Finite Group Databasebeta

← #14650409

Subgroups — #14650409

Order 2816.

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

normal subgroups only

This group has 374 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#13079775C211yesmaximal, characteristic
2#13067232C211yesmaximal, characteristic
3#13067231C211yesmaximal, characteristic
4#13067090C211yesmaximal, characteristic
5#13066477C211yesmaximal, characteristic
6#13066446C211yesmaximal, 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#10622706C411yescharacteristic
17#10622706C411yescharacteristic
18#10622692C411yescharacteristic
19#10622691C411yescharacteristic
20#10622676—22no—
21#10622609—22no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25#10622181—22no—
26#10622103—22no—
27#10622094—21no—
28#10622094—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#125D412yes—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117D412yes—
37C2×C42×C11C2311yescharacteristic
38#66979—21no—
39#66977—21no—
40#66977—21no—
41C22×C11⋊C8—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⋊C8—21no—
53C11×#97—22no—
54C11×#97D412yes—
55C4×C8×C11—22no—
56C4×C8×C11D411yescharacteristic
57C4×C8×C11D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—22no—
61#66874—22no—
62#66872—22no—
63#66871—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8C2×C411yescharacteristic
70C4×C11⋊C8C2×C411yescharacteristic
71#9286—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×C8×C11—21no—
80C2×C8×C11—22no—
81C2×C8×C11—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4C22⋊C412yes—
87C11×C4⋊C4C22⋊C412yes—
88C11×C22⋊C4—22no—
89C42×C11—22no—
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C22⋊Dic11—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#3231—111no—
109#2985D1111yescharacteristic
110#1531—111no—
111#1531—111no—
112#1497—111no—
113#1287—111no—
114#1275—111no—
115C23×C11#12311yescharacteristic
116Q8×C11—41no—
117Q8×C11—41no—
118Q8×C11—81no—
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#12111yescharacteristic
131C2×Dic11—41no—
132C2×Dic11—41no—
133Dic22—42no—
134Dic22—41no—
135Dic22—41no—
136C8×C11—41no—
137C8×C11—42no—
138C8×C11—41no—
139C11⋊C8—41no—
140C11⋊C8—41no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143#533—111no—
144#533C2×D1111yescharacteristic
145#500—111no—
146#498—111no—
147#487—111no—
148#487—111no—
149#485—222no—
150#479—222no—
151#446—22no—
152#446—21no—
153C8×Q8—21no—
154#433—22no—
155#432—111no—
156#432C2×D1111yescharacteristic
157#431—111no—
158#431C2×D1111yescharacteristic
159C2×#97—111no—
160#330—222no—
161#330—222no—
162Q8⋊C8—221no—
163Q8⋊C8—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11#38611yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—42no—
175C4×C11#44311yescharacteristic
176C4×C11#44411yescharacteristic
177Dic11—81no—
178Dic11—81no—
179C22×C8—221no—
180C4⋊Q8—111no—
181C4⋊Q8—111no—
182C4⋊Q8C4×D1111yescharacteristic
183C4⋊Q8C4×D1111yescharacteristic
184#125—221no—
185#125D4412yes—
186C22⋊Q8—21no—
187C22⋊Q8—21no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C4×Q8—21no—
191C4×Q8—21no—
192C4×Q8—221no—
193C4×Q8—221no—
194#117—221no—
195#117C22⋊D1112yes—
196C2×C42C22×D1111yescharacteristic
197#107—222no—
198#106—222no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205#103—222no—
206#103—222no—
207C22⋊C8—21no—
208C22⋊C8—21no—
209C22⋊C8—221no—
210C22⋊C8—221no—
211#97—22no—
212#97—221no—
213#97—221no—
214#97—221no—
215#97C22⋊D1112yes—
216C4×C8—22no—
217C4×C8—111no—
218C4×C8—111no—
219C4×C8C22⋊D1111yescharacteristic
220C4×C8C22⋊D1111yescharacteristic
221C2×C11—41no—
222C2×C11#187611yescharacteristic
223C2×C11#190211yescharacteristic
224C2×C11#191211yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—221no—
228C2×Q8—221no—
229C22×C4#433911yescharacteristic
230C22×C4#433911yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—21no—
235C2×C8—222no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8—441no—
239C2×C8—441no—
240C2×C8—441no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C4⋊C4(C2×D11)⋊C412yes—
252C4⋊C4(C2×D11)⋊C412yes—
253C22⋊C4—22no—
254C22⋊C4—441no—
255C42—22no—
256C42—441no—
257C42C2×C4×D1111yescharacteristic
258C42C2×D4411yescharacteristic
259C42C2×C22⋊D1111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#928611yescharacteristic, complemented, Sylow
262C23#6698211yescharacteristic
263Q8—41no—
264Q8—41no—
265Q8—81no—
266Q8—442no—
267Q8—441no—
268Q8—441no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4C2×(C2×D11)⋊C411yescharacteristic
278C2×C4C4×C22⋊D1111yescharacteristic
279C2×C4C4×C22⋊D1111yescharacteristic
280C2×C4#6698311yescharacteristic
281C2×C4#6698311yescharacteristic
282C2×C4#6700611yescharacteristic
283C8—41no—
284C8—42no—
285C8—41no—
286C8—442no—
287C8—441no—
288C8—441no—
289C8—881no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22#1062282611yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—42no—
300C4—42no—
301C4—881no—
302C4—881no—
303C4#1062275711yescharacteristic
304C4#1062275811yescharacteristic
305C2—41no—
306C2#1306894311yescharacteristic
307C2#1306908911yescharacteristic
308C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2985C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#2985D11
hypocenterC11#9286
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
261. C11#9286semidirect

Maximal subgroups

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

subgroupindex
#130797752
#130672322
#130672312
#130670902
#130664772
#130664462
C11×#29852
#928611