Finite Group Databasebeta

← D11×#2381 #14916404

Subgroups — D11×#2381 #14916404

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13071797C211yesmaximal, characteristic, complemented
3#13071796C212yesmaximal, complemented
4#13071795C214yesmaximal, complemented
5#13071794C218yesmaximal, complemented
6D11×#391C214yesmaximal
7D11×#387C218yesmaximal
8D11×#383C212yesmaximal
9C11×#2381C211yesmaximal, characteristic, complemented
10C22×Q8×D11C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997C2212yes—
13D11×C4⋊Q8C4116yescomplemented
14C2×C4⋊C4×D11C2214yes—
15C2×C4⋊C4×D11C2214yes—
16C2×#66941C2214yes—
17C2×C42×D11C2214yes—
18C2×C42×D11C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#391C2214yes—
21C11×#387C2218yes—
22C11×#383C2212yes—
23#10622843C2214yes—
24#10622594C2218yes—
25#10622591C2218yes—
26#10622587C2214yes—
27#10622550C2212yes—
28#10622546C2218yes—
29#10622542C2214yes—
30D11×#95C2214yes—
31D11×#95C2214yes—
32D11×#95C2214yes—
33D11×#95C2218yes—
34#10622268C2218yes—
35#10622267C2218yes—
36#10622266C2218yes—
37#10622265C2218yes—
38#10622264C2214yes—
39#10622264C2214yes—
40#10622264C2214yes—
41#10622259C2218yes—
42#10622259C2218yes—
43C22×Q8×C11C2312yes—
44C2×Q8×D11—44no—
45C2×Q8×D11—44no—
46C2×Q8×D11C2×C4116yes—
47C22×C4×D11C2318yes—
48C22×C4×D11C2314yes—
49C22×C4×D11C2312yes—
50C22×C4×D11C2311yescharacteristic
51C22×Dic22C2312yes—
52C22×Dic22C2314yes—
53C11×C4⋊Q8C2×C418yescomplemented
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C42×C11C2314yes—
57C2×C42×C11C2311yescharacteristic
58#66997C2×C4116yescomplemented
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2314yes—
61C2×Dic11⋊C4C2318yes—
62C2×Dic11⋊C4C2318yes—
63C2×C4×Dic11C2318yes—
64C2×C4×Dic11C2314yes—
65C2×C4×Dic11C2312yes—
66C2×C4×Dic11C2311yescharacteristic
67C4⋊C4×D11—48no—
68C4⋊C4×D11C2×C4132yes—
69#66941C2×C4132yescomplemented
70C42×D11—48no—
71C42×D11C2×C418yes—
72#66922C2×C418yescomplemented
73C11×#95C2314yes—
74C11×#95C2318yes—
75C11×#95C2314yes—
76C11×#95C2314yes—
77C11⋊#95C2318yes—
78C11⋊#95C2314yes—
79C11⋊#95C2318yes—
80C11⋊#95C2318yes—
81C11⋊#95C2318yes—
82C11⋊#95C2318yes—
83C11⋊#95C2318yes—
84C11⋊#95C2314yes—
85C11⋊#95C2314yes—
86C2×#2381—111nomaximal, Sylow
87C23×D11C2411yescharacteristic
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11C22×C418yes—
91C22×C4×C11C2418yes—
92C22×C4×C11C2412yes—
93C22×C4×C11C2411yescharacteristic
94C22×C4×C11C2414yes—
95C22×Dic11C2418yes—
96C22×Dic11C2412yes—
97C22×Dic11C2411yescharacteristic
98C22×Dic11C2414yes—
99Q8×D11—432no—
100C2×C4×D11—28no—
101C2×C4×D11—28no—
102C2×C4×D11—24no—
103C2×C4×D11—216no—
104C2×C4×D11—28no—
105C2×C4×D11—232no—
106C2×C4×D11C22×C418yes—
107C2×C4×D11C22×C414yes—
108C2×C4×D11C22×C4116yes—
109C2×Dic22—44no—
110C2×Dic22—44no—
111C2×Dic22—42no—
112C2×Dic22—42no—
113C2×Dic22C22×C418yes—
114C2×Dic22C22×C4116yes—
115C11×C4⋊C4—44no—
116C11×C4⋊C4C22×C4116yes—
117C42×C11—44no—
118C42×C11C22×C414yes—
119C4⋊Dic11—44no—
120C4⋊Dic11C22×C4116yes—
121Dic11⋊C4—48no—
122Dic11⋊C4C22×C4132yes—
123C4×Dic11—44no—
124C4×Dic11—48no—
125C4×Dic11C22×C418yes—
126C4×Dic11C22×C414yes—
127C22×C4⋊Q8—111no—
128#2381—114no—
129#2381—118no—
130#2381—112no—
131#2381—111no—
132#2381D1111yescharacteristic, direct product factor
133C2×#391—114no—
134C2×#387—118no—
135C2×#383—112no—
136C23×C11C2511yescharacteristic
137C22×D11C23×C412yes—
138C22×D11H(5,𝔽2)14yes—
139C22×D112−1+418yes—
140Q8×C11—48no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—28no—
146C2×C4×C11—216no—
147C2×C4×C11C23×C414yes—
148C2×C4×C11C23×C412yes—
149C2×C4×C11C23×C418yes—
150C2×Dic11—24no—
151C2×Dic11—24no—
152C2×Dic11—22no—
153C2×Dic11—24no—
154C2×Dic11—28no—
155C2×Dic11—216no—
156C2×Dic11C23×C414yes—
157C2×Dic11C23×C412yes—
158C2×Dic11C23×C418yes—
159C4×D11—232no—
160C4×D11—28no—
161C4×D11—216no—
162C4×D11—432no—
163Dic22—416no—
164Dic22—48no—
165C23×Q8—112no—
166C2×C4⋊Q8—112no—
167C2×C4⋊Q8—1116no—
168C2×C4⋊Q8—114no—
169C2×C4⋊Q8—111no—
170C2×C4⋊Q8C2×D1111yescharacteristic
171C22×C4⋊C4—114no—
172C22×C4⋊C4—114no—
173C22×C42—111no—
174C22×C42—114no—
175#391—114no—
176#391—114no—
177#391—114no—
178#391—118no—
179#391—118no—
180#391C2×D1114yes—
181#387—118no—
182#387—118no—
183#387—118no—
184#387—118no—
185#387—118no—
186#387—118no—
187#387—118no—
188#387C2×D1118yes—
189#383—112no—
190#383—114no—
191#383—114no—
192#383—114no—
193#383C2×D1112yes—
194C2×#95—114no—
195C2×#95—114no—
196C2×#95—114no—
197C2×#95—118no—
198C22×C11C24×C411yescharacteristic
199C22×C11C2×H(5,𝔽2)12yes—
200C22×C11C2×2−1+414yes—
201C2×D11#51814yes—
202C2×D11#51918yes—
203C2×D11#563116yes—
204C4×C11—22no—
205C4×C11—28no—
206C4×C11—24no—
207C4×C11—48no—
208Dic11—22no—
209Dic11—28no—
210Dic11—24no—
211Dic11—48no—
212C22×Q8—1116no—
213C22×Q8—114no—
214C22×Q8—112no—
215C22×Q8—444no—
216C22×Q8—444no—
217C22×Q8C22×D1112yes—
218C23×C4—114no—
219C23×C4—112no—
220C23×C4—111no—
221C23×C4—118no—
222C4⋊Q8—1116no—
223C4⋊Q8—1132no—
224C4⋊Q8—118no—
225C4⋊Q8C4×D1118yescomplemented
226C2×C4⋊C4—118no—
227C2×C4⋊C4—114no—
228C2×C4⋊C4—1132no—
229C2×C4⋊C4—118no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—448no—
232C2×C4⋊C4C22×D1114yes—
233C2×C4⋊C4C22×D1114yes—
234C2×C42—111no—
235C2×C42—112no—
236C2×C42—118no—
237C2×C42—118no—
238C2×C42—114no—
239C2×C42—448no—
240C2×C42C22×D1114yes—
241C2×C42C22×D1111yescharacteristic
242#95—118no—
243#95—118no—
244#95—114no—
245#95—114no—
246#95—118no—
247#95—114no—
248#95—118no—
249#95—118no—
250#95—118no—
251#95C22×D1114yes—
252#95C22×D1114yes—
253#95C22×D1114yes—
254#95C22×D1118yes—
255C2×C11C2×#51811yescharacteristic
256C2×C11C2×#51912yes—
257C2×C11C2×#56314yes—
258D11#238118yesdirect product factor
259C24—111no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—1116no—
263C2×Q8—118no—
264C2×Q8—444no—
265C2×Q8—444no—
266C2×Q8—442no—
267C2×Q8—442no—
268C2×Q8—4432no—
269C2×Q8C2×C4×D1118yes—
270C22×C4—112no—
271C22×C4—111no—
272C22×C4—114no—
273C22×C4—118no—
274C22×C4—114no—
275C22×C4—1116no—
276C22×C4—118no—
277C22×C4—228no—
278C22×C4—228no—
279C22×C4—224no—
280C22×C4—228no—
281C22×C4—2216no—
282C22×C4—2232no—
283C22×C4C23×D1118yes—
284C22×C4C23×D1112yes—
285C22×C4C23×D1111yescharacteristic
286C22×C4C23×D1114yes—
287C4⋊C4—44no—
288C4⋊C4—1132no—
289C4⋊C4—1116no—
290C4⋊C4—448no—
291C4⋊C4—444no—
292C4⋊C4C2×C4×D11116yes—
293C42—44no—
294C42—114no—
295C42—118no—
296C42—444no—
297C42—448no—
298C42C2×C4×D1114yes—
299C11C2×#238111yescharacteristic, complemented, Sylow
300C23—112no—
301C23—114no—
302C23—118no—
303C23C24×D1111yescharacteristic
304Q8—48no—
305Q8—448no—
306Q8—4416no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—216no—
313C2×C4—114no—
314C2×C4—112no—
315C2×C4—118no—
316C2×C4—228no—
317C2×C4—2232no—
318C2×C4—2216no—
319C2×C4—224no—
320C2×C4—224no—
321C2×C4—222no—
322C2×C4—224no—
323C2×C4—228no—
324C2×C4—2216no—
325C2×C4—4432no—
326C2×C4C22×C4×D1114yes—
327C2×C4C22×C4×D1112yes—
328C2×C4C22×C4×D1118yes—
329C22—1116no—
330C22—114no—
331C22—118no—
332C22C23×C4×D1111yescharacteristic
333C22D11×H(5,𝔽2)12yes—
334C22D11×2−1+414yes—
335C4—22no—
336C4—28no—
337C4—24no—
338C4—48no—
339C4—222no—
340C4—228no—
341C4—224no—
342C4—448no—
343C2—118no—
344C2D11×#51811yescharacteristic
345C2D11×#51912yes—
346C2D11×#56314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2381C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2381D11
hypocenterC11C2×#2381
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2381

Complements

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

NH ≅ G/Ntype
2. #13071797C2semidirect
3. #13071796C2semidirect
4. #13071795C2semidirect
5. #13071794C2semidirect
9. C11×#2381C2semidirect
13. D11×C4⋊Q8C4semidirect
53. C11×C4⋊Q8C2×C4semidirect
58. #66997C2×C4semidirect
69. #66941C2×C4semidirect
72. #66922C2×C4semidirect
132. #2381D11direct (N × H)
225. C4⋊Q8C4×D11semidirect
258. D11#2381direct (N × H)
299. C11C2×#2381semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130717972
#130717962
#130717952
#130717942
D11×#3912
D11×#3872
D11×#3832
C11×#23812
C2×#238111