Finite Group Databasebeta

← #14810461

Subgroups — #14810461

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
1C22×#66923C211yesmaximal, characteristic
2C2×#10622695C212yesmaximal, complemented
3#13069767C214yesmaximal, complemented
4#13069584C212yesmaximal, complemented
5#13068924C214yesmaximal
6#13068378C211yesmaximal, characteristic
7C11×#2857C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2212yes—
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×Dic11⋊C4—22no—
13C2×#66923—22no—
14C2×#66923—28no—
15C2×#66923C2212yes—
16C2×#66923C2212yes—
17C11×#391C2212yes—
18C11×#389—22no—
19C11×#384C2211yescharacteristic
20C11×#380—22no—
21C2×#66899C2218yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622695—28no—
24C2×#66867C2212yes—
25#10622167C2218yes—
26#10622162C2212yes—
27C22×Q8×C11C2312yes—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—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×C4⋊Dic11—22no—
43C2×C4⋊Dic11—28no—
44C2×C4⋊Dic11C2314yes—
45C2×Dic11⋊C4—216no—
46C2×Dic11⋊C4—24no—
47C2×Dic11⋊C4—24no—
48C22×C11⋊C8C2314yes—
49#66923—216no—
50#66923—24no—
51#66923—28no—
52#66923D418yes—
53C11×#95—24no—
54#66899—216no—
55C22⋊(C11⋊C8)—24no—
56#66867—24no—
57#25912—111nomaximal, Sylow
58C24×C11C2×D411yescharacteristic
59C2×Q8×C11—24no—
60C2×Q8×C11—24no—
61C2×Q8×C11—24no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—42no—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4114yes—
73C22×C4×C11C2411yescharacteristic
74C22×Dic11—28no—
75C22×Dic11—24no—
76C22×Dic11—44no—
77C22×Dic11—44no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—44no—
80C11×C4⋊C4—44no—
81C11×C4⋊C4—44no—
82C11×C22⋊C4—44no—
83C42×C11—24no—
84C42×C11—22no—
85C42×C11C2×D414yes—
86C4⋊Dic11—28no—
87C4⋊Dic11—24no—
88C4⋊Dic11C2×D418yes—
89Dic11⋊C4—216no—
90Dic11⋊C4—216no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—24no—
94C22×#125—111no—
95C2×#491—112no—
96#2857D1111yescharacteristic
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
107Q8×C11—48no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
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×C11C22×D412yes—
125C2×C4×C11C2×#4112yes—
126C2×C4×C112−1+412yes—
127C2×Dic11—28no—
128C2×Dic11—416no—
129C2×Dic11—44no—
130C2×Dic11—44no—
131C11⋊C8—44no—
132C2×C4⋊Q8C2×D1111yescharacteristic
133C2×#125—112no—
134C2×#125—112no—
135C2×#125—228no—
136C2×#125—222no—
137C2×C22⋊Q8C2×D1112yes—
138C22×C4⋊C4—112no—
139C22×C4⋊C4—222no—
140C22×C42C2×D1111yescharacteristic
141#491—228no—
142C2×#103—118no—
143C2×C22⋊C8—112no—
144C2×#97—112no—
145#391C2×D1112yes—
146#389—22no—
147#384C2×D1111yescharacteristic
148#380—22no—
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—82no—
165C4×C11—82no—
166C4×C11#54814yes—
167Dic11—48no—
168C22×Q8C22×D1112yes—
169C23×C4—222no—
170C23×C4C22⋊D1112yes—
171C23×C4C22×D1111yescharacteristic
172C22×C8—114no—
173C4⋊Q8—24no—
174#125—118no—
175#125—228no—
176#125—2216no—
177#125—224no—
178C22⋊Q8—28no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—114no—
183C2×C4⋊C4—228no—
184C2×C4⋊C4—2216no—
185C2×C4⋊C4—222no—
186C2×C4⋊C4—224no—
187C2×C4⋊C4—224no—
188C2×C4⋊C4C22×D1112yes—
189C2×C22⋊C4—22no—
190C2×C42—24no—
191C2×C42C22⋊D1112yes—
192C2×C42C22×D1111yescharacteristic
193C2×C42C22×D1111yescharacteristic
194#103—2216no—
195C22⋊C8—224no—
196#97—224no—
197#95—24no—
198C2×C11—24no—
199C2×C11#243611yescharacteristic
200C2×C11#300712yes—
201C2×C11C2×#49111yescharacteristic
202C2×C11#314211yescharacteristic
203C2×C11#323612yes—
204C24C2×C22⋊D1111yescharacteristic
205C2×Q8—24no—
206C2×Q8—24no—
207C2×Q8—24no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—228no—
216C22×C4—224no—
217C22×C4—444no—
218C22×C4—444no—
219C22×C4#434114yes—
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—24no—
228C4⋊C4—44no—
229C4⋊C4—44no—
230C4⋊C4—44no—
231C4⋊C4—118no—
232C4⋊C4—2216no—
233C4⋊C4—228no—
234C4⋊C4—2216no—
235C4⋊C4—224no—
236C22⋊C4—44no—
237C42—24no—
238C42—22no—
239C42D4×D1114yes—
240C11#2591211yescharacteristic, complemented, Sylow
241C23—21no—
242C23—22no—
243C23—21no—
244C23#6698912yes—
245C23#6699514yes—
246C23C22×C22⋊D1111yescharacteristic
247Q8—48no—
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—48no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—228no—
263C2×C4—4416no—
264C2×C4—444no—
265C2×C4—444no—
266C2×C4#6698912yes—
267C2×C4#6699014yes—
268C2×C4C2×D4×D1112yes—
269C2×C4C2×#434112yes—
270C2×C4#6704312yes—
271C8—444no—
272C22—24no—
273C22—24no—
274C22—22no—
275C22—22no—
276C22#1062269514yescomplemented
277C22C2×#6698911yescharacteristic
278C22C2×#6699011yescharacteristic
279C22C2×#6699512yes—
280C22#1062335312yes—
281C22#1062335611yescharacteristic
282C4—24no—
283C4—22no—
284C4—42no—
285C4—82no—
286C4—82no—
287C4—448no—
288C4#1062312914yes—
289C2—24no—
290C2#1307227511yescharacteristic
291C2#1307787412yes—
292C2C2×#1062269511yescharacteristic
293C2#1307901611yescharacteristic
294C2#1307981812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2857C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2857D11
hypocenterC11#25912
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×#10622695C2semidirect
3. #13069767C2semidirect
4. #13069584C2semidirect
155. C22×C11#491semidirect
240. C11#25912semidirect
276. C22#10622695semidirect

Maximal subgroups

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

subgroupindex
C22×#669232
C2×#106226952
#130697672
#130695842
#130689242
#130683782
C11×#28572
#2591211