Finite Group Databasebeta

← #14651335

Subgroups — #14651335

Order 2816.

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

normal subgroups only

This group has 444 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#13079012C211yesmaximal, characteristic
2#13071797C211yesmaximal, characteristic, complemented
3#13067164C211yesmaximal, characteristic
4#13067164C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic, complemented
6#13066482C211yesmaximal, characteristic, complemented
7C11×#1556C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622843—22no—
13#10622706C412yescomplemented
14#10622702—22no—
15#10622701C412yescomplemented
16#10622594—22no—
17#10622594—22no—
18#10622579—22no—
19#10622550C2211yescharacteristic
20#10622550C2211yescharacteristic
21C4×#4318C2211yescharacteristic
22C11×#332—22no—
23#10622108—22no—
24#10622108—22no—
25C22×Q8×C11—21no—
26C2×#4339—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8C2×C412yes—
30C11×C4⋊Q8D412yes—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D412yes—
33C2×C42×C11C2311yescharacteristic
34#66983—21no—
35#66983—21no—
36C2×C4⋊Dic11—22no—
37C2×C4×Dic11—22no—
38C2×#4318—21no—
39#66928—21no—
40#66927C2×C411yescharacteristic
41C4×D44—21no—
42C4×D44—21no—
43#66922C2×C411yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#97—21no—
49C11×#97—21no—
50C11⋊#95—24no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95D412yes—
56C11⋊#95D412yes—
57#66874—24no—
58#66873—24no—
59#66867—21no—
60C4×C11⋊C8C2×C412yes—
61#9430—111nomaximal, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—22no—
64C2×Q8×C11—81no—
65C2×Q8×C11—81no—
66C22×C4×C11—22no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—41no—
71C22×Dic11—22no—
72C22×Dic11—22no—
73#4339—44no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×C4×D11—41no—
78C2×Dic22—21no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4C22⋊C414yes—
85C42×C11C22×C411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—82no—
94C4×Dic11—82no—
95#4318—42no—
96C2×C11⋊C8—22no—
97#3141—111no—
98#2381—111no—
99#1556D1111yescharacteristic, complemented
100#1514—111no—
101#1514—111no—
102#1288—111no—
103#1288—111no—
104C23×C11#12011yescharacteristic
105C22×D11—41no—
106Q8×C11—82no—
107Q8×C11—82no—
108C2×C4×C11—22no—
109C2×C4×C11—24no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12311yescharacteristic
120C22⋊D11—82no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—41no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128D44—42no—
129D44—81no—
130D44—81no—
131C4×D11—82no—
132Dic22—42no—
133C8×C11—81no—
134C8×C11—81no—
135C11⋊C8—42no—
136#532—111no—
137C2×C4⋊Q8C2×D1111yescharacteristic
138#489—222no—
139#487—112no—
140#486—112no—
141#432C2×D1111yescharacteristic
142#432C2×D1111yescharacteristic
143#417—222no—
144C4×M16—111no—
145#391—222no—
146#387—222no—
147#387—222no—
148#383—111no—
149#383—111no—
150#332—22no—
151#327—222no—
152#327—222no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#38611yescharacteristic
156C22×C11#45412yes—
157C2×D11—81no—
158C2×D11—81no—
159C2×D11—81no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—44no—
167Dic11—82no—
168Dic11—82no—
169Dic11—81no—
170C2×#41—221no—
171C22×Q8—21no—
172C2×M16—221no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—111no—
176C4⋊Q8C4×D1112yes—
177C4⋊Q8C22⋊D1112yes—
178#127—111no—
179#124—221no—
180#121—221no—
181#121—221no—
182C4×D4—221no—
183C4×D4—221no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—222no—
186C2×C4⋊C4D4412yes—
187C2×C42—222no—
188C2×C42C22×D1111yescharacteristic
189C4⋊C8—21no—
190C4⋊C8—21no—
191#103—224no—
192#102—224no—
193C22⋊C8—21no—
194C22⋊C8—21no—
195#97—21no—
196#97—21no—
197#97—221no—
198C4×C8—112no—
199#95—112no—
200#95—112no—
201#95—224no—
202#95—221no—
203#95—221no—
204#95—221no—
205#95—221no—
206C2×C11—22no—
207C2×C11#188811yescharacteristic
208C2×C11#190411yescharacteristic
209C2×C11#190511yescharacteristic
210D11—161no—
211#41—444no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—81no—
215C2×Q8—81no—
216C2×Q8—221no—
217C2×D4—221no—
218C2×D4—221no—
219C2×D4—221no—
220C2×D4—441no—
221C22×C4—22no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—441no—
225C22×C4C2×D4411yescharacteristic
226C22×C4D4×D1111yescharacteristic
227C22×C4D4×D1111yescharacteristic
228M16—442no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—222no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—882no—
238C4⋊C4(C2×D11)⋊C414yes—
239C22⋊C4—441no—
240C22⋊C4—441no—
241C42—882no—
242C42C2×C4×D1111yescharacteristic
243C42#434111yescharacteristic
244C42#434111yescharacteristic
245C42C2×C22⋊D1111yescharacteristic
246C11#943011yescharacteristic, complemented, Sylow
247C23—441no—
248C23#6693511yescharacteristic
249Q8—82no—
250Q8—82no—
251Q8—442no—
252D4—442no—
253D4—881no—
254D4—881no—
255D4—882no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—441no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—882no—
270C2×C4(C22⋊D11)⋊C411yescharacteristic
271C2×C4(C22⋊D11)⋊C411yescharacteristic
272C2×C4#6693911yescharacteristic
273C2×C4C2×(C2×D11)⋊C411yescharacteristic
274C2×C4#6699211yescharacteristic
275C2×C4#6699211yescharacteristic
276C8—81no—
277C8—81no—
278C8—442no—
279C22—21no—
280C22—21no—
281C22—881no—
282C22—881no—
283C22—881no—
284C22#1062236612yes—
285C22#1062257111yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—44no—
293C4—882no—
294C4—882no—
295C4—881no—
296C2—22no—
297C2—1761no—
298C2#1306901711yescharacteristic
299C2#1306910111yescharacteristic
300C2#1306910811yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1556C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1556D11
hypocenterC11#9430
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
2. #13071797C2semidirect
5. #13066482C2semidirect
6. #13066482C2semidirect
7. C11×#1556C2semidirect
13. #10622706C4semidirect
15. #10622701C4semidirect
99. #1556D11semidirect
246. C11#9430semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130717972
#130671642
#130664822
C11×#15562
#943011