Finite Group Databasebeta

← #14681977

Subgroups — #14681977

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622594C214yesmaximal
2#13066884C214yesmaximal
3#13066869C212yesmaximal
4#13066848C212yesmaximal
5#13066843C212yesmaximal
6C2×C11×#384C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2214yes—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×C4×Dic11C2212yes—
13C11×#384C418yescomplemented
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2212yes—
16C2×C11⋊#95C2214yes—
17C2×C11⋊#95C2214yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22#10622594—216no—
23C23×C4×C11C2312yes—
24C23×C4×C11C2312yes—
25C23×C4×C11C2312yes—
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2314yes—
28C23×Dic11C2314yes—
29C2×C11×C4⋊C4—28no—
30C2×C11×C4⋊C4—28no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4C2×C4116yes—
36C2×C11×C4⋊C4C2×C414yes—
37C2×C11×C4⋊C4C2×C414yes—
38C2×C42×C11—24no—
39C2×C42×C11C2×C414yes—
40C2×C4⋊Dic11—28no—
41C2×C4⋊Dic11—42no—
42C2×C4×Dic11—28no—
43C2×C4×Dic11—42no—
44C11⋊#95—28no—
45C11⋊#95—28no—
46C11⋊#95—24no—
47C11⋊#95—28no—
48C11⋊#95—28no—
49C11⋊#95—42no—
50C11⋊#95—42no—
51C11⋊#95D418yes—
52#14424—111nomaximal, Sylow
53C24×C11C2411yescharacteristic
54C22×C4×C11—24no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—24no—
59C22×C4×C11—24no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11C22×C414yes—
68C22×C4×C11C22×C414yes—
69C22×C4×C11C22×C412yes—
70C22×C4×C11C22×C414yes—
71C22×C4×C11C2×D414yes—
72C22×C4×C11#4114yes—
73C22×C4×C11#4114yes—
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×Dic11—24no—
87C22×Dic11C2×D418yes—
88C11×C4⋊C4—232no—
89C11×C4⋊C4—44no—
90C11×C4⋊C4—44no—
91C42×C11—28no—
92C4⋊Dic11—48no—
93C4×Dic11—48no—
94C2×#387—114no—
95C2×#384D1111yescharacteristic
96#1445—114no—
97#1441—112no—
98#1436—112no—
99#1434—112no—
100C23×C11C23×C411yescharacteristic
101C23×C11C22×D412yes—
102C23×C11C2×#4112yes—
103C23×C11C2×#4112yes—
104C23×C11H(5,𝔽2)11yescharacteristic
105C23×C11H(5,𝔽2)11yescharacteristic
106C23×C112−1+412yes—
107C23×C112−1+414yes—
108C2×C4×C11—24no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—28no—
115C2×C4×C11—28no—
116C2×C4×C11—28no—
117C2×C4×C11—28no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11#11714yes—
127C2×C4×C11C4×D418yes—
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—
142C22×C4⋊C4—112no—
143C22×C4⋊C4C2×D1114yes—
144C22×C4⋊C4C2×D1111yescharacteristic
145C22×C4⋊C4C2×D1111yescharacteristic
146C22×C42—112no—
147C22×C42C2×D1111yescharacteristic
148#387—2216no—
149#384Dic1118yescomplemented
150C2×#95—112no—
151C2×#95—114no—
152C2×#95—112no—
153C2×#95—114no—
154C2×#95—114no—
155C2×#95—114no—
156C2×#95—112no—
157C2×#95—112no—
158C22×C11C2×#11711yescharacteristic
159C22×C11C2×C4×D412yes—
160C22×C11#51811yescharacteristic
161C22×C11#51911yescharacteristic
162C22×C11#51912yes—
163C22×C11#53614yes—
164C22×C11#53912yes—
165C22×C11#53912yes—
166C22×C11#54114yes—
167C22×C11D4211yescharacteristic
168C22×C11#54714yes—
169C22×C11#55012yes—
170C22×C11#55214yes—
171C22×C11#55911yescharacteristic
172C22×C11#56312yes—
173C22×C11#56312yes—
174C4×C11—24no—
175C4×C11—28no—
176C4×C11—44no—
177C4×C11—44no—
178Dic11—48no—
179Dic11—84no—
180C23×C4—114no—
181C23×C4—114no—
182C23×C4C22×D1112yes—
183C23×C4C22×D1112yes—
184C23×C4C22×D1111yescharacteristic
185C23×C4C22×D1112yes—
186C2×C4⋊C4—28no—
187C2×C4⋊C4—28no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—228no—
193C2×C4⋊C4—442no—
194C2×C4⋊C4C2×Dic11116yes—
195C2×C4⋊C4C2×Dic1114yes—
196C2×C4⋊C4C2×Dic1114yes—
197C2×C42—24no—
198C2×C42—228no—
199C2×C42—442no—
200C2×C42C2×Dic1114yes—
201#95—118no—
202#95—228no—
203#95—228no—
204#95—228no—
205#95—228no—
206#95—224no—
207#95—442no—
208#95—442no—
209C2×C11#231311yescharacteristic
210C2×C11#232712yes—
211C2×C11#234412yes—
212C2×C11#236611yescharacteristic
213C2×C11#238111yescharacteristic
214C2×C11#268012yes—
215C2×C11#272114yes—
216C2×C11#279412yes—
217C24C23×D1111yescharacteristic
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—118no—
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—224no—
244C22×C4—224no—
245C22×C4#433914yes—
246C22×C4D4×D1114yes—
247C22×C4#434114yes—
248C22×C4C22×Dic1114yes—
249C22×C4C22×Dic1114yes—
250C22×C4C22×Dic1112yes—
251C22×C4C22×Dic1114yes—
252C4⋊C4—232no—
253C4⋊C4—44no—
254C4⋊C4—44no—
255C4⋊C4—448no—
256C42—28no—
257C42—448no—
258C11#1442411yescharacteristic, complemented, Sylow
259C23C2×#433912yes—
260C23C2×D4×D1112yes—
261C23C2×#434112yes—
262C23#6703711yescharacteristic
263C23#6703711yescharacteristic
264C23#6704012yes—
265C23#6704014yes—
266C23C23×Dic1111yescharacteristic
267C2×C4—28no—
268C2×C4—28no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—228no—
286C2×C4—228no—
287C2×C4—228no—
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—444no—
299C2×C4#6697914yes—
300C2×C4D4×Dic1118yes—
301C22#1062303814yes—
302C22#1062304414yes—
303C22#1062304612yes—
304C22#1062304612yes—
305C22#1062324411yescharacteristic
306C22#1062324811yescharacteristic
307C22#1062324912yes—
308C22#1062325514yes—
309C22#1062326214yes—
310C22#1062326612yes—
311C22#1062326612yes—
312C22C2×#6697911yescharacteristic
313C22C2×D4×Dic1112yes—
314C22#1062332911yescharacteristic
315C22#1062334311yescharacteristic
316C22#1062334312yes—
317C4—24no—
318C4—28no—
319C4—44no—
320C4—44no—
321C4—448no—
322C4—884no—
323C2#1307121911yescharacteristic
324C2#1307133612yes—
325C2#1307148512yes—
326C2#1307168111yescharacteristic
327C2#1307179711yescharacteristic
328C2#1307495612yes—
329C2#1307550614yes—
330C2#1307643612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#384C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#384D11
hypocenterC11#14424
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
149. #384Dic11semidirect
258. C11#14424semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
#130668842
#130668692
#130668482
#130668432
C2×C11×#3842
#1442411