Finite Group Databasebeta

← #14682754

Subgroups — #14682754

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066887C212yesmaximal
2#13066878C214yesmaximal
3#13066848C212yesmaximal
4#13066843C212yesmaximal
5#13066841C214yesmaximal
6C2×C11×#391C211yesmaximal, characteristic
7C23×Q8×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4×Dic11C2212yes—
11C11×#391C418yescomplemented
12C2×C11×#95C2214yes—
13C2×C11⋊#95C2214yes—
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2214yes—
16C2×C11⋊#95C2212yes—
17C2×C11⋊#95C2212yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C22×Q8×C11—24no—
23C22×Q8×C11—42no—
24C22×Q8×C11—41no—
25C22×Q8×C11—41no—
26C22×Q8×C11C2×C414yes—
27C23×C4×C11C2312yes—
28C23×C4×C11C2312yes—
29C23×C4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11C2314yes—
32C23×Dic11C2314yes—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4C2×C414yes—
36C2×C42×C11—42no—
37C2×C42×C11C2×C414yes—
38C2×C4×Dic11—28no—
39C2×C4×Dic11—42no—
40C11×#95C2×C4116yes—
41C11⋊#95—28no—
42C11⋊#95—28no—
43C11⋊#95—28no—
44C11⋊#95—42no—
45C11⋊#95—44no—
46C11⋊#95—42no—
47C11⋊#95—42no—
48C11⋊#95—42no—
49C11⋊#95—42no—
50#14489—111nomaximal, Sylow
51C24×C11C2411yescharacteristic
52C2×Q8×C11—28no—
53C2×Q8×C11—44no—
54C2×Q8×C11—44no—
55C2×Q8×C11—48no—
56C2×Q8×C11—48no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—24no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—24no—
72C22×C4×C11C22×C414yes—
73C22×C4×C11C22×C414yes—
74C22×C4×C11C22×C414yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11#4114yes—
77C22×Dic11—24no—
78C22×Dic11—24no—
79C22×Dic11—24no—
80C22×Dic11—24no—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11—24no—
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11#4118yes—
91C11×C4⋊C4—44no—
92C42×C11—44no—
93C4×Dic11—48no—
94C2×#391D1111yescharacteristic
95#1446—112no—
96#1443—114no—
97#1436—112no—
98#1434—112no—
99#1434—114no—
100C23×C11C23×C411yescharacteristic
101C23×C11C2×#4112yes—
102C23×C11C2×#4114yes—
103C23×C11H(5,𝔽2)12yes—
104C23×C11H(5,𝔽2)11yescharacteristic
105C23×C11H(5,𝔽2)11yescharacteristic
106C23×C112−1+414yes—
107Q8×C11—416no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—24no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—28no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11#11714yes—
128C2×Dic11—28no—
129C2×Dic11—28no—
130C2×Dic11—28no—
131C2×Dic11—44no—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—44no—
141C2×Dic11—44no—
142C23×Q8C2×D1111yescharacteristic
143C22×C4⋊C4C2×D1111yescharacteristic
144C22×C42—112no—
145C22×C42C2×D1111yescharacteristic
146#391Dic1118yescomplemented
147C2×#95—114no—
148C2×#95—114no—
149C2×#95—114no—
150C2×#95—112no—
151C2×#95—112no—
152C2×#95—112no—
153C2×#95—114no—
154C2×#95—112no—
155C2×#95—112no—
156C2×#95C2×D1114yes—
157C22×C11C2×#11711yescharacteristic
158C22×C11C4×#4112yes—
159C22×C11#51811yescharacteristic
160C22×C11#51811yescharacteristic
161C22×C11#51912yes—
162C22×C11#53812yes—
163C22×C11#53812yes—
164C22×C11#53914yes—
165C22×C11#54214yes—
166C22×C11#55112yes—
167C22×C11#55214yes—
168C22×C11#55512yes—
169C22×C11#55614yes—
170C22×C11#56312yes—
171C22×C11#56312yes—
172C4×C11—24no—
173C4×C11—44no—
174C4×C11—44no—
175C4×C11—44no—
176Dic11—48no—
177Dic11—84no—
178C22×Q8—24no—
179C22×Q8—42no—
180C22×Q8—41no—
181C22×Q8—41no—
182C22×Q8C2×Dic1114yes—
183C23×C4—114no—
184C23×C4—114no—
185C23×C4C22×D1112yes—
186C23×C4C22×D1112yes—
187C23×C4C22×D1112yes—
188C23×C4C22×D1111yescharacteristic
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×Dic1114yes—
192C2×C42—42no—
193C2×C42—228no—
194C2×C42—442no—
195C2×C42C2×Dic1114yes—
196#95—228no—
197#95—228no—
198#95—228no—
199#95—442no—
200#95—442no—
201#95—442no—
202#95—444no—
203#95—442no—
204#95—442no—
205#95C2×Dic11116yes—
206C2×C11#231211yescharacteristic
207C2×C11#233212yes—
208C2×C11#235612yes—
209C2×C11#237211yescharacteristic
210C2×C11#238111yescharacteristic
211C2×C11#274514yes—
212C2×C11#277514yes—
213C24C23×D1111yescharacteristic
214C2×Q8—28no—
215C2×Q8—44no—
216C2×Q8—44no—
217C2×Q8—48no—
218C2×Q8—48no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—118no—
235C22×C4—224no—
236C22×C4—224no—
237C22×C4—224no—
238C22×C4—224no—
239C22×C4—224no—
240C22×C4—224no—
241C22×C4—224no—
242C22×C4—224no—
243C22×C4—224no—
244C22×C4—224no—
245C22×C4—224no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4#433914yes—
249C22×C4C22×Dic1114yes—
250C22×C4C22×Dic1114yes—
251C22×C4C22×Dic1114yes—
252C22×C4C22×Dic1112yes—
253C4⋊C4—44no—
254C42—44no—
255C42—448no—
256C11#1448911yescharacteristic, complemented, Sylow
257C23C2×#433912yes—
258C23#6703711yescharacteristic
259C23#6703711yescharacteristic
260C23#6703712yes—
261C23#6704014yes—
262C23#41×D1114yes—
263C23C23×Dic1111yescharacteristic
264Q8—416no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—28no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—228no—
285C2×C4—228no—
286C2×C4—228no—
287C2×C4—444no—
288C2×C4—444no—
289C2×C4—444no—
290C2×C4—444no—
291C2×C4—444no—
292C2×C4—444no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—444no—
296C2×C4—444no—
297C2×C4—444no—
298C2×C4#6697914yes—
299C22#1062302512yes—
300C22#1062302512yes—
301C22#1062309914yes—
302C22#1062311214yes—
303C22#1062316914yes—
304C22#1062317114yes—
305C22#1062320112yes—
306C22#1062321012yes—
307C22#1062326612yes—
308C22#1062326612yes—
309C22C2×#6697911yescharacteristic
310C22#1062332911yescharacteristic
311C22#1062332911yescharacteristic
312C22#1062334312yes—
313C22#41×Dic1112yes—
314C4—24no—
315C4—44no—
316C4—44no—
317C4—44no—
318C4—448no—
319C4—884no—
320C2#1307121411yescharacteristic
321C2#1307137412yes—
322C2#1307158112yes—
323C2#1307172811yescharacteristic
324C2#1307179711yescharacteristic
325C2#1307578614yes—
326C2#1307618414yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#14489
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
11. C11×#391C4semidirect
146. #391Dic11semidirect
256. C11#14489semidirect

Maximal subgroups

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

subgroupindex
#130668872
#130668782
#130668482
#130668432
#130668412
C2×C11×#3912
#1448911