Finite Group Databasebeta

← #14763230

Subgroups — #14763230

Order 2816.

990 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 315 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#13071219C212yesmaximal
2#13069602C218yesmaximal
3#13068693C214yesmaximal
4C2×C11×#544C211yesmaximal, characteristic
5C11×#544—28no—
6C2×C11×C4⋊Q8C414yescomplemented
7C2×C11×#125C414yescomplemented
8C2×C11×C22⋊Q8C2214yes—
9C2×C11×#117C2212yes—
10C22×C11×C4⋊C4C2211yescharacteristic
11#10622825C2214yes—
12#10622824C2214yes—
13C4×C22⋊Dic11C2214yes—
14#10622594—28no—
15#10622164C22116yes—
16C22×Q8×C11C2×C414yes—
17C23×C4×C11C2311yescharacteristic
18C23×C4×C11C2312yes—
19C11×C4⋊Q8—216no—
20C11×#125—216no—
21C11×C22⋊Q8—28no—
22C11×C22⋊Q8—28no—
23C11×#117—28no—
24C2×C11×C4⋊C4C2×C412yes—
25C2×C11×C4⋊C4C2×C412yes—
26C2×C11×C4⋊C4C2×C414yes—
27C2×C11×C4⋊C4C2×C418yes—
28C2×C11×C4⋊C4C2×C414yes—
29C2×C11×C4⋊C4D418yes—
30C2×C11×C22⋊C4C2314yes—
31C2×C42×C11C2×C414yes—
32C2×C22⋊Dic11C2318yes—
33C2×C4⋊Dic11—24no—
34C2×C4×Dic11—24no—
35C11⋊#95—24no—
36C11⋊#95—28no—
37C11⋊#95—24no—
38#21828—111nomaximal, Sylow
39C24×C11C2411yescharacteristic
40C2×Q8×C11—28no—
41C2×Q8×C11—84no—
42C22×C4×C11—24no—
43C22×C4×C11—82no—
44C22×C4×C11C22×C412yes—
45C22×C4×C11C22×C414yes—
46C22×C4×C11C22×C414yes—
47C22×C4×C11C22×C414yes—
48C22×C4×C11C2×D414yes—
49C22×C4×C11C2×D414yes—
50C22×C4×C11C2×D414yes—
51C22×Dic11—28no—
52C11×C4⋊C4—24no—
53C11×C4⋊C4—24no—
54C11×C4⋊C4—28no—
55C11×C4⋊C4—216no—
56C11×C4⋊C4C22⋊C4116yes—
57C11×C22⋊C4—28no—
58C42×C11—28no—
59C22⋊Dic11—216no—
60C4⋊Dic11—84no—
61C4×Dic11—84no—
62C2×#544D1111yescharacteristic
63#2313—112no—
64#1996—118no—
65#1820—114no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11C23×C411yescharacteristic
69C23×C11C22×D412yes—
70C23×C112−1+414yes—
71Q8×C11—88no—
72C2×C4×C11—24no—
73C2×C4×C11—28no—
74C2×C4×C11—24no—
75C2×C4×C11—24no—
76C2×C4×C11—44no—
77C2×C4×C11—44no—
78C2×C4×C11—44no—
79C2×C4×C11—44no—
80C2×C4×C11—44no—
81C2×C4×C11C2×C22⋊C414yes—
82C2×C4×C11C2×C22⋊C418yes—
83C2×Dic11—48no—
84C2×Dic11—48no—
85C2×Dic11—48no—
86#544—28no—
87C2×C4⋊Q8Dic1114yescomplemented
88C2×#125Dic1114yescomplemented
89C2×C22⋊Q8C2×D1114yes—
90C2×#117C2×D1112yes—
91C22×C4⋊C4C2×D1111yescharacteristic
92#387—228no—
93#381—114no—
94#380—114no—
95C4×C22⋊C4—114no—
96#342—1116no—
97C22×C11—21no—
98C22×C11—22no—
99C22×C11—21no—
100C22×C11—22no—
101C22×C11—44no—
102C22×C11C22×C22⋊C411yescharacteristic
103C22×C11#51912yes—
104C22×C11#53614yes—
105C4×C11—24no—
106C4×C11—28no—
107C4×C11—44no—
108C4×C11—44no—
109Dic11—88no—
110C22×Q8C2×Dic1114yes—
111C23×C4C22×D1111yescharacteristic
112C23×C4C22×D1112yes—
113C4⋊Q8—216no—
114#125—216no—
115C22⋊Q8—28no—
116C22⋊Q8—28no—
117#117—28no—
118C2×C4⋊C4—224no—
119C2×C4⋊C4C2×Dic1112yes—
120C2×C4⋊C4C2×Dic1112yes—
121C2×C4⋊C4C2×Dic1114yes—
122C2×C4⋊C4C2×Dic1118yes—
123C2×C4⋊C4C2×Dic1114yes—
124C2×C4⋊C4C22⋊D1118yes—
125C2×C22⋊C4—118no—
126C2×C22⋊C4C22×D1114yes—
127C2×C42—224no—
128C2×C42C2×Dic1114yes—
129#95—224no—
130#95—224no—
131#95—228no—
132C2×C11—24no—
133C2×C11—22no—
134C2×C11#231011yescharacteristic
135C2×C11#288311yescharacteristic
136C2×C11#288411yescharacteristic
137C24C23×D1111yescharacteristic
138C2×Q8—28no—
139C2×Q8—84no—
140C22×C4—24no—
141C22×C4—82no—
142C22×C4—228no—
143C22×C4C22×Dic1112yes—
144C22×C4C22×Dic1114yes—
145C22×C4C22×Dic1114yes—
146C22×C4C22×Dic1114yes—
147C22×C4C2×C22⋊D1114yes—
148C22×C4C2×C22⋊D1114yes—
149C22×C4C2×C22⋊D1114yes—
150C4⋊C4—24no—
151C4⋊C4—24no—
152C4⋊C4—28no—
153C4⋊C4—216no—
154C4⋊C4—884no—
155C4⋊C4C22⋊Dic11116yes—
156C22⋊C4—28no—
157C22⋊C4—2216no—
158C42—28no—
159C42—884no—
160C11#2182811yescharacteristic, complemented, Sylow
161C23—41no—
162C23—41no—
163C23#6704014yes—
164C23C23×Dic1111yescharacteristic
165C23C22×C22⋊D1112yes—
166Q8—88no—
167C2×C4—24no—
168C2×C4—28no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—448no—
177C2×C4—448no—
178C2×C4—448no—
179C2×C4C2×C22⋊Dic1114yes—
180C2×C4C2×C22⋊Dic1118yes—
181C22—21no—
182C22—22no—
183C22—21no—
184C22—22no—
185C22—44no—
186C22#1062334312yes—
187C22#1062334714yes—
188C22C22×C22⋊Dic1111yescharacteristic
189C4—28no—
190C4—24no—
191C4—44no—
192C4—44no—
193C4—888no—
194C2—24no—
195C2—22no—
196C2#1307120211yescharacteristic
197C2#1307707711yescharacteristic
198C2#1307708011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#544C2
socleC22×C11C22×C22⋊C4
prime radical, cosocleC24×C11C24
hypercenterC2×#544D11
hypocenterC11#21828
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
6. C2×C11×C4⋊Q8C4semidirect
7. C2×C11×#125C4semidirect
87. C2×C4⋊Q8Dic11semidirect
88. C2×#125Dic11semidirect
160. C11#21828semidirect

Maximal subgroups

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

subgroupindex
#130712192
#130696022
#130686932
C2×C11×#5442
#2182811