Finite Group Databasebeta

← #14651252

Subgroups — #14651252

Order 2816.

380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079357C211yesmaximal, characteristic
2#13077721C211yesmaximal, characteristic
3#13067254C211yesmaximal, characteristic
4#13067166C211yesmaximal, characteristic
5#13066489C211yesmaximal, characteristic
6#13066480C211yesmaximal, characteristic
7C11×#1515C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#383C2211yescharacteristic
12#10622706C411yescharacteristic, complemented
13#10622705C411yescharacteristic, complemented
14#10622694C411yescharacteristic, complemented
15#10622692C411yescharacteristic, complemented
16#10622665—22no—
17#10622643—22no—
18#10622539C2211yescharacteristic
19#10622539C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21#10622441—22no—
22#10622333—22no—
23#10622314—22no—
24C11×#328—22no—
25#10622181—22no—
26#10622090—22no—
27C11×C4⋊Q8C2×C411yescharacteristic
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×#125—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C11×#117—21no—
35C2×C42×C11C2311yescharacteristic
36C2×#4326—22no—
37#66979—21no—
38#66977—21no—
39#66977D412yes—
40C2×#4318—21no—
41#66923—21no—
42#66922C2×C411yescharacteristic
43#66922C2×C411yescharacteristic
44C4×Dic22—21no—
45C4×Dic22D412yes—
46C11×C4⋊C8—21no—
47C11×C22⋊C8D412yes—
48C11×#97—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52#66899—22no—
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)—21no—
55#66879—22no—
56Dic11⋊C8—24no—
57C8×Dic11—22no—
58#66874—22no—
59#66872—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62#66867—21no—
63#66867—21no—
64#66867D412yes—
65C4×C11⋊C8C2×C411yescharacteristic
66C4×C11⋊C8C2×C411yescharacteristic
67#9416—111nomaximal, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×Dic22—21no—
75C2×Dic22C22⋊C412yes—
76C2×C8×C11—22no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—41no—
85C42×C11C22×C411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89C22⋊Dic11—22no—
90#4326—44no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C22⋊C412yes—
95Dic11⋊C4—22no—
96Dic11⋊C4—22no—
97C4×Dic11—22no—
98#4318—42no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103#3185—111no—
104#2987—111no—
105#1537—111no—
106#1515—111no—
107#1515D1111yescharacteristic
108#1291—111no—
109#1288—111no—
110C23×C11#12111yescharacteristic
111Q8×C11—42no—
112Q8×C11—81no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×Dic11—22no—
128C2×Dic11—22no—
129Dic22—42no—
130Dic22—81no—
131C8×C11—42no—
132C11⋊C8—22no—
133C11⋊C8—42no—
134C11⋊C8—41no—
135C11⋊C8—81no—
136#533—111no—
137#533C2×D1111yescharacteristic
138#498—111no—
139#494—111no—
140#487—111no—
141#487—111no—
142#470—222no—
143#446—222no—
144#446—222no—
145#441—222no—
146#433—222no—
147#432—111no—
148#432—111no—
149#432C2×D1111yescharacteristic
150C4×M16—111no—
151#383C2×D1111yescharacteristic
152#330—222no—
153#328—22no—
154#328—222no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#38611yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—81no—
166C4×C11—81no—
167C4×C11—161no—
168Dic11—42no—
169Dic11—42no—
170C2×Q16—222no—
171C2×M16—221no—
172C4⋊Q8—111no—
173C4⋊Q8—111no—
174C4⋊Q8C4×D1111yescharacteristic
175C4⋊Q8C4×D1111yescharacteristic
176#125—21no—
177#125—221no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C22⋊Q8—112no—
181C22⋊Q8—221no—
182C4×Q8—21no—
183C4×Q8—21no—
184C4×Q8—112no—
185C4×Q8—221no—
186#117—21no—
187#117—221no—
188C2×C42C22×D1111yescharacteristic
189#106—222no—
190C4⋊C8—21no—
191C4⋊C8—224no—
192C4⋊C8—221no—
193C4⋊C8—221no—
194#103—222no—
195#103—222no—
196C22⋊C8—221no—
197C22⋊C8—221no—
198C22⋊C8C22⋊D1112yes—
199#97—21no—
200#97—112no—
201#97—222no—
202#97—221no—
203#97—221no—
204C4×C8—111no—
205C4×C8—111no—
206C4×C8—222no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C11—41no—
211C2×C11#188411yescharacteristic
212C2×C11#190211yescharacteristic
213C2×C11#190511yescharacteristic
214C2×Q8—21no—
215C2×Q8—21no—
216C2×Q8—112no—
217C2×Q8—221no—
218C22×C4—41no—
219C22×C4D4×D1111yescharacteristic
220C22×C4#434111yescharacteristic
221C22×C4C2×C22⋊D1111yescharacteristic
222Q16—444no—
223M16—442no—
224C2×C8—22no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—222no—
228C2×C8—441no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—112no—
236C4⋊C4—221no—
237C4⋊C4—222no—
238C4⋊C4—222no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C22⋊C4—41no—
242C22⋊C4—222no—
243C42—41no—
244C42—222no—
245C42C2×C4×D1111yescharacteristic
246C42#433911yescharacteristic
247C42D4×D1111yescharacteristic
248C42D4×D1111yescharacteristic
249C11#941611yescharacteristic, complemented, Sylow
250C23#6699111yescharacteristic
251Q8—42no—
252Q8—81no—
253Q8—442no—
254Q8—881no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4C22⋊C4×D1111yescharacteristic
266C2×C4(C22⋊D11)⋊C411yescharacteristic
267C2×C4#6693611yescharacteristic
268C2×C4#6693711yescharacteristic
269C2×C4C4×C22⋊D1111yescharacteristic
270C2×C4#6699011yescharacteristic
271C8—42no—
272C8—222no—
273C8—441no—
274C8—442no—
275C8—881no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1062256911yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—81no—
287C4—81no—
288C4—161no—
289C4—442no—
290C4—442no—
291C2—41no—
292C2#1306899611yescharacteristic
293C2#1306908611yescharacteristic
294C2#1306911311yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1515C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1515D11
hypocenterC11#9416
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. #10622705C4semidirect
14. #10622694C4semidirect
15. #10622692C4semidirect
249. C11#9416semidirect

Maximal subgroups

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

subgroupindex
#130793572
#130777212
#130672542
#130671662
#130664892
#130664802
C11×#15152
#941611