Finite Group Databasebeta

← #14651390

Subgroups — #14651390

Order 2816.

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

normal subgroups only

This group has 490 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#13079002C211yesmaximal, characteristic
2#13071728C211yesmaximal, characteristic
3#13067129C212yesmaximal, complemented
4#13066508C212yesmaximal, complemented
5C11×#1533C211yesmaximal, characteristic
6C2×C11×#124C2211yescharacteristic
7#10623001C2211yescharacteristic
8C11×#432C2212yes—
9#10622843—21no—
10#10622838—21no—
11#10622833—21no—
12#10622828—21no—
13#10622669—22no—
14#10622668C414yescomplemented
15#10622564—22no—
16C22⋊C4×Dic11—22no—
17#10622545C2212yes—
18C4×#4318C2211yescharacteristic
19C11×#329—22no—
20#10622105—22no—
21#10622105—22no—
22C22×Q8×C11D411yescharacteristic
23C22×D4×C11D411yescharacteristic
24C23×Dic11—21no—
25C11×#124—22no—
26C11×#124C2×C412yes—
27C11×#124D412yes—
28C2×C11×C22⋊C4—22no—
29C2×C42×C11C2311yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11—21no—
32#66979—21no—
33C2×C4⋊Dic11—21no—
34#66977—22no—
35C2×C4×Dic11—22no—
36C2×C4×Dic11—21no—
37C2×#4318—21no—
38#66923—21no—
39#66922C2×C412yescomplemented
40C4×Dic22—22no—
41C11×C4⋊C8—22no—
42C11×C22⋊C8—22no—
43C11×#97—22no—
44#66899—24no—
45#66896—24no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95D412yes—
49C11⋊#95D412yes—
50#66867C2×C412yescomplemented
51C4×C11⋊C8—21no—
52#9439—111nomaximal, Sylow
53C24×C11—21no—
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11C22⋊C412yes—
58C2×D4×C11—21no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11C22⋊C412yes—
62C22×C4×C11—21no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—44no—
68C22×Dic11—81no—
69C2×Dic22—22no—
70C2×C8×C11—42no—
71C11×C22⋊C4—24no—
72C11×C22⋊C4—24no—
73C42×C11C22×C411yescharacteristic
74C42×C11C2×D411yescharacteristic
75C42×C11#4112yes—
76C22⋊Dic11—44no—
77C22⋊Dic11—41no—
78C22⋊Dic11—81no—
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81C4⋊Dic11—81no—
82Dic11⋊C4—42no—
83C4×Dic11—44no—
84C4×Dic11—41no—
85C4×Dic11—81no—
86#4318—41no—
87#4318—41no—
88C2×C11⋊C8—22no—
89#3140—111no—
90#2372—111no—
91#1533D1111yescharacteristic
92#1506—112no—
93#1300—112no—
94C23×C11—22no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#12011yescharacteristic
100Q8×C11—42no—
101Q8×C11—81no—
102D4×C11—42no—
103D4×C11—81no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11C4×D412yes—
112C2×C4×C11#12112yes—
113C2×C4×C11#12311yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—84no—
122Dic22—82no—
123C8×C11—82no—
124C11⋊C8—42no—
125#533—111no—
126C2×#124C2×D1111yescharacteristic
127#489—114no—
128#488—222no—
129#432C2×D1112yes—
130#419—221no—
131#418—221no—
132C4×M16—111no—
133#391—221no—
134#388—222no—
135#386—221no—
136C4×C22⋊C4—222no—
137#376—112no—
138#329—22no—
139#328—222no—
140#328—222no—
141C22×C11—22no—
142C22×C11—42no—
143C22×C11—44no—
144C22×C11—81no—
145C22×C11—82no—
146C22×C11—81no—
147C22×C11#38611yescharacteristic
148C22×C11#45511yescharacteristic
149C22×C11#45511yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—42no—
155Dic11—44no—
156Dic11—82no—
157Dic11—82no—
158C22×Q8D4411yescharacteristic
159C22×D4D4411yescharacteristic
160C23×C4—221no—
161C2×M16—221no—
162C4⋊Q8—112no—
163#125—221no—
164#124—22no—
165#124C4×D1112yes—
166#124C22⋊D1112yes—
167C22⋊Q8—222no—
168C4×Q8—222no—
169#117—221no—
170C2×C4⋊C4—221no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—222no—
173C2×C22⋊C4—221no—
174C2×C42—222no—
175C2×C42—221no—
176C2×C42C22×D1111yescharacteristic
177C4⋊C8—22no—
178#103—224no—
179#102—224no—
180C22⋊C8—22no—
181#97—22no—
182#97—112no—
183C4×C8—221no—
184#95—112no—
185#95—112no—
186#95—222no—
187#95—222no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—82no—
191C2×C11#188511yescharacteristic
192C2×C11#190612yes—
193C24—21no—
194C2×Q8—21no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—222no—
198C2×Q8(C2×D11)⋊C412yes—
199C2×D4—21no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4(C2×D11)⋊C412yes—
203C22×C4—21no—
204C22×C4—222no—
205C22×C4—222no—
206C22×C4—444no—
207C22×C4—881no—
208C22×C4C2×D4411yescharacteristic
209C22×C4D4×D1112yes—
210M16—441no—
211M16—441no—
212C2×C8—42no—
213C2×C8—222no—
214C4⋊C4—222no—
215C4⋊C4—222no—
216C4⋊C4—442no—
217C4⋊C4—881no—
218C22⋊C4—24no—
219C22⋊C4—24no—
220C22⋊C4—444no—
221C22⋊C4—441no—
222C22⋊C4—881no—
223C42—444no—
224C42—441no—
225C42—881no—
226C42C2×C4×D1111yescharacteristic
227C42#434112yes—
228C42C2×C22⋊D1111yescharacteristic
229C11#943911yescharacteristic, complemented, Sylow
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23#6693511yescharacteristic
236Q8—42no—
237Q8—81no—
238Q8—882no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—224no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—884no—
255C2×C4(C22⋊D11)⋊C412yes—
256C2×C4#6693911yescharacteristic
257C2×C4C2×(C2×D11)⋊C411yescharacteristic
258C2×C4#6699212yes—
259C8—82no—
260C8—442no—
261C22—22no—
262C22—44no—
263C22—42no—
264C22—81no—
265C22—81no—
266C22—82no—
267C22#1062235911yescharacteristic
268C22#1062235911yescharacteristic
269C22#1062257111yescharacteristic
270C4—22no—
271C4—22no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—444no—
276C4—882no—
277C4—882no—
278C2—21no—
279C2—21no—
280C2—82no—
281C2#1306900211yescharacteristic
282C2#1306911512yes—
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1533C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1533D11
hypocenterC11#9439
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1533

Complements

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

NH ≅ G/Ntype
3. #13067129C2semidirect
4. #13066508C2semidirect
14. #10622668C4semidirect
39. #66922C2×C4semidirect
50. #66867C2×C4semidirect
229. C11#9439semidirect

Maximal subgroups

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

subgroupindex
#130790022
#130717282
#130671292
#130665082
C11×#15332
#943911