Finite Group Databasebeta

← #14810397

Subgroups — #14810397

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2C2×#10622694C212yesmaximal, complemented
3#13069767C214yesmaximal, complemented
4#13069576C212yesmaximal, complemented
5#13068929C214yesmaximal
6C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
7C11×#2857C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2212yes—
10C22×C42×C11C2211yescharacteristic
11C2×#66979C2212yes—
12C2×#66977—22no—
13#10623001—28no—
14C2×#66923C2212yes—
15C2×#66922C2212yes—
16C2×C4×Dic22—22no—
17C11×#391C2212yes—
18C11×#389—22no—
19C11×#384C2211yescharacteristic
20C11×#380—22no—
21C2×#66899C2218yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622694—28no—
24C2×C4×C11⋊C8C2212yes—
25#10622167C2218yes—
26#10622162C2212yes—
27C22×Q8×C11C2312yes—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C22×Dic22—22no—
31C11×C4⋊Q8—24no—
32C11×C22⋊Q8—28no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4C2312yes—
37C2×C11×C22⋊C4—22no—
38C2×C42×C11—24no—
39C2×C42×C11D412yes—
40C2×C42×C11C2311yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11—22no—
43#66979—28no—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11C2314yes—
46#66977—216no—
47C2×Dic11⋊C4—24no—
48C2×C4×Dic11—22no—
49C22×C11⋊C8C2314yes—
50#66923—28no—
51#66922—24no—
52#66922D418yes—
53C4×Dic22—216no—
54C11×#95—24no—
55#66899—216no—
56C22⋊(C11⋊C8)—24no—
57C4×C11⋊C8—24no—
58#25904—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C2×Q8×C11—24no—
61C2×Q8×C11—24no—
62C2×Q8×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11#4114yes—
74C22×C4×C11C2411yescharacteristic
75C22×Dic11—24no—
76C2×Dic22—28no—
77C2×Dic22—44no—
78C2×Dic22—44no—
79C11×C4⋊C4—24no—
80C11×C4⋊C4—44no—
81C11×C4⋊C4—44no—
82C11×C4⋊C4—44no—
83C11×C22⋊C4—44no—
84C42×C11—24no—
85C42×C11—22no—
86C42×C11C2×D414yes—
87C22⋊Dic11—28no—
88C4⋊Dic11—28no—
89C4⋊Dic11—24no—
90C4⋊Dic11C2×D418yes—
91Dic11⋊C4—216no—
92C4×Dic11—28no—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—24no—
95C2×C11⋊C8—24no—
96C2×#533—111no—
97C2×#487—112no—
98#2857D1111yescharacteristic
99#2026—114no—
100#1990—112no—
101#1873—114no—
102C4×C22⋊C8—111no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11#12412yes—
108C23×C11C22×D411yescharacteristic
109Q8×C11—48no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—28no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—48no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11#12014yes—
123C2×C4×C11#12412yes—
124C2×C4×C11#13514yes—
125C2×C4×C11#13714yes—
126C2×C4×C11C22×D412yes—
127C2×C4×C11C2×#4112yes—
128C2×C4×C112−1+412yes—
129C2×Dic11—28no—
130C2×Dic11—44no—
131C2×Dic11—44no—
132Dic22—416no—
133C11⋊C8—44no—
134#533—228no—
135C2×C4⋊Q8—112no—
136C2×C4⋊Q8C2×D1111yescharacteristic
137C2×#125—112no—
138C2×C22⋊Q8—222no—
139C2×C22⋊Q8C2×D1112yes—
140C2×C4×Q8—222no—
141C2×#117—112no—
142C22×C42C2×D1111yescharacteristic
143#487—228no—
144C2×#103—118no—
145C2×C22⋊C8—112no—
146C2×C4×C8—112no—
147#391C2×D1112yes—
148#389—22no—
149#384C2×D1111yescharacteristic
150#380—22no—
151#340—118no—
152#336—112no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11C2×#12011yescharacteristic
159C22×C11C2×#12411yescharacteristic
160C22×C11#53611yescharacteristic
161C22×C11C2×#13512yes—
162C22×C11C2×#13712yes—
163C4×C11—22no—
164C4×C11—42no—
165C4×C11—82no—
166C4×C11—82no—
167C4×C11#45218yes—
168C4×C11#54814yes—
169Dic11—48no—
170C22×Q8—222no—
171C22×Q8C22×D1112yes—
172C23×C4C22⋊D1112yes—
173C23×C4C22×D1111yescharacteristic
174C22×C8—114no—
175C4⋊Q8—24no—
176C4⋊Q8—118no—
177C4⋊Q8—224no—
178#125—228no—
179C22⋊Q8—28no—
180C22⋊Q8—2216no—
181C4×Q8—2216no—
182#117—228no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—114no—
187C2×C4⋊C4—224no—
188C2×C4⋊C4—222no—
189C2×C4⋊C4C22×D1112yes—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—222no—
192C2×C42—24no—
193C2×C42—222no—
194C2×C42C22⋊D1112yes—
195C2×C42C22×D1111yescharacteristic
196C2×C42C22×D1111yescharacteristic
197#103—2216no—
198C22⋊C8—224no—
199C4×C8—224no—
200#95—24no—
201C2×C11—42no—
202C2×C11#243611yescharacteristic
203C2×C11C2×#45212yes—
204C2×C11#313111yescharacteristic
205C2×C11#313911yescharacteristic
206C2×C11#323112yes—
207C24C2×C22⋊D1111yescharacteristic
208C2×Q8—24no—
209C2×Q8—24no—
210C2×Q8—24no—
211C2×Q8—228no—
212C2×Q8—444no—
213C2×Q8—444no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—224no—
222C22×C4#434114yes—
223C22×C4C2×C22⋊D1112yes—
224C22×C4C2×C22⋊D1111yescharacteristic
225C22×C4C2×C22⋊D1112yes—
226C22×C4C23×D1111yescharacteristic
227C2×C8—224no—
228C2×C8—224no—
229C2×C8—224no—
230C4⋊C4—24no—
231C4⋊C4—44no—
232C4⋊C4—44no—
233C4⋊C4—44no—
234C4⋊C4—118no—
235C4⋊C4—2216no—
236C4⋊C4—228no—
237C4⋊C4—224no—
238C22⋊C4—44no—
239C22⋊C4—228no—
240C42—24no—
241C42—22no—
242C42—228no—
243C42D4×D1114yes—
244C11#2590411yescharacteristic, complemented, Sylow
245C23—21no—
246C23—22no—
247C23—22no—
248C23—21no—
249C23#6698912yes—
250C23C22×C22⋊D1111yescharacteristic
251Q8—48no—
252Q8—4416no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—28no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—48no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—228no—
266C2×C4—444no—
267C2×C4—444no—
268C2×C4#6698912yes—
269C2×C4#6699014yes—
270C2×C4#6699514yes—
271C2×C4#6700314yes—
272C2×C4C2×D4×D1112yes—
273C2×C4C2×#434112yes—
274C2×C4#6704312yes—
275C8—444no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22C2×#6698911yescharacteristic
282C22C2×#6699011yescharacteristic
283C22C2×#6699512yes—
284C22C2×#6700312yes—
285C22#1062335611yescharacteristic
286C4—22no—
287C4—42no—
288C4—82no—
289C4—82no—
290C4—448no—
291C4#1062266018yes—
292C4#1062312914yes—
293C2—42no—
294C2#1307227511yescharacteristic
295C2C2×#1062266012yes—
296C2#1307893811yescharacteristic
297C2#1307899611yescharacteristic
298C2#1307977112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2857C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2857D11
hypocenterC11#25904
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
2. C2×#10622694C2semidirect
3. #13069767C2semidirect
4. #13069576C2semidirect
244. C11#25904semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106226942
#130697672
#130695762
#130689292
C4×C22⋊(C11⋊C8)2
C11×#28572
#2590411