Finite Group Databasebeta

← #14810456

Subgroups — #14810456

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C212yesmaximal, complemented
2#13076968C211yesmaximal, characteristic
3#13069764C214yesmaximal, complemented
4#13069586C212yesmaximal, complemented
5#13068923C214yesmaximal
6#13068378C211yesmaximal, characteristic
7C22×C11×#125C211yesmaximal, characteristic
8C2×C11×#125—28no—
9C2×C11×#125—22no—
10C2×C11×#125C2212yes—
11C2×C11×#125C2212yes—
12C22×C11×C4⋊C4—22no—
13C22×C11×C4⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66977C2212yes—
16C2×#66922C2211yescharacteristic
17#10622825—22no—
18C2×C22⋊(C11⋊C8)C2212yes—
19#10622682—28no—
20C2×#66874C2218yes—
21#10622548C2211yescharacteristic
22#10622542C2212yes—
23#10622541—22no—
24C2×#66867C2212yes—
25#10622167C2218yes—
26#10622162C2212yes—
27C23×C4×C11—22no—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C22×Dic22C2312yes—
31C11×#125—216no—
32C11×#125—28no—
33C11×#125—24no—
34C11×#125D418yes—
35C2×C11×C4⋊C4—216no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—28no—
40C2×C11×C4⋊C4C2314yes—
41C2×C42×C11—24no—
42C2×C42×C11D412yes—
43C2×C42×C11C2311yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×C22⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11C2312yes—
49#66977—28no—
50C2×Dic11⋊C4—22no—
51C22×C11⋊C8C2314yes—
52#66922—24no—
53C11⋊#95—24no—
54C22⋊(C11⋊C8)—24no—
55#66874—216no—
56#66867—24no—
57#25912—111nomaximal, Sylow
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—28no—
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—24no—
65C22×C4×C11—42no—
66C22×C4×C11—44no—
67C22×C4×C11—44no—
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4114yes—
72C22×C4×C11C2411yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C2×Dic22—24no—
76C2×Dic22—24no—
77C2×Dic22—24no—
78C11×C4⋊C4—28no—
79C11×C4⋊C4—216no—
80C11×C4⋊C4—216no—
81C11×C4⋊C4—24no—
82C11×C4⋊C4C2×D418yes—
83C42×C11—24no—
84C42×C11—22no—
85C42×C11C2×D414yes—
86C22⋊Dic11—44no—
87C4⋊Dic11—24no—
88C4⋊Dic11—44no—
89C4⋊Dic11—44no—
90Dic11⋊C4—44no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—24no—
94C22×#125D1111yescharacteristic
95C2×#491—112no—
96#2857—111no—
97#2026—114no—
98#1992—112no—
99#1872—114no—
100#1749—111no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—22no—
104C23×C11#12412yes—
105C23×C11#13714yes—
106C23×C11C22×D411yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—28no—
112C2×C4×C11—22no—
113C2×C4×C11—28no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—48no—
117C2×C4×C11—416no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11#12014yes—
121C2×C4×C11#12412yes—
122C2×C4×C11C22×D412yes—
123C2×C4×C11C2×#4112yes—
124C2×C4×C112−1+412yes—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—44no—
130Dic22—48no—
131C11⋊C8—44no—
132C2×C4⋊Q8—111no—
133C2×#125—28no—
134C2×#125—22no—
135C2×#125C2×D1112yes—
136C2×#125C2×D1112yes—
137C2×C22⋊Q8—112no—
138C22×C4⋊C4—22no—
139C22×C4⋊C4C2×D1112yes—
140C22×C42C2×D1111yescharacteristic
141#491—228no—
142C2×#103—118no—
143C2×C22⋊C8—112no—
144C2×#97—112no—
145#391—112no—
146#389—222no—
147#384—111no—
148#380—222no—
149#340—118no—
150#336—112no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—24no—
154C22×C11—24no—
155C22×C11#49114yescomplemented
156C22×C11C2×#12011yescharacteristic
157C22×C11C2×#12411yescharacteristic
158C22×C11#53611yescharacteristic
159C22×C11C2×#13712yes—
160C22×C11#57512yes—
161C4×C11—22no—
162C4×C11—24no—
163C4×C11—42no—
164C4×C11—48no—
165C4×C11#54814yes—
166Dic11—82no—
167Dic11—82no—
168C22×Q8—112no—
169C23×C4—22no—
170C23×C4C22⋊D1112yes—
171C23×C4C22×D1111yescharacteristic
172C22×C8—114no—
173C4⋊Q8—224no—
174#125—216no—
175#125—28no—
176#125—24no—
177#125C22⋊D1118yes—
178C22⋊Q8—228no—
179C2×C4⋊C4—216no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—28no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—222no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4C22×D1114yes—
189C2×C22⋊C4—222no—
190C2×C42—24no—
191C2×C42C22⋊D1112yes—
192C2×C42C22×D1111yescharacteristic
193C2×C42C22×D1111yescharacteristic
194#103—2216no—
195C22⋊C8—224no—
196#97—224no—
197#95—224no—
198C2×C11—24no—
199C2×C11#243611yescharacteristic
200C2×C11#300712yes—
201C2×C11C2×#49111yescharacteristic
202C2×C11#314211yescharacteristic
203C2×C11#323612yes—
204C24C2×C22⋊D1111yescharacteristic
205C2×Q8—224no—
206C2×Q8—224no—
207C2×Q8—224no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—28no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—42no—
215C22×C4—44no—
216C22×C4—44no—
217C22×C4—222no—
218C22×C4—222no—
219C22×C4#434314yes—
220C22×C4C2×C22⋊D1112yes—
221C22×C4C2×C22⋊D1111yescharacteristic
222C22×C4C2×C22⋊D1112yes—
223C22×C4C23×D1111yescharacteristic
224C2×C8—224no—
225C2×C8—224no—
226C2×C8—224no—
227C4⋊C4—28no—
228C4⋊C4—216no—
229C4⋊C4—216no—
230C4⋊C4—24no—
231C4⋊C4—224no—
232C4⋊C4—444no—
233C4⋊C4—444no—
234C4⋊C4—444no—
235C4⋊C4C2×C22⋊D1118yes—
236C22⋊C4—444no—
237C42—24no—
238C42—22no—
239C42C2×C22⋊D1114yes—
240C11#2591211yescharacteristic, complemented, Sylow
241C23—21no—
242C23—22no—
243C23—21no—
244C23#6700012yes—
245C23#6700414yes—
246C23C22×C22⋊D1111yescharacteristic
247Q8—448no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—28no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—28no—
257C2×C4—48no—
258C2×C4—416no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—444no—
265C2×C4—442no—
266C2×C4#6700012yes—
267C2×C4#6700614yes—
268C2×C4C2×#434312yes—
269C2×C4#6704012yes—
270C2×C4C22×C22⋊D1112yes—
271C8—444no—
272C22—24no—
273C22—24no—
274C22—22no—
275C22—22no—
276C22#1062268214yescomplemented
277C22C2×#6700011yescharacteristic
278C22#1062334711yescharacteristic
279C22#1062335312yes—
280C22C2×#6700412yes—
281C22C2×#6700611yescharacteristic
282C4—24no—
283C4—22no—
284C4—42no—
285C4—48no—
286C4—882no—
287C4—882no—
288C4#1062334814yes—
289C2—24no—
290C2#1307227011yescharacteristic
291C2#1307787612yes—
292C2C2×#1062268211yescharacteristic
293C2#1307901911yescharacteristic
294C2#1307982212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#125C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC22×#125D11
hypocenterC11#25912
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
3. #13069764C2semidirect
4. #13069586C2semidirect
155. C22×C11#491semidirect
240. C11#25912semidirect
276. C22#10622682semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
#130769682
#130697642
#130695862
#130689232
#130683782
C22×C11×#1252
#2591211