Finite Group Databasebeta

← #14651497

Subgroups — #14651497

Order 2816.

512 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073097C211yesmaximal, characteristic
2#13068696C211yesmaximal, characteristic
3#13067148C212yesmaximal
4#13066468C212yesmaximal
5C11×#2313C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#387—24no—
9C11×#381C2212yes—
10C11×#380—21no—
11C4×C11×C22⋊C4—21no—
12#10622824—21no—
13#10622824—21no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2212yes—
16#10622595—22no—
17#10622590C412yescomplemented
18#10622587C412yescomplemented
19#10622168—22no—
20#10622090—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11—22no—
32C2×C22⋊Dic11—21no—
33C2×C22⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35#66977—22no—
36#66977—22no—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11C2×C412yes—
39C2×#4318—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95D414yes—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#9460—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—24no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C22×C4×C11#4112yes—
67C22×Dic11—22no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C2×Dic22—22no—
71C2×Dic22—42no—
72C11×C4⋊C4—24no—
73C11×C4⋊C4—24no—
74C11×C4⋊C4—82no—
75C11×C22⋊C4—44no—
76C42×C11—82no—
77C22⋊Dic11—42no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C4⋊Dic11—22no—
81Dic11⋊C4—42no—
82C4×Dic11—42no—
83#4318—44no—
84C2×C11⋊C8—42no—
85#2503—111no—
86#2313D1111yescharacteristic
87#1821—111no—
88#1511—112no—
89#1284—112no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—41no—
93C23×C11C2×C22⋊C411yescharacteristic
94C23×C11#12011yescharacteristic
95C23×C11#12311yescharacteristic
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—44no—
107C2×C4×C11—44no—
108C2×C4×C11—44no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11C4×D412yes—
112C2×C4×C11#12112yes—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120Dic22—82no—
121C11⋊C8—82no—
122C2×C22⋊Q8—111no—
123C22×C4⋊C4C2×D1111yescharacteristic
124#407—112no—
125#400—222no—
126#391—112no—
127#387—24no—
128#382—112no—
129#381—221no—
130#381—221no—
131#381C2×D1112yes—
132#380—21no—
133C4×C22⋊C4—21no—
134C4×C22⋊C4—111no—
135#343—222no—
136#328—224no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—44no—
145C22×C11#38611yescharacteristic
146C22×C11#41012yes—
147C22×C11#45512yes—
148C4×C11—22no—
149C4×C11—22no—
150C4×C11—42no—
151C4×C11—42no—
152C4×C11—84no—
153Dic11—82no—
154Dic11—81no—
155Dic11—81no—
156C22×Q8—111no—
157C23×C4C22⋊D1111yescharacteristic
158C23×C4C22⋊D1111yescharacteristic
159C23×C4C22×D1111yescharacteristic
160C2×M16—222no—
161C22⋊Q8—222no—
162C22⋊Q8—222no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—111no—
167C2×C4⋊C4—221no—
168C2×C4⋊C4C4×D1112yes—
169C2×C4⋊C4D4412yes—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—221no—
172C2×C22⋊C4—221no—
173C2×C42—22no—
174C2×C42—112no—
175C22⋊C8—222no—
176C22⋊C8—222no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—222no—
181#95—222no—
182#95—222no—
183#95—222no—
184#95—221no—
185#95C22⋊D1114yes—
186C2×C11—22no—
187C2×C11—22no—
188C2×C11—41no—
189C2×C11#188511yescharacteristic
190C2×C11#189911yescharacteristic
191C2×C11#191211yescharacteristic
192C24C2×C22⋊D1111yescharacteristic
193C2×Q8—222no—
194C2×Q8—442no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—24no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—222no—
204C22×C4—221no—
205C22×C4—221no—
206C22×C4(C2×D11)⋊C412yes—
207C22×C4(C2×D11)⋊C412yes—
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4C2×D4411yescharacteristic
210C22×C4#433912yes—
211C22×C4C2×C22⋊D1112yes—
212M16—444no—
213C2×C8—442no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—82no—
217C4⋊C4—222no—
218C4⋊C4—442no—
219C22⋊C4—44no—
220C22⋊C4—442no—
221C22⋊C4—441no—
222C22⋊C4—441no—
223C42—82no—
224C42—442no—
225C11#946011yescharacteristic, complemented, Sylow
226C23—22no—
227C23—22no—
228C23—41no—
229C23C2×(C2×D11)⋊C411yescharacteristic
230C23#6698211yescharacteristic
231C23#6700611yescharacteristic
232Q8—882no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4C4×C22⋊D1112yes—
256C2×C4#6698312yes—
257C8—882no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22#1062261912yes—
267C22#1062282611yescharacteristic
268C22#1062285512yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—882no—
275C4—881no—
276C4—881no—
277C2—22no—
278C2—22no—
279C2—41no—
280C2#1306900411yescharacteristic
281C2#1306907411yescharacteristic
282C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2313C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2313D11
hypocenterC11#9460
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
17. #10622590C4semidirect
18. #10622587C4semidirect
225. C11#9460semidirect

Maximal subgroups

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

subgroupindex
#130730972
#130686962
#130671482
#130664682
C11×#23132
#946011