Finite Group Databasebeta

← #14651308

Subgroups — #14651308

Order 2816.

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

normal subgroups only

This group has 534 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#13078990C211yesmaximal, characteristic
2#13071793C211yesmaximal, characteristic
3#13067168C212yesmaximal, complemented
4#13066482C212yesmaximal, complemented
5C11×#1555C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7#10623001C2211yescharacteristic
8C11×#432C2212yes—
9#10622833—22no—
10#10622833—24no—
11#10622828—22no—
12#10622684—22no—
13#10622683C414yescomplemented
14#10622550C2212yes—
15C4×#4318C2211yescharacteristic
16C11×#331—22no—
17#10622105—24no—
18C22×D4×C11—22no—
19C22×D4×C11D412yes—
20C23×Dic11—22no—
21C11×#127—22no—
22C11×#127C2×C412yes—
23C11×#127D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C22⋊Dic11—24no—
26C2×C22⋊Dic11—22no—
27#66979—21no—
28#66977—22no—
29C2×#4318—21no—
30#66923—21no—
31#66922C2×C412yescomplemented
32C4×Dic22—22no—
33C11×C4⋊C8—22no—
34C11×C22⋊C8—22no—
35C11×#97—22no—
36#66896—28no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95D414yes—
40#66867—21no—
41C4×C11⋊C8C2×C412yescomplemented
42#9425—111nomaximal, Sylow
43C24×C11—22no—
44C2×D4×C11—24no—
45C2×D4×C11—24no—
46C2×D4×C11—22no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—82no—
50C2×D4×C11—82no—
51C2×D4×C11C22⋊C414yes—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D412yes—
54C22×Dic11—24no—
55C22×Dic11—84no—
56C22×Dic11—82no—
57C2×Dic22—22no—
58C2×C8×C11—42no—
59C42×C11C22×C411yescharacteristic
60C42×C11C2×D411yescharacteristic
61C42×C11#4112yes—
62C22⋊Dic11—41no—
63C22⋊Dic11—84no—
64C22⋊Dic11—82no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67Dic11⋊C4—42no—
68C4×Dic11—41no—
69#4318—42no—
70C2×C11⋊C8—22no—
71#3138—111no—
72#2380—111no—
73#1555D1111yescharacteristic
74#1515—112no—
75#1288—112no—
76C23×C11—24no—
77C23×C11—44no—
78C23×C11—44no—
79C23×C11—42no—
80C23×C11—42no—
81C23×C11#12011yescharacteristic
82D4×C11—44no—
83D4×C11—82no—
84D4×C11—84no—
85D4×C11—84no—
86C2×C4×C11—22no—
87C2×C4×C11—42no—
88C2×C4×C11C2×C22⋊C411yescharacteristic
89C2×C4×C11C4×D412yes—
90C2×C4×C11#12112yes—
91C2×C4×C11#12311yescharacteristic
92C2×Dic11—48no—
93C2×Dic11—42no—
94C2×Dic11—44no—
95C2×Dic11—88no—
96Dic22—82no—
97C8×C11—82no—
98C11⋊C8—42no—
99#533—111no—
100C2×#127C2×D1111yescharacteristic
101#490—222no—
102#486—114no—
103#432C2×D1112yes—
104#418—222no—
105C4×M16—111no—
106#386—224no—
107#386—222no—
108#383—112no—
109#331—22no—
110#328—224no—
111C22×C11—22no—
112C22×C11—44no—
113C22×C11—48no—
114C22×C11—82no—
115C22×C11—84no—
116C22×C11—82no—
117C22×C11#38611yescharacteristic
118C22×C11#45512yes—
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—22no—
122C4×C11—22no—
123Dic11—84no—
124Dic11—82no—
125C22×D4—22no—
126C22×D4D4412yes—
127C23×C4—222no—
128C2×M16—221no—
129C4⋊Q8—112no—
130#127—22no—
131#127C4×D1112yes—
132#127C22⋊D1112yes—
133#125—221no—
134C22⋊Q8—222no—
135C4×Q8—222no—
136#117—221no—
137C2×C22⋊C4—224no—
138C2×C22⋊C4—222no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—22no—
141#102—228no—
142C22⋊C8—22no—
143#97—22no—
144#97—221no—
145C4×C8—112no—
146#95—114no—
147#95—222no—
148#95—222no—
149C2×C11—22no—
150C2×C11—84no—
151C2×C11#188511yescharacteristic
152C2×C11#190412yes—
153C24—22no—
154C2×Q8—222no—
155C2×D4—24no—
156C2×D4—22no—
157C2×D4—24no—
158C2×D4—42no—
159C2×D4—42no—
160C2×D4—82no—
161C2×D4—82no—
162C2×D4(C2×D11)⋊C414yes—
163C22×C4—224no—
164C22×C4—884no—
165C22×C4—882no—
166C22×C4C2×D4411yescharacteristic
167C22×C4D4×D1112yes—
168M16—442no—
169C2×C8—42no—
170C2×C8—222no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—442no—
174C22⋊C4—441no—
175C22⋊C4—884no—
176C22⋊C4—882no—
177C42—441no—
178C42C2×C4×D1111yescharacteristic
179C42#434112yes—
180C42C2×C22⋊D1111yescharacteristic
181C11#942511yescharacteristic, complemented, Sylow
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#6693511yescharacteristic
188Q8—882no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—448no—
196C2×C4—442no—
197C2×C4—444no—
198C2×C4—888no—
199C2×C4(C22⋊D11)⋊C412yes—
200C2×C4#6693911yescharacteristic
201C2×C4C2×(C2×D11)⋊C411yescharacteristic
202C2×C4#6699212yes—
203C8—82no—
204C8—442no—
205C22—22no—
206C22—48no—
207C22—44no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1062235912yes—
212C22#1062257111yescharacteristic
213C4—22no—
214C4—22no—
215C4—21no—
216C4—21no—
217C4—884no—
218C4—882no—
219C2—22no—
220C2—84no—
221C2#1306900211yescharacteristic
222C2#1306910112yes—
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1555C2
socleC22×C11#386
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1555D11
hypocenterC11#9425
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
3. #13067168C2semidirect
4. #13066482C2semidirect
13. #10622683C4semidirect
31. #66922C2×C4semidirect
41. C4×C11⋊C8C2×C4semidirect
181. C11#9425semidirect

Maximal subgroups

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

subgroupindex
#130789902
#130717932
#130671682
#130664822
C11×#15552
#942511