Finite Group Databasebeta

← #14651312

Subgroups — #14651312

Order 2816.

422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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#13078998C211yesmaximal, characteristic
2#13071796C211yesmaximal, characteristic
3#13067341C211yesmaximal, characteristic
4#13067167C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic
6#13066480C211yesmaximal, characteristic
7C11×#1515C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#383C2211yescharacteristic
12#10622706C412yescomplemented
13#10622706C412yescomplemented
14#10622682—22no—
15#10622617—22no—
16#10622550C2211yescharacteristic
17#10622539C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622267—22no—
20#10622266—22no—
21#10622259—22no—
22C11×#328—22no—
23#10622176—22no—
24#10622119—22no—
25C22×Dic22D412yes—
26C11×C4⋊Q8C2×C411yescharacteristic
27C11×C4⋊Q8C2×C411yescharacteristic
28C11×#125—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C11×#117—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—22no—
39C2×#4318—21no—
40#66922—21no—
41#66922—21no—
42#66922C2×C412yes—
43#66922D412yes—
44C11×C4⋊C8—21no—
45C11×C22⋊C8—21no—
46C11×#97—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95D412yes—
50C11⋊#95—24no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95D412yes—
54C22⋊(C11⋊C8)—21no—
55#66874—24no—
56#66874—24no—
57C4⋊(C11⋊C8)—21no—
58#66867—21no—
59#66867—21no—
60C4×C11⋊C8C2×C412yes—
61#9426—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11—22no—
70C2×Dic22—22no—
71C2×Dic22—42no—
72C2×Dic22—42no—
73C2×Dic22C22⋊C414yes—
74C2×C8×C11—41no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11—41no—
83C42×C11C22×C411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91Dic11⋊C4—82no—
92C4×Dic11—82no—
93#4318—42no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96#3139—111no—
97#2381—111no—
98#1558—111no—
99#1515—111no—
100#1515D1111yescharacteristic
101#1288—111no—
102#1288—111no—
103C23×C11#12011yescharacteristic
104Q8×C11—81no—
105Q8×C11—81no—
106C2×C4×C11—22no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12311yescharacteristic
120C2×Dic11—24no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126Dic22—44no—
127Dic22—82no—
128C8×C11—81no—
129C11⋊C8—42no—
130C11⋊C8—81no—
131#533C2×D1111yescharacteristic
132C2×C4⋊Q8—111no—
133#491—222no—
134#487—112no—
135#487—112no—
136#432—111no—
137#432C2×D1111yescharacteristic
138#419—222no—
139C4×M16—111no—
140#391—222no—
141#387—222no—
142#387—222no—
143#383—111no—
144#383C2×D1111yescharacteristic
145#333—222no—
146#328—22no—
147#328—222no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11#38611yescharacteristic
151C22×C11#45512yes—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—82no—
159C4×C11—81no—
160C4×C11—81no—
161Dic11—44no—
162Dic11—82no—
163C22×Q8—112no—
164C2×M16—221no—
165C4⋊Q8—112no—
166C4⋊Q8—112no—
167C4⋊Q8—221no—
168C4⋊Q8—221no—
169C4⋊Q8C4×D1111yescharacteristic
170C4⋊Q8C4×D1111yescharacteristic
171#125—21no—
172C22⋊Q8—21no—
173C22⋊Q8—21no—
174C4×Q8—21no—
175C4×Q8—21no—
176#117—21no—
177C2×C4⋊C4—221no—
178C2×C4⋊C4—221no—
179C2×C4⋊C4—222no—
180C2×C42—222no—
181C2×C42C22×D1111yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—221no—
184#103—224no—
185#103—224no—
186C22⋊C8—21no—
187C22⋊C8—221no—
188#97—21no—
189#97—221no—
190#97—221no—
191C4×C8—112no—
192#95—21no—
193#95—21no—
194#95—112no—
195#95—224no—
196#95—221no—
197#95—221no—
198#95C22⋊D1112yes—
199C2×C11—22no—
200C2×C11#188511yescharacteristic
201C2×C11#190511yescharacteristic
202C2×C11#190511yescharacteristic
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—114no—
206C2×Q8—222no—
207C2×Q8—442no—
208C2×Q8—442no—
209C22×C4—22no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4D4×D1111yescharacteristic
213C22×C4D4×D1111yescharacteristic
214C22×C4C2×C22⋊D1111yescharacteristic
215M16—442no—
216C2×C8—41no—
217C2×C8—222no—
218C2×C8—441no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C4⋊C4—222no—
228C4⋊C4—222no—
229C4⋊C4—882no—
230C22⋊C4—41no—
231C42—41no—
232C42—882no—
233C42C2×C4×D1111yescharacteristic
234C42#433911yescharacteristic
235C42D4×D1111yescharacteristic
236C42#434111yescharacteristic
237C11#942611yescharacteristic, complemented, Sylow
238C23#6699011yescharacteristic
239Q8—81no—
240Q8—81no—
241Q8—444no—
242Q8—882no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—224no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4C22⋊C4×D1111yescharacteristic
258C2×C4(C22⋊D11)⋊C411yescharacteristic
259C2×C4#6693611yescharacteristic
260C2×C4#6693711yescharacteristic
261C2×C4C4×C22⋊D1111yescharacteristic
262C2×C4#6699111yescharacteristic
263C8—81no—
264C8—442no—
265C8—881no—
266C22—21no—
267C22—21no—
268C22#1062256911yescharacteristic
269C22#1062281512yes—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—82no—
277C4—81no—
278C4—81no—
279C4—444no—
280C4—882no—
281C2—22no—
282C2#1306900111yescharacteristic
283C2#1306910711yescharacteristic
284C2#1306911311yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1515C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1515D11
hypocenterC11#9426
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
12. #10622706C4semidirect
13. #10622706C4semidirect
237. C11#9426semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130717962
#130673412
#130671672
#130664822
#130664802
C11×#15152
#942611