Finite Group Databasebeta

← #14651221

Subgroups — #14651221

Order 2816.

644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 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#13074096C211yesmaximal, characteristic
2#13070973C211yesmaximal, characteristic, complemented
3#13067133C212yesmaximal
4#13066501C212yesmaximal, complemented
5C11×#1463C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66979—21no—
9C11×#407C2212yes—
10#10622826—21no—
11#10622826—21no—
12C4×C22⋊Dic11—21no—
13C4×C22⋊Dic11C2211yescharacteristic
14C4×C22⋊Dic11C2212yes—
15#10622604C412yescomplemented
16#10622603—22no—
17#10622599C412yescomplemented
18C4⋊C4×Dic11—24no—
19C11×#324—22no—
20#10622108—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C2×C11×M16—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4D412yes—
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—21no—
33#66983—22no—
34#66983—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—22no—
38#66979—28no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×C4×Dic11—22no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11—22no—
44C2×C4×Dic11—21no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95C2×C412yes—
51C11⋊#95D414yes—
52#9410—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C23×D11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—24no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—81no—
61C22×C4×C11—81no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4112yes—
68C2×C22⋊D11—44no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C22×Dic11—21no—
72C22×Dic11—22no—
73C22×Dic11—24no—
74C2×D44—22no—
75C2×D44—81no—
76C11×M16—82no—
77C2×C8×C11—42no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—24no—
80C22⋊Dic11—28no—
81C22⋊Dic11—42no—
82(C2×D11)⋊C4—44no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—82no—
85C4⋊Dic11—28no—
86C4⋊Dic11—22no—
87C4×Dic11—28no—
88C4×Dic11—82no—
89C4×Dic11—81no—
90C4×Dic11—82no—
91#2591—111no—
92#2274—111no—
93#1507—112no—
94#1463D1111yescharacteristic, complemented
95#1297—112no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—41no—
99C23×C11C2×C22⋊C411yescharacteristic
100C23×C11#12011yescharacteristic
101C23×C11#12311yescharacteristic
102C22×D11—42no—
103C22×D11—42no—
104C22×D11—41no—
105C22×D11—42no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—24no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—81no—
119C2×C4×C11#10414yes—
120C2×C4×C11C4×D412yes—
121C2×C4×C11#12112yes—
122C22⋊D11—82no—
123C22⋊D11—82no—
124C2×Dic11—28no—
125C2×Dic11—44no—
126C2×Dic11—44no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—41no—
131C2×Dic11—42no—
132D44—82no—
133C8×C11—82no—
134C2×#121—111no—
135C2×#117—221no—
136C22×C4⋊C4C2×D1111yescharacteristic
137#407C2×D1112yes—
138#400—112no—
139#394—112no—
140#388—222no—
141#386—221no—
142#386—221no—
143C4×C4⋊C4—224no—
144C4×C22⋊C4—111no—
145C4×C22⋊C4—112no—
146C4×C22⋊C4—221no—
147#327—224no—
148#324—22no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—44no—
157C22×C11#38611yescharacteristic
158C22×C11C2×#10412yes—
159C22×C11#45412yes—
160C2×D11—84no—
161C2×D11—81no—
162C2×D11—81no—
163C2×D11—81no—
164C4×C11—24no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—42no—
168Dic11—48no—
169Dic11—82no—
170Dic11—81no—
171C22×D4—111no—
172C22×D4—221no—
173C23×C4D4411yescharacteristic
174C23×C4D4411yescharacteristic
175C23×C4C22×D1111yescharacteristic
176C2×M16—22no—
177#121—222no—
178#121—222no—
179#117—228no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—222no—
184C2×C4⋊C4C4×D1112yes—
185C2×C4⋊C4C22⋊D1112yes—
186C2×C22⋊C4—222no—
187C2×C22⋊C4—221no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—221no—
190C2×C22⋊C4—222no—
191C2×C42—222no—
192C2×C42—222no—
193C2×C42—222no—
194C2×C42—221no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197#95—112no—
198#95—114no—
199#95—222no—
200#95—222no—
201#95—222no—
202C2×C11—22no—
203C2×C11—22no—
204C2×C11—41no—
205C2×C11#188811yescharacteristic
206C2×C11#189611yescharacteristic
207C2×C11#191311yescharacteristic
208D11—161no—
209C24—221no—
210C24C2×D4411yescharacteristic
211C2×D4—222no—
212C2×D4—444no—
213C2×D4—441no—
214C2×D4—441no—
215C2×D4—881no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—81no—
222C22×C4—81no—
223C22×C4—224no—
224C22×C4—222no—
225C22×C4—221no—
226C22×C4(C2×D11)⋊C412yes—
227C22×C4(C2×D11)⋊C412yes—
228C22×C4C2×C4×D1111yescharacteristic
229C22×C4D4×D1112yes—
230C22×C4#434112yes—
231C22×C4C2×C22⋊D1111yescharacteristic
232M16—82no—
233C2×C8—42no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—228no—
237C4⋊C4—222no—
238C22⋊C4—228no—
239C22⋊C4—442no—
240C22⋊C4—444no—
241C22⋊C4—442no—
242C22⋊C4—882no—
243C42—228no—
244C42—882no—
245C42—881no—
246C42—882no—
247C11#941011yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—41no—
251C23—442no—
252C23—442no—
253C23—442no—
254C23—441no—
255C23#6693511yescharacteristic
256C23#6693911yescharacteristic
257C23C2×(C2×D11)⋊C411yescharacteristic
258D4—882no—
259D4—882no—
260D4—882no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—228no—
275C2×C4—444no—
276C2×C4—444no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4—441no—
282C2×C4#6688914yes—
283C2×C4(C22⋊D11)⋊C412yes—
284C2×C4#6699212yes—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—884no—
295C22—881no—
296C22—881no—
297C22—881no—
298C22#1062236612yes—
299C22#1062257111yescharacteristic
300C22C2×#6688912yes—
301C4—24no—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—448no—
306C4—882no—
307C4—881no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—1761no—
312C2#1306901711yescharacteristic
313C2#1306905711yescharacteristic
314C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1463C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1463D11
hypocenterC11#9410
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #13070973C2semidirect
4. #13066501C2semidirect
5. C11×#1463C2semidirect
15. #10622604C4semidirect
17. #10622599C4semidirect
94. #1463D11semidirect
247. C11#9410semidirect

Maximal subgroups

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

subgroupindex
#130740962
#130709732
#130671332
#130665012
C11×#14632
#941011