Finite Group Databasebeta

← #14651405

Subgroups — #14651405

Order 2816.

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

normal subgroups only

This group has 456 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#13079019C211yesmaximal, characteristic
2#13071722C211yesmaximal, characteristic, complemented
3#13067125C212yesmaximal
4#13066508C212yesmaximal, complemented
5C11×#1534C211yesmaximal, characteristic, complemented
6C2×C11×#125C2211yescharacteristic
7#10623008C2211yescharacteristic
8C11×#432C2212yes—
9#10622682C412yescomplemented
10#10622681—22no—
11#10622680C412yescomplemented
12#10622594—22no—
13#10622594—22no—
14C4⋊C4×Dic11—22no—
15#10622579—22no—
16#10622545C2212yes—
17C4×#4318C2211yescharacteristic
18C11×#330—22no—
19#10622108—22no—
20#10622108—22no—
21C2×#4339—21no—
22C11×#125—22no—
23C11×#125C2×C412yes—
24C11×#125D412yes—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4D412yes—
27C2×C42×C11C2311yescharacteristic
28#66983—22no—
29C2×C4⋊Dic11—22no—
30C2×C4×Dic11—22no—
31C2×C4×Dic11—22no—
32C2×#4318—21no—
33#66928—21no—
34#66927C2×C411yescharacteristic
35C4×D44—22no—
36#66922C2×C411yescharacteristic
37C11×C4⋊C8—22no—
38C11×C22⋊C8—22no—
39C11×#97—22no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44C11⋊#95D412yes—
45#66874—24no—
46#66873—24no—
47#66867C2×C412yes—
48C4×C11⋊C8—21no—
49#9442—111nomaximal, Sylow
50C22×C4×C11—22no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C2×C22⋊D11—41no—
54C22×Dic11—22no—
55C22×Dic11—22no—
56#4339—44no—
57C2×D44—21no—
58C2×D44—22no—
59C2×C4×D11—41no—
60C2×Dic22—21no—
61C2×C8×C11—42no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4—24no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4C22⋊C414yes—
66C42×C11C22×C411yescharacteristic
67C42×C11C2×D411yescharacteristic
68C42×C11#4112yes—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—22no—
71C4⋊Dic11—44no—
72C4×Dic11—44no—
73C4×Dic11—44no—
74#4318—42no—
75C2×C11⋊C8—22no—
76#3142—111no—
77#2371—111no—
78#1534D1111yescharacteristic, complemented
79#1505—112no—
80#1300—112no—
81C23×C11#12011yescharacteristic
82C22×D11—41no—
83C2×C4×C11—22no—
84C2×C4×C11—24no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11C2×C22⋊C411yescharacteristic
89C2×C4×C11C4×D412yes—
90C2×C4×C11#12112yes—
91C2×C4×C11#12311yescharacteristic
92C22⋊D11—82no—
93C2×Dic11—24no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—41no—
99C2×Dic11—42no—
100D44—42no—
101D44—82no—
102C4×D11—82no—
103Dic22—42no—
104C8×C11—82no—
105C11⋊C8—42no—
106#532—111no—
107C2×#125C2×D1111yescharacteristic
108#491—112no—
109#490—112no—
110#488—222no—
111#432C2×D1112yes—
112#417—222no—
113C4×M16—111no—
114#387—222no—
115#387—222no—
116C4×C4⋊C4—222no—
117#376—112no—
118#330—22no—
119#327—222no—
120#327—222no—
121C22×C11—22no—
122C22×C11#38611yescharacteristic
123C22×C11#45412yes—
124C2×D11—81no—
125C2×D11—82no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—22no—
129C4×C11—22no—
130C4×C11—44no—
131Dic11—44no—
132Dic11—82no—
133Dic11—81no—
134C2×#41—221no—
135C2×M16—221no—
136C4⋊Q8—111no—
137#127—111no—
138#125—22no—
139#125C4×D1112yes—
140#125C22⋊D1112yes—
141#124—221no—
142#121—222no—
143C4×D4—222no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4D4412yes—
147C2×C42—222no—
148C2×C42—222no—
149C2×C42C22×D1111yescharacteristic
150C4⋊C8—22no—
151#103—224no—
152#102—224no—
153C22⋊C8—22no—
154#97—22no—
155#97—112no—
156C4×C8—221no—
157#95—112no—
158#95—112no—
159#95—222no—
160#95—222no—
161#95—222no—
162C2×C11—22no—
163C2×C11#188811yescharacteristic
164C2×C11#190612yes—
165D11—161no—
166#41—444no—
167C2×Q8—221no—
168C2×D4—222no—
169C2×D4—221no—
170C2×D4—441no—
171C22×C4—22no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4—441no—
175C22×C4C2×D4411yescharacteristic
176C22×C4D4×D1112yes—
177M16—442no—
178C2×C8—42no—
179C2×C8—222no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—24no—
183C4⋊C4—222no—
184C4⋊C4—444no—
185C4⋊C4(C2×D11)⋊C414yes—
186C22⋊C4—442no—
187C42—444no—
188C42—444no—
189C42C2×C4×D1111yescharacteristic
190C42#434112yes—
191C42C2×C22⋊D1111yescharacteristic
192C11#944211yescharacteristic, complemented, Sylow
193C23—441no—
194C23#6693511yescharacteristic
195Q8—442no—
196D4—442no—
197D4—882no—
198D4—882no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—224no—
205C2×C4—442no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—441no—
210C2×C4—442no—
211C2×C4—882no—
212C2×C4(C22⋊D11)⋊C412yes—
213C2×C4#6693911yescharacteristic
214C2×C4C2×(C2×D11)⋊C411yescharacteristic
215C2×C4#6699212yes—
216C8—82no—
217C8—442no—
218C22—22no—
219C22—882no—
220C22—881no—
221C22#1062236612yes—
222C22#1062257111yescharacteristic
223C4—22no—
224C4—22no—
225C4—21no—
226C4—21no—
227C4—44no—
228C4—444no—
229C4—882no—
230C4—881no—
231C2—22no—
232C2—1761no—
233C2#1306901711yescharacteristic
234C2#1306911512yes—
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1534C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1534D11
hypocenterC11#9442
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
2. #13071722C2semidirect
4. #13066508C2semidirect
5. C11×#1534C2semidirect
9. #10622682C4semidirect
11. #10622680C4semidirect
78. #1534D11semidirect
192. C11#9442semidirect

Maximal subgroups

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

subgroupindex
#130790192
#130717222
#130671252
#130665082
C11×#15342
#944211