Finite Group Databasebeta

← #14650365

Subgroups — #14650365

Order 2816.

382 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077711C211yesmaximal, characteristic
3#13067127C211yesmaximal, characteristic
4#13067088C211yesmaximal, characteristic
5#13066477C211yesmaximal, characteristic
6#13066445C211yesmaximal, characteristic
7C11×#1506C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622694C411yescharacteristic, complemented
13#10622694C411yescharacteristic, complemented
14#10622692C411yescharacteristic, complemented
15#10622691C411yescharacteristic, complemented
16#10622658—22no—
17#10622637—22no—
18#10622637—21no—
19Q8×C11⋊C8—21no—
20#10622635—22no—
21#10622613—22no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25C11×#328—22no—
26#10622122—21no—
27#10622122—21no—
28#10622090—22no—
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×C11—21no—
38C2×C42×C11C2311yescharacteristic
39#66979—21no—
40#66977—21no—
41#66977—21no—
42#66923—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#95—21no—
51C11×#95—21no—
52#66899—22no—
53#66899—22no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)D412yes—
57#66872—22no—
58#66871—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—22no—
65#66867—21no—
66C4×C11⋊C8—22no—
67C4×C11⋊C8C2×C411yescharacteristic
68C4×C11⋊C8C2×C411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9280—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11C22⋊C412yes—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4C22⋊C412yes—
87C11×C22⋊C4—22no—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11—41no—
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—41no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—21no—
108#3231—111no—
109#2985—111no—
110#1506—111no—
111#1506D1111yescharacteristic
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×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×Dic11—41no—
135C2×Dic11—41no—
136Dic22—41no—
137Dic22—41no—
138Dic22—81no—
139C8×C11—81no—
140C11⋊C8—41no—
141C11⋊C8—42no—
142C11⋊C8—41no—
143C11⋊C8—41no—
144C11⋊C8—41no—
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—221no—
154#446—222no—
155C8×Q8—221no—
156#433—222no—
157#432—111no—
158#432C2×D1111yescharacteristic
159#431—111no—
160#431—111no—
161#376C2×D1111yescharacteristic
162#328—22no—
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—82no—
178C4×C11#44311yescharacteristic
179C4×C11#44411yescharacteristic
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⋊Q8C22⋊D1112yes—
192C4×Q8—21no—
193C4×Q8—221no—
194C4×Q8—221no—
195C4×Q8D4412yes—
196#117—21no—
197#117—221no—
198C2×C42—21no—
199C2×C42C22×D1111yescharacteristic
200#107—222no—
201#106—222no—
202C4⋊C8—21no—
203C4⋊C8—222no—
204C4⋊C8—222no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#103—222no—
209#103—222no—
210C22⋊C8—21no—
211C22⋊C8—112no—
212C22⋊C8—221no—
213C22⋊C8—221no—
214#97—21no—
215#97—222no—
216#97—221no—
217C4×C8—111no—
218C4×C8—111no—
219C4×C8—111no—
220C4×C8—111no—
221C4×C8—222no—
222#95—21no—
223#95—21no—
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—41no—
233C22×C4D4×D1111yescharacteristic
234C22×C4#434111yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236C2×C8—41no—
237C2×C8—221no—
238C2×C8—221no—
239C2×C8—222no—
240C2×C8—221no—
241C2×C8—221no—
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—22no—
258C42—41no—
259C42—441no—
260C42C2×C4×D1111yescharacteristic
261C42C2×D4411yescharacteristic
262C42D4×D1111yescharacteristic
263C42#434111yescharacteristic
264C11#928011yescharacteristic, complemented, Sylow
265C23#6699211yescharacteristic
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—42no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4(C22⋊D11)⋊C411yescharacteristic
284C2×C4(C22⋊D11)⋊C411yescharacteristic
285C2×C4#6693511yescharacteristic
286C2×C4#6693911yescharacteristic
287C2×C4C2×(C2×D11)⋊C411yescharacteristic
288C2×C4#6699211yescharacteristic
289C8—81no—
290C8—441no—
291C8—441no—
292C8—442no—
293C8—441no—
294C8—441no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1062257111yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—82no—
307C4—881no—
308C4—881no—
309C4#1062243611yescharacteristic
310C4#1062243711yescharacteristic
311C2—41no—
312C2#1306894111yescharacteristic
313C2#1306910811yescharacteristic
314C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1506D11
hypocenterC11#9280
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
12. #10622694C4semidirect
13. #10622694C4semidirect
14. #10622692C4semidirect
15. #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
#130777112
#130671272
#130670882
#130664772
#130664452
C11×#15062
#928011