Finite Group Databasebeta

← #14650367

Subgroups — #14650367

Order 2816.

382 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079771C211yesmaximal, characteristic
2#13067129C211yesmaximal, characteristic
3#13067128C211yesmaximal, characteristic
4#13067090C211yesmaximal, characteristic
5#13066479C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#2985C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#446—22no—
11C11×#446—21no—
12C8×Q8×C11—21no—
13C11×#433—22no—
14C11×#432C2211yescharacteristic
15C11×#431C2211yescharacteristic
16#10622694C411yescharacteristic, complemented
17#10622694C411yescharacteristic, complemented
18#10622692C411yescharacteristic, complemented
19#10622691C411yescharacteristic, complemented
20#10622658—22no—
21#10622635—22no—
22#10622545C2211yescharacteristic
23#10622539C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622176—22no—
26#10622105—22no—
27#10622094—21no—
28#10622094—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8D412yes—
34C4×Q8×C11—21no—
35C4×Q8×C11D412yes—
36C11×#117—21no—
37C2×C42×C11C2311yescharacteristic
38#66979—21no—
39#66977—21no—
40#66977—21no—
41C2×C4×Dic11—21no—
42#66923—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—22no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8D412yes—
53C11×#97—22no—
54C11×#97—21no—
55C4×C8×C11—22no—
56C4×C8×C11D411yescharacteristic
57C4×C8×C11D411yescharacteristic
58#66899—22no—
59#66899—22no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64#66872—22no—
65#66871—22no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69C4×C11⋊C8C2×C411yescharacteristic
70C4×C11⋊C8C2×C411yescharacteristic
71#9280—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11C22⋊C412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—41no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×C8×C11—21no—
81C2×C8×C11—22no—
82C2×C8×C11—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4C22⋊C412yes—
89C11×C22⋊C4—22no—
90C42×C11—22no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C22⋊Dic11—41no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—22no—
103C4×Dic11—41no—
104C4×Dic11—41no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108#3231—111no—
109#2985D1111yescharacteristic
110#1506—111no—
111#1506—111no—
112#1497—111no—
113#1287—111no—
114#1274—111no—
115C23×C11#12111yescharacteristic
116Q8×C11—42no—
117Q8×C11—41no—
118Q8×C11—41no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11C2×C22⋊C411yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×Dic11—42no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136Dic22—41no—
137Dic22—41no—
138Dic22—81no—
139C8×C11—41no—
140C8×C11—42no—
141C8×C11—41no—
142C11⋊C8—41no—
143C11⋊C8—41no—
144C11⋊C8—81no—
145#533—111no—
146#533C2×D1111yescharacteristic
147#500—111no—
148#498—111no—
149#487—111no—
150#487—111no—
151#485—222no—
152#479—222no—
153#446—22no—
154#446—21no—
155C8×Q8—21no—
156#433—22no—
157#432—111no—
158#432C2×D1111yescharacteristic
159#431—111no—
160#431C2×D1111yescharacteristic
161#376—111no—
162#328—222no—
163#328—222no—
164Q8⋊C8—221no—
165Q8⋊C8—221no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—42no—
176C4×C11—42no—
177C4×C11#44311yescharacteristic
178C4×C11#44411yescharacteristic
179Dic11—82no—
180Dic11—81no—
181Dic11—81no—
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184C4⋊Q8C4×D1111yescharacteristic
185C4⋊Q8C4×D1111yescharacteristic
186#125—21no—
187#125—221no—
188C22⋊Q8—21no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191C22⋊Q8D4412yes—
192C4×Q8—21no—
193C4×Q8—221no—
194C4×Q8—221no—
195C4×Q8C22⋊D1112yes—
196#117—21no—
197#117—221no—
198C2×C42—221no—
199C2×C42C22×D1111yescharacteristic
200#107—222no—
201#106—222no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#103—222no—
209#103—222no—
210C22⋊C8—21no—
211C22⋊C8—221no—
212C22⋊C8—221no—
213C22⋊C8C22⋊D1112yes—
214#97—22no—
215#97—21no—
216#97—221no—
217C4×C8—22no—
218C4×C8—111no—
219C4×C8—111no—
220C4×C8C22⋊D1111yescharacteristic
221C4×C8C22⋊D1111yescharacteristic
222#95—221no—
223#95—221no—
224C2×C11—41no—
225C2×C11#187611yescharacteristic
226C2×C11#190511yescharacteristic
227C2×C11#190911yescharacteristic
228C2×Q8—21no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8(C2×D11)⋊C412yes—
232C22×C4—441no—
233C22×C4C2×D4411yescharacteristic
234C22×C4#433911yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236C2×C8—21no—
237C2×C8—22no—
238C2×C8—21no—
239C2×C8—221no—
240C2×C8—221no—
241C2×C8—441no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4(C2×D11)⋊C412yes—
254C22⋊C4—22no—
255C22⋊C4—441no—
256C42—22no—
257C42—222no—
258C42—441no—
259C42—441no—
260C42C2×C4×D1111yescharacteristic
261C42#433911yescharacteristic
262C42C2×C22⋊D1111yescharacteristic
263C42C2×C22⋊D1111yescharacteristic
264C11#928011yescharacteristic, complemented, Sylow
265C23#6698311yescharacteristic
266Q8—42no—
267Q8—41no—
268Q8—41no—
269Q8—441no—
270Q8—441no—
271Q8—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—442no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—881no—
282C2×C4—881no—
283C2×C4C2×(C2×D11)⋊C411yescharacteristic
284C2×C4C4×C22⋊D1111yescharacteristic
285C2×C4C4×C22⋊D1111yescharacteristic
286C2×C4#6698211yescharacteristic
287C2×C4#6698311yescharacteristic
288C2×C4#6700611yescharacteristic
289C8—41no—
290C8—42no—
291C8—41no—
292C8—441no—
293C8—441no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1062282611yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—882no—
307C4—881no—
308C4—881no—
309C4#1062275711yescharacteristic
310C4#1062275811yescharacteristic
311C2—41no—
312C2#1306894311yescharacteristic
313C2#1306911011yescharacteristic
314C2#1306913811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2985C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#2985D11
hypocenterC11#9280
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2985

Complements

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

NH ≅ G/Ntype
16. #10622694C4semidirect
17. #10622694C4semidirect
18. #10622692C4semidirect
19. #10622691C4semidirect
264. C11#9280semidirect

Maximal subgroups

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

subgroupindex
#130797712
#130671292
#130671282
#130670902
#130664792
#130664442
C11×#29852
#928011