446no—
272C23—446no—
273C23C2×Q8×D1111yescharacteristic
274C2×C4—23no—
275C2×C4—41no—
276C2×C4—43no—
277C2×C4—113no—
278C2×C4—113no—
279C2×C4—111no—
280C2×C4—113no—
281C2×C4—113no—
282C2×C4—113no—
283C2×C4—116no—
284C2×C4—223no—
285C2×C4—441no—
286C2×C4—443no—
287C2×C4—441no—
288C2×C4—443no—
289C2×C4—441no—
290C2×C4—443no—
291C2×C4—441no—
292C2×C4—443no—
293C2×C4C2×D4×D1113yes—
294C2×C4#41×D1113yes—
295C8—26no—
296C8—43no—
297C8—226no—
298C8—443no—
299C22—26no—
300C22—41no—
301C22—43no—
302C22—41no—
303C22—111no—
304C22—113no—
305C22—226no—
306C22—226no—
307C22—443no—
308C22—443no—
309C22—444no—
310C22—4412no—
311C22—441no—
312C22D11×C22⋊Q813yes—
313C4—41no—
314C4—111no—
315C4—113no—
316C4—441no—
317C4D11×#12313yes—
318C4D11×#12711yescharacteristic
319C2—23no—
320C2—42no—
321C2—112no—
322C2—223no—
323C2—442no—
324C2D11×#39911yescharacteristic
subgroupG/H
centerC4D11×#127
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2091C2
socleC2×C11C2×#399
prime radicalC24×D11Q8
hypercenter#2091D11
hypocenterC11C2×#2091
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2091

Complements

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

NH ≅ G/Ntype
1. D11×#430C2semidirect
3. #13070133C2semidirect
4. #13070132C2semidirect
5. #13070131C2semidirect
6. D11×#338C2semidirect
7. C11×#2091C2semidirect
11. C11×#430C22semidirect
16. #10622738C22semidirect
17. #10622737C22semidirect
22. C11×#338C22semidirect
23. C11⋊#338C22semidirect
103. #2091D11direct (N × H)
150. #430C2×D11semidirect
159. #338C2×D11semidirect
215. D11#2091direct (N × H)
259. C11C2×#2091semidirect

Maximal subgroups

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

subgroupindex
D11×#4302
D11×#4072
#130701332
#130701322
#130701312
D11×#3382
C11×#20912
C2×#209111