Finite Group Databasebeta

← #14682589

Subgroups — #14682589

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066873C214yesmaximal
2#13066869C212yesmaximal
3#13066848C212yesmaximal
4#13066843C212yesmaximal
5#13066841C214yesmaximal
6C2×C11×#382C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11C2212yes—
11C22×C4×Dic11C2212yes—
12C11×#382C418yescomplemented
13C2×C11×#95C2214yes—
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2214yes—
16C2×C11⋊#95C2214yes—
17C2×C11⋊#95C2212yes—
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C23×C4×C11C2312yes—
23C23×C4×C11C2312yes—
24C23×C4×C11C2312yes—
25C23×C4×C11C2311yescharacteristic
26C23×Dic11C2314yes—
27C23×Dic11C2314yes—
28C2×C11×C4⋊C4—41no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C414yes—
33C2×C11×C4⋊C4C2×C414yes—
34C2×C42×C11—24no—
35C2×C42×C11C2×C414yes—
36C2×C4⋊Dic11—44no—
37C2×C4⋊Dic11—42no—
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—
49#14476—111nomaximal, Sylow
50C24×C11C2411yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—24no—
55C22×C4×C11—24no—
56C22×C4×C11—24no—
57C22×C4×C11—24no—
58C22×C4×C11—22no—
59C22×C4×C11—24no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11C22×C414yes—
67C22×C4×C11C22×C414yes—
68C22×C4×C11C22×C414yes—
69C22×C4×C11C22×C412yes—
70C22×C4×C11#4114yes—
71C22×Dic11—24no—
72C22×Dic11—24no—
73C22×Dic11—24no—
74C22×Dic11—24no—
75C22×Dic11—24no—
76C22×Dic11—24no—
77C22×Dic11—24no—
78C22×Dic11—24no—
79C22×Dic11—24no—
80C22×Dic11—24no—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11#4118yes—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—44no—
87C42×C11—28no—
88C4⋊Dic11—48no—
89C4×Dic11—48no—
90C2×#382D1111yescharacteristic
91#1442—114no—
92#1441—112no—
93#1436—112no—
94#1434—112no—
95#1434—114no—
96C23×C11C23×C411yescharacteristic
97C23×C11C2×#4112yes—
98C23×C11C2×#4114yes—
99C23×C11H(5,𝔽2)11yescharacteristic
100C23×C11H(5,𝔽2)11yescharacteristic
101C23×C11H(5,𝔽2)12yes—
102C23×C112−1+412yes—
103C23×C112−1+412yes—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—28no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—28no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—42no—
123C2×C4×C11#11714yes—
124C2×Dic11—28no—
125C2×Dic11—28no—
126C2×Dic11—28no—
127C2×Dic11—44no—
128C2×Dic11—44no—
129C2×Dic11—44no—
130C2×Dic11—44no—
131C2×Dic11—44no—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C2×Dic11—44no—
138C22×C4⋊C4—112no—
139C22×C4⋊C4C2×D1111yescharacteristic
140C22×C4⋊C4C2×D1111yescharacteristic
141C22×C42—112no—
142C22×C42C2×D1111yescharacteristic
143#382Dic1118yescomplemented
144C2×#95—114no—
145C2×#95—114no—
146C2×#95—114no—
147C2×#95—112no—
148C2×#95—112no—
149C2×#95—114no—
150C2×#95—112no—
151C2×#95—112no—
152C2×#95C2×D1114yes—
153C22×C11C2×#11711yescharacteristic
154C22×C11C4×#4112yes—
155C22×C11#51811yescharacteristic
156C22×C11#51911yescharacteristic
157C22×C11#52012yes—
158C22×C11#53912yes—
159C22×C11#53912yes—
160C22×C11#53914yes—
161C22×C11#54114yes—
162C22×C11#55112yes—
163C22×C11#55214yes—
164C22×C11#55514yes—
165C22×C11#55512yes—
166C22×C11H(3,𝔽4)11yescharacteristic
167C22×C11#56212yes—
168C22×C11#56311yescharacteristic
169C4×C11—24no—
170C4×C11—44no—
171C4×C11—44no—
172C4×C11—44no—
173Dic11—48no—
174Dic11—84no—
175C23×C4—114no—
176C23×C4—114no—
177C23×C4C22×D1112yes—
178C23×C4C22×D1112yes—
179C23×C4C22×D1112yes—
180C23×C4C22×D1111yescharacteristic
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—442no—
186C2×C4⋊C4—444no—
187C2×C4⋊C4C2×Dic1114yes—
188C2×C4⋊C4C2×Dic1114yes—
189C2×C42—24no—
190C2×C42—228no—
191C2×C42—442no—
192C2×C42C2×Dic1114yes—
193#95—228no—
194#95—228no—
195#95—228no—
196#95—442no—
197#95—442no—
198#95—442no—
199#95—442no—
200#95—444no—
201#95C2×Dic11116yes—
202C2×C11#231311yescharacteristic
203C2×C11#233612yes—
204C2×C11#234612yes—
205C2×C11#237211yescharacteristic
206C2×C11#237911yescharacteristic
207C2×C11#274414yes—
208C2×C11#276912yes—
209C2×C11#278512yes—
210C24C23×D1111yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—118no—
227C22×C4—224no—
228C22×C4—224no—
229C22×C4—224no—
230C22×C4—224no—
231C22×C4—224no—
232C22×C4—224no—
233C22×C4—224no—
234C22×C4—224no—
235C22×C4—224no—
236C22×C4—224no—
237C22×C4—224no—
238C22×C4—224no—
239C22×C4—224no—
240C22×C4#433914yes—
241C22×C4C22×Dic1114yes—
242C22×C4C22×Dic1114yes—
243C22×C4C22×Dic1114yes—
244C22×C4C22×Dic1112yes—
245C4⋊C4—44no—
246C4⋊C4—44no—
247C4⋊C4—448no—
248C42—28no—
249C42—448no—
250C11#1447611yescharacteristic, complemented, Sylow
251C23C2×#433912yes—
252C23#6703711yescharacteristic
253C23#6703711yescharacteristic
254C23#6704012yes—
255C23#41×D1114yes—
256C23#6704212yes—
257C23#6704312yes—
258C23C23×Dic1111yescharacteristic
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—28no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—28no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—228no—
279C2×C4—228no—
280C2×C4—228no—
281C2×C4—444no—
282C2×C4—444no—
283C2×C4—444no—
284C2×C4—444no—
285C2×C4—444no—
286C2×C4—444no—
287C2×C4—444no—
288C2×C4—444no—
289C2×C4—444no—
290C2×C4—444no—
291C2×C4—444no—
292C2×C4#6697914yes—
293C22#1062304612yes—
294C22#1062304612yes—
295C22#1062306014yes—
296C22#1062306314yes—
297C22#1062320112yes—
298C22#1062320311yescharacteristic
299C22#1062321012yes—
300C22#1062321411yescharacteristic
301C22#1062321512yes—
302C22#1062322314yes—
303C22#1062322714yes—
304C22C2×#6697911yescharacteristic
305C22#1062332911yescharacteristic
306C22#1062334311yescharacteristic
307C22#41×Dic1112yes—
308C22#1062335812yes—
309C4—24no—
310C4—44no—
311C4—44no—
312C4—44no—
313C4—448no—
314C4—884no—
315C2#1307121911yescharacteristic
316C2#1307142212yes—
317C2#1307150112yes—
318C2#1307172811yescharacteristic
319C2#1307179011yescharacteristic
320C2#1307577114yes—
321C2#1307610612yes—
322C2#1307632212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#382C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#382D11
hypocenterC11#14476
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
12. C11×#382C4semidirect
143. #382Dic11semidirect
250. C11#14476semidirect

Maximal subgroups

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

subgroupindex
#130668732
#130668692
#130668482
#130668432
#130668412
C2×C11×#3822
#1447611