Finite Group Databasebeta

← Dic11×#395 #14675586

Subgroups — Dic11×#395 #14675586

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C213yesmaximal
3#13066887C211yesmaximal, characteristic
4#13066881C213yesmaximal
5#13066869C213yesmaximal
6#95×Dic11C213yesmaximal
7C2×C11×#395C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2213yes—
10C2×Q8×Dic11—212no—
11C22×C4⋊Dic11C2213yes—
12C22×C4⋊Dic11C2213yes—
13C22×C4×Dic11C2211yescharacteristic
14C22×C4×Dic11C2213yes—
15C22×C4×Dic11C2213yes—
16C11×#395C418yescomplemented
17C2×C11×#95C2213yes—
18C2×C11⋊#95C2216yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C4⋊C4×Dic11—212no—
23C22×Q8×C11—26no—
24C22×Q8×C11—26no—
25C22×Q8×C11C2×C414yes—
26C23×C4×C11C2311yescharacteristic
27C23×C4×C11C2313yes—
28C23×C4×C11C2313yes—
29C23×Dic11C2313yes—
30C23×Dic11C2313yes—
31C23×Dic11C2311yescharacteristic
32C23×Dic11C2311yescharacteristic
33C2×C11×C4⋊C4—26no—
34C2×C11×C4⋊C4—26no—
35C2×C11×C4⋊C4C2×C4112yes—
36Q8×Dic11—232no—
37C2×C4⋊Dic11—26no—
38C2×C4⋊Dic11—26no—
39C2×C4⋊Dic11—212no—
40C2×C4⋊Dic11—26no—
41C2×C4⋊Dic11—26no—
42C2×C4×Dic11—212no—
43C2×C4×Dic11—26no—
44C2×C4×Dic11—26no—
45C2×C4×Dic11—26no—
46C2×C4×Dic11D4112yes—
47C2×C4×Dic11Q8112yescomplemented
48C11×#95C2×C4112yes—
49C11⋊#95—26no—
50C11⋊#95—26no—
51C11⋊#95—212no—
52C11⋊#95—26no—
53C4×#395—111nomaximal, Sylow
54C24×C11C2411yescharacteristic
55C2×Q8×C11—28no—
56C2×Q8×C11—224no—
57C2×Q8×C11—224no—
58C22×C4×C11—23no—
59C22×C4×C11—26no—
60C22×C4×C11—23no—
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11—26no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11C22×C412yes—
67C22×C4×C11C22×C416yes—
68C22×C4×C11C22×C416yes—
69C22×C4×C11C2×D416yes—
70C22×C4×C11C2×Q816yes—
71C22×C4×C11#4116yes—
72C22×C4×C11#4116yes—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—26no—
76C22×Dic11—26no—
77C22×Dic11—26no—
78C22×Dic11—26no—
79C22×Dic11—23no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11C2×D416yes—
84C22×Dic11C2×D416yes—
85C22×Dic11C2×Q816yes—
86C22×Dic11C2×Q816yes—
87C22×Dic11#4112yes—
88C22×Dic11#4112yes—
89C11×C4⋊C4—224no—
90C4⋊Dic11—224no—
91C4⋊Dic11—224no—
92C4×Dic11—224no—
93C4×Dic11—224no—
94C4×Dic11—44no—
95C22×C4×Q8—111no—
96C2×#395D1111yescharacteristic
97C2×C4×C4⋊C4—113no—
98#1446—111no—
99#1444—113no—
100#1441—113no—
101C4×#95—113no—
102C23×C11C23×C411yescharacteristic
103C23×C11C22×D413yes—
104C23×C11C22×Q813yes—
105C23×C11C2×#4113yes—
106C23×C11C2×#4113yes—
107C23×C11C2×#4111yescharacteristic
108C23×C11C2×#4111yescharacteristic
109Q8×C11—232no—
110C2×C4×C11—26no—
111C2×C4×C11—212no—
112C2×C4×C11—26no—
113C2×C4×C11—26no—
114C2×C4×C11—26no—
115C2×C4×C11—26no—
116C2×C4×C11—26no—
117C2×C4×C11—212no—
118C2×C4×C11—26no—
119C2×C4×C11—26no—
120C2×C4×C11—26no—
121C2×C4×C11—41no—
122C2×C4×C11—43no—
123C2×C4×C11C4×D4112yes—
124C2×C4×C11C4×Q8112yescomplemented
125C2×Dic11—26no—
126C2×Dic11—26no—
127C2×Dic11—26no—
128C2×Dic11—26no—
129C2×Dic11—26no—
130C2×Dic11—212no—
131C2×Dic11—41no—
132C2×Dic11—43no—
133C2×Dic11—46no—
134C2×Dic11—46no—
135C2×Dic11—43no—
136C2×Dic11—46no—
137C2×Dic11—43no—
138C2×Dic11#12014yes—
139C2×Dic11C22⋊Q8112yes—
140C2×Dic11C4⋊Q8112yes—
141C23×Q8C2×D1111yescharacteristic
142C2×C4×Q8—2212no—
143C22×C4⋊C4—113no—
144C22×C4⋊C4—113no—
145C22×C4⋊C4C2×D1113yes—
146C22×C42—113no—
147C22×C42—113no—
148C22×C42—111no—
149#395Dic1118yesdirect product factor
150C4×C4⋊C4—2212no—
151C2×#95—116no—
152C2×#95—113no—
153C2×#95—113no—
154C2×#95—113no—
155C2×#95C2×D1113yes—
156C22×C11C2×C4×D413yes—
157C22×C11C2×C4×Q813yes—
158C22×C11C4×#4111yescharacteristic
159C22×C11C2×#12011yescharacteristic
160C22×C11C2×C22⋊Q813yes—
161C22×C11#52513yes—
162C22×C11#52513yes—
163C22×C11#52913yes—
164C22×C11C2×C4⋊Q813yes—
165C22×C11#53213yes—
166C22×C11#53316yes—
167C22×C11#53313yes—
168C4×C11—212no—
169C4×C11—212no—
170C4×C11—42no—
171Dic11—46no—
172Dic11—42no—
173Dic11—46no—
174Dic11#39518yesdirect product factor
175C22×Q8—26no—
176C22×Q8—26no—
177C22×Q8C2×Dic1114yes—
178C23×C4—111no—
179C23×C4—113no—
180C23×C4—111no—
181C23×C4—113no—
182C23×C4C22×D1111yescharacteristic
183C23×C4C22×D1113yes—
184C23×C4C22×D1113yes—
185C4×Q8—2232no—
186C2×C4⋊C4—26no—
187C2×C4⋊C4—26no—
188C2×C4⋊C4—2212no—
189C2×C4⋊C4—226no—
190C2×C4⋊C4—226no—
191C2×C4⋊C4—226no—
192C2×C4⋊C4—226no—
193C2×C4⋊C4C2×Dic11112yes—
194C2×C42—1112no—
195C2×C42—1112no—
196C2×C42—2212no—
197C2×C42—226no—
198C2×C42—226no—
199C2×C42—226no—
200#95—226no—
201#95—226no—
202#95—226no—
203#95—2212no—
204#95C2×Dic11112yes—
205C2×C11C4×#12011yescharacteristic
206C2×C11C4×C22⋊Q813yes—
207C2×C11C4×C4⋊Q813yes—
208C2×C11C2×#39511yescharacteristic
209C2×C11#238811yescharacteristic
210C2×C11#239613yes—
211C2×C11#239913yes—
212C24C23×D1111yescharacteristic
213C2×Q8—28no—
214C2×Q8—224no—
215C2×Q8—224no—
216C22×C4—23no—
217C22×C4—26no—
218C22×C4—23no—
219C22×C4—26no—
220C22×C4—23no—
221C22×C4—23no—
222C22×C4—23no—
223C22×C4—23no—
224C22×C4—116no—
225C22×C4—116no—
226C22×C4—112no—
227C22×C4—116no—
228C22×C4—116no—
229C22×C4—112no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4—226no—
233C22×C4—226no—
234C22×C4—226no—
235C22×C4—226no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4—223no—
239C22×C4—223no—
240C22×C4D4×D1116yes—
241C22×C4#434116yes—
242C22×C4Q8×D1116yes—
243C22×C4#434316yes—
244C22×C4C22×Dic1112yes—
245C22×C4C22×Dic1116yes—
246C22×C4C22×Dic1116yes—
247C4⋊C4—224no—
248C4⋊C4—2224no—
249C4⋊C4—2224no—
250C42—2224no—
251C42—2224no—
252C42—444no—
253C11C4×#39511yescharacteristic, complemented, Sylow
254C23C2×D4×D1113yes—
255C23C2×#434113yes—
256C23C2×Q8×D1113yes—
257C23C2×#434313yes—
258C23#41×D1111yescharacteristic
259C23#41×D1111yescharacteristic
260C23C23×Dic1111yescharacteristic
261Q8—232no—
262C2×C4—26no—
263C2×C4—212no—
264C2×C4—26no—
265C2×C4—26no—
266C2×C4—212no—
267C2×C4—26no—
268C2×C4—26no—
269C2×C4—26no—
270C2×C4—26no—
271C2×C4—26no—
272C2×C4—26no—
273C2×C4—43no—
274C2×C4—41no—
275C2×C4—1112no—
276C2×C4—114no—
277C2×C4—1112no—
278C2×C4—226no—
279C2×C4—2212no—
280C2×C4—226no—
281C2×C4—226no—
282C2×C4—226no—
283C2×C4—226no—
284C2×C4—443no—
285C2×C4—443no—
286C2×C4—446no—
287C2×C4—443no—
288C2×C4—441no—
289C2×C4—446no—
290C2×C4—446no—
291C2×C4D4×Dic11112yes—
292C2×C4Q8×Dic11112yescomplemented
293C22#1062311713yes—
294C22D11×#12011yescharacteristic
295C22#1062315313yes—
296C22#1062315513yes—
297C22D11×C22⋊Q813yes—
298C22#1062315813yes—
299C22D11×C4⋊Q813yes—
300C22#1062325613yes—
301C22#1062325916yes—
302C22C2×D4×Dic1113yes—
303C22C2×Q8×Dic1113yes—
304C22#41×Dic1111yescharacteristic
305C4—212no—
306C4—212no—
307C4—42no—
308C4—118no—
309C4—446no—
310C4—446no—
311C4—442no—
312C2#120×Dic1111yescharacteristic
313C2C22⋊Q8×Dic1113yes—
314C2C4⋊Q8×Dic1113yes—
315C2D11×#39511yescharacteristic
316C2#1307183411yescharacteristic
317C2#1307188713yes—
318C2#1307190613yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#395C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#395D11
hypocenterC11C4×#395
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
16. C11×#395C4semidirect
47. C2×C4×Dic11Q8semidirect
124. C2×C4×C11C4×Q8semidirect
149. #395Dic11direct (N × H)
174. Dic11#395direct (N × H)
253. C11C4×#395semidirect
292. C2×C4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×C4⋊C4×Dic112
#130668872
#130668812
#130668692
#95×Dic112
C2×C11×#3952
C4×#39511