Finite Group Databasebeta

← #14651262

Subgroups — #14651262

Order 2816.

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

normal subgroups only

This group has 442 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#13079350C211yesmaximal, characteristic
2#13067250C211yesmaximal, characteristic, complemented
3#13067164C211yesmaximal, characteristic, complemented
4#13067163C211yesmaximal, characteristic, complemented
5#13066489C211yesmaximal, characteristic, complemented
6#13066482C211yesmaximal, characteristic, complemented
7C11×#2980C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#435—22no—
11C11×#435—22no—
12C11×#432C2211yescharacteristic
13C11×#432C2211yescharacteristic
14C11×#408—22no—
15#10622701C411yescharacteristic, complemented
16#10622692C411yescharacteristic, complemented
17#10622686C411yescharacteristic, complemented
18#10622683C411yescharacteristic, complemented
19#10622652—22no—
20#10622627—22no—
21#10622550C2211yescharacteristic
22#10622539C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622175—22no—
25#10622108—22no—
26#10622102—22no—
27C2×C11×#41—21no—
28C2×#4339—21no—
29C2×C11×M16—22no—
30C22×C8×C11—22no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#127C2×C411yescharacteristic
33C11×#124—21no—
34C11×#121—21no—
35C11×#121D412yes—
36C4×D4×C11—21no—
37C4×D4×C11D412yes—
38C2×C42×C11C2311yescharacteristic
39C2×#4323—22no—
40#66983—21no—
41#66983—21no—
42C2×#4318—21no—
43#66928—21no—
44#66927C2×C411yescharacteristic
45C4×D44—21no—
46C4×D44—21no—
47#66922C2×C411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—24no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8D412yes—
53C11×#97—21no—
54C11×#97D412yes—
55#66896—22no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—21no—
60#66873—22no—
61#66872—22no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8C2×C411yescharacteristic
66C4×C11⋊C8C2×C411yescharacteristic
67#9417—111nomaximal, Sylow
68C11×#41—81no—
69C11×#41—81no—
70C2×Q8×C11—21no—
71C2×D4×C11—22no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11C22⋊C412yes—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—41no—
80C22×Dic11—41no—
81#4339—82no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C11×M16—82no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—82no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4C22⋊C412yes—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99#4323—44no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104#4318—42no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108#3184—111no—
109#2980D1111yescharacteristic, complemented
110#1536—111no—
111#1514—111no—
112#1514—111no—
113#1291—111no—
114#1288—111no—
115C23×C11—22no—
116C23×C11#12111yescharacteristic
117C22×D11—41no—
118Q8×C11—81no—
119D4×C11—42no—
120D4×C11—81no—
121D4×C11—81no—
122D4×C11—82no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11C2×C22⋊C411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C22⋊D11—82no—
136C2×Dic11—41no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140D44—42no—
141D44—81no—
142D44—81no—
143C4×D11—82no—
144Dic22—81no—
145C8×C11—42no—
146C8×C11—42no—
147C11⋊C8—22no—
148C11⋊C8—41no—
149C11⋊C8—81no—
150#532—111no—
151#532C2×D1111yescharacteristic
152#498—111no—
153#493—111no—
154#486—111no—
155#486—111no—
156#469—222no—
157#442—222no—
158#435—22no—
159#435—22no—
160#432—111no—
161#432C2×D1111yescharacteristic
162#432C2×D1111yescharacteristic
163#408—22no—
164C4×M16—111no—
165#383—111no—
166#329—222no—
167#327—222no—
168#327—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11#38611yescharacteristic
176C2×D11—81no—
177C2×D11—81no—
178C2×D11—81no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186Dic11—81no—
187Dic11—161no—
188C2×#41—21no—
189C2×#41—221no—
190C2×D8—222no—
191C2×M16—22no—
192C2×M16—221no—
193C22×C8—22no—
194C4⋊Q8—111no—
195C4⋊Q8C4×D1111yescharacteristic
196#127—111no—
197#127C4×D1111yescharacteristic
198#124—21no—
199#124—221no—
200#121—21no—
201#121—221no—
202#121—221no—
203#121D4412yes—
204C4×D4—21no—
205C4×D4—221no—
206C4×D4—221no—
207C4×D4C22⋊D1112yes—
208C2×C42C22×D1111yescharacteristic
209#106—222no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—221no—
213#102—222no—
214#102—222no—
215C22⋊C8—24no—
216C22⋊C8—21no—
217C22⋊C8—221no—
218C22⋊C8C22⋊D1112yes—
219#97—21no—
220#97—221no—
221#97—221no—
222#97C22⋊D1112yes—
223C4×C8—111no—
224C4×C8—111no—
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11—41no—
229C2×C11—82no—
230C2×C11#188411yescharacteristic
231C2×C11#190311yescharacteristic
232C2×C11#190411yescharacteristic
233D11—161no—
234#41—81no—
235#41—81no—
236#41—882no—
237C2×Q8—21no—
238C2×Q8—221no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—441no—
246C2×D4(C2×D11)⋊C412yes—
247C22×C4—22no—
248C22×C4—441no—
249C22×C4—441no—
250C22×C4C2×D4411yescharacteristic
251C22×C4#433911yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253D8—444no—
254M16—82no—
255M16—442no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—82no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4(C2×D11)⋊C412yes—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—441no—
269C22⋊C4—441no—
270C42C2×C4×D1111yescharacteristic
271C42#433911yescharacteristic
272C42C2×C22⋊D1111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#941711yescharacteristic, complemented, Sylow
275C23—22no—
276C23—441no—
277C23#6698311yescharacteristic
278Q8—81no—
279Q8—881no—
280D4—42no—
281D4—81no—
282D4—81no—
283D4—82no—
284D4—442no—
285D4—881no—
286D4—881no—
287D4—882no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—441no—
295C2×C4—882no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4C2×(C2×D11)⋊C411yescharacteristic
300C2×C4C4×C22⋊D1111yescharacteristic
301C2×C4C4×C22⋊D1111yescharacteristic
302C2×C4#6698211yescharacteristic
303C2×C4#6698311yescharacteristic
304C2×C4#6700611yescharacteristic
305C8—42no—
306C8—42no—
307C8—222no—
308C8—441no—
309C8—881no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22#1062282611yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—881no—
328C4—1761no—
329C2—41no—
330C2—82no—
331C2—1761no—
332C2#1306899911yescharacteristic
333C2#1306909611yescharacteristic
334C2#1306910311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2980C2
socleC22×C11#386
prime radical#13079350C2
cosocleC2×C42×C11C23
hypercenter#2980D11
hypocenterC11#9417
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #13067250C2semidirect
3. #13067164C2semidirect
4. #13067163C2semidirect
5. #13066489C2semidirect
6. #13066482C2semidirect
7. C11×#2980C2semidirect
15. #10622701C4semidirect
16. #10622692C4semidirect
17. #10622686C4semidirect
18. #10622683C4semidirect
109. #2980D11semidirect
274. C11#9417semidirect

Maximal subgroups

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

subgroupindex
#130793502
#130672502
#130671642
#130671632
#130664892
#130664822
C11×#29802
#941711