Finite Group Databasebeta

← #14682325

Subgroups — #14682325

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066869C212yesmaximal
2#13066869C214yesmaximal
3#13066848C212yesmaximal
4#13066848C214yesmaximal
5#13066843C212yesmaximal
6C2×C11×#384C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C11×C4⋊C4C2214yes—
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×C4×Dic11C2212yes—
13C11×#384C418yescomplemented
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2214yes—
16C2×C11⋊#95C2212yes—
17C2×C11⋊#95C2214yes—
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2214yes—
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—44no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4—44no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4C2×C414yes—
35C2×C11×C4⋊C4C2×C414yes—
36C2×C11×C4⋊C4C2×C4116yes—
37C2×C42×C11—24no—
38C2×C42×C11C2×C414yes—
39C2×C4⋊Dic11—42no—
40C2×C4⋊Dic11—44no—
41C2×C4×Dic11—42no—
42C2×C4×Dic11—44no—
43C11⋊#95—28no—
44C11⋊#95—28no—
45C11⋊#95—24no—
46C11⋊#95—42no—
47C11⋊#95—44no—
48C11⋊#95—44no—
49C11⋊#95—42no—
50C11⋊#95Q818yes—
51#14454—111nomaximal, Sylow
52C24×C11C2411yescharacteristic
53C22×C4×C11—24no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—24no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—22no—
63C22×C4×C11—24no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11C22×C414yes—
67C22×C4×C11C22×C414yes—
68C22×C4×C11C22×C412yes—
69C22×C4×C11C22×C414yes—
70C22×C4×C11C2×Q814yes—
71C22×C4×C11#4114yes—
72C22×C4×C11#4114yes—
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—24no—
85C22×Dic11—24no—
86C22×Dic11C2×Q818yes—
87C11×C4⋊C4—44no—
88C11×C4⋊C4—44no—
89C11×C4⋊C4—416no—
90C42×C11—28no—
91C4⋊Dic11—48no—
92C4×Dic11—48no—
93C2×#384D1111yescharacteristic
94#1441—114no—
95#1441—112no—
96#1436—112no—
97#1436—114no—
98#1434—112no—
99C23×C11C23×C411yescharacteristic
100C23×C11C22×Q812yes—
101C23×C11C2×#4112yes—
102C23×C11C2×#4112yes—
103C23×C11H(5,𝔽2)11yescharacteristic
104C23×C11H(5,𝔽2)11yescharacteristic
105C23×C11H(5,𝔽2)14yes—
106C23×C112−1+412yes—
107C2×C4×C11—24no—
108C2×C4×C11—22no—
109C2×C4×C11—24no—
110C2×C4×C11—22no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—28no—
114C2×C4×C11—28no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—28no—
118C2×C4×C11—28no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11#11714yes—
126C2×C4×C11C4×Q818yes—
127C2×Dic11—28no—
128C2×Dic11—28no—
129C2×Dic11—28no—
130C2×Dic11—44no—
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—
141C22×C4⋊C4—112no—
142C22×C4⋊C4C2×D1111yescharacteristic
143C22×C4⋊C4C2×D1114yes—
144C22×C4⋊C4C2×D1111yescharacteristic
145C22×C42—112no—
146C22×C42C2×D1111yescharacteristic
147#384Dic1118yescomplemented
148C2×#95—112no—
149C2×#95—114no—
150C2×#95—114no—
151C2×#95—112no—
152C2×#95—112no—
153C2×#95—114no—
154C2×#95—114no—
155C2×#95—112no—
156C22×C11C2×#11711yescharacteristic
157C22×C11C2×C4×Q812yes—
158C22×C11#51811yescharacteristic
159C22×C11#51812yes—
160C22×C11#51911yescharacteristic
161C22×C11#53912yes—
162C22×C11#53912yes—
163C22×C11#54214yes—
164C22×C11#54414yes—
165C22×C11#55314yes—
166C22×C11#55412yes—
167C22×C11#55414yes—
168C22×C11#55511yescharacteristic
169C22×C11Q8211yescharacteristic
170C22×C11#56012yes—
171C22×C11#56012yes—
172C4×C11—24no—
173C4×C11—28no—
174C4×C11—44no—
175C4×C11—44no—
176Dic11—48no—
177Dic11—84no—
178C23×C4—114no—
179C23×C4—114no—
180C23×C4C22×D1112yes—
181C23×C4C22×D1112yes—
182C23×C4C22×D1111yescharacteristic
183C23×C4C22×D1112yes—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—442no—
191C2×C4⋊C4—444no—
192C2×C4⋊C4C2×Dic1114yes—
193C2×C4⋊C4C2×Dic1114yes—
194C2×C4⋊C4C2×Dic11116yes—
195C2×C42—24no—
196C2×C42—444no—
197C2×C42—442no—
198C2×C42C2×Dic1114yes—
199#95—118no—
200#95—228no—
201#95—228no—
202#95—224no—
203#95—442no—
204#95—444no—
205#95—444no—
206#95—442no—
207C2×C11#231311yescharacteristic
208C2×C11#233112yes—
209C2×C11#234512yes—
210C2×C11#236911yescharacteristic
211C2×C11#238011yescharacteristic
212C2×C11#279014yes—
213C2×C11#279212yes—
214C2×C11#279512yes—
215C24C23×D1111yescharacteristic
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—118no—
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—224no—
241C22×C4—224no—
242C22×C4—224no—
243C22×C4#433914yes—
244C22×C4Q8×D1114yes—
245C22×C4#434314yes—
246C22×C4C22×Dic1114yes—
247C22×C4C22×Dic1114yes—
248C22×C4C22×Dic1112yes—
249C22×C4C22×Dic1114yes—
250C4⋊C4—44no—
251C4⋊C4—44no—
252C4⋊C4—416no—
253C4⋊C4—448no—
254C42—28no—
255C42—448no—
256C11#1445411yescharacteristic, complemented, Sylow
257C23C2×#433912yes—
258C23#6703711yescharacteristic
259C23#6703714yes—
260C23#6703711yescharacteristic
261C23C2×Q8×D1112yes—
262C23C2×#434312yes—
263C23#6704012yes—
264C23C23×Dic1111yescharacteristic
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—228no—
284C2×C4—228no—
285C2×C4—228no—
286C2×C4—444no—
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#6697914yes—
298C2×C4Q8×Dic1118yes—
299C22#1062304214yes—
300C22#1062304514yes—
301C22#1062304612yes—
302C22#1062304612yes—
303C22#1062325112yes—
304C22#1062325112yes—
305C22#1062325311yescharacteristic
306C22#1062326014yes—
307C22#1062326112yes—
308C22#1062326414yes—
309C22#1062326511yescharacteristic
310C22C2×#6697911yescharacteristic
311C22#1062332912yes—
312C22#1062332911yescharacteristic
313C22C2×Q8×Dic1112yes—
314C22#1062334311yescharacteristic
315C4—24no—
316C4—28no—
317C4—44no—
318C4—44no—
319C4—448no—
320C4—884no—
321C2#1307121911yescharacteristic
322C2#1307136512yes—
323C2#1307149312yes—
324C2#1307170611yescharacteristic
325C2#1307179311yescharacteristic
326C2#1307638214yes—
327C2#1307641212yes—
328C2#1307644512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#384C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#384D11
hypocenterC11#14454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
13. C11×#384C4semidirect
147. #384Dic11semidirect
256. C11#14454semidirect

Maximal subgroups

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

subgroupindex
#130668692
#130668482
#130668432
C2×C11×#3842
#1445411