Finite Group Databasebeta

← #14684824

Subgroups — #14684824

Order 2816.

1334 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 411 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
1C2×#10622549C212yesmaximal
2#13066884C214yesmaximal
3#13066869C218yesmaximal
4C22×C11×#125C211yesmaximal, characteristic
5C2×C11×#125—28no—
6C2×C11×#125C418yescomplemented
7C22×C11×C4⋊C4C2214yes—
8C22×C11×C4⋊C4C2212yes—
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11C2214yes—
11C2×C11⋊#95C2214yes—
12C2×C11⋊#95C2214yes—
13C2×C11⋊#95C22116yes—
14#10622549—28no—
15C23×C4×C11C2314yes—
16C23×C4×C11C2312yes—
17C23×C4×C11C2311yescharacteristic
18C23×Dic11C2318yes—
19C11×#125—232no—
20C2×C11×C4⋊C4—28no—
21C2×C11×C4⋊C4—24no—
22C2×C11×C4⋊C4—24no—
23C2×C11×C4⋊C4—28no—
24C2×C11×C4⋊C4C2×C4116yes—
25C2×C11×C4⋊C4C2×C418yes—
26C2×C42×C11C2×C414yes—
27C2×C42×C11D418yes—
28C2×C4⋊Dic11—28no—
29C2×C4⋊Dic11—48no—
30C11⋊#95—28no—
31C11⋊#95—28no—
32C11⋊#95—416no—
33#14664—111nomaximal, Sylow
34C24×C11C2411yescharacteristic
35C22×C4×C11—24no—
36C22×C4×C11—24no—
37C22×C4×C11—24no—
38C22×C4×C11—24no—
39C22×C4×C11—24no—
40C22×C4×C11—28no—
41C22×C4×C11—28no—
42C22×C4×C11C22×C418yes—
43C22×C4×C11C22×C412yes—
44C22×C4×C11C22×C414yes—
45C22×C4×C11C2×D414yes—
46C22×C4×C11C2×D414yes—
47C22×C4×C11C2×D414yes—
48C22×Dic11—28no—
49C22×Dic11—28no—
50C22×Dic11—216no—
51C22×Dic11—216no—
52C22×Dic11—28no—
53C11×C4⋊C4—216no—
54C11×C4⋊C4—232no—
55C42×C11C22⋊C4116yes—
56C4⋊Dic11—416no—
57C22×#125D1111yescharacteristic
58C2×#382—112no—
59#1445—114no—
60#1441—118no—
61C23×C11C23×C411yescharacteristic
62C23×C11C22×D412yes—
63C23×C11H(5,𝔽2)14yes—
64C23×C112−1+414yes—
65C23×C112−1+414yes—
66C2×C4×C11—24no—
67C2×C4×C11—28no—
68C2×C4×C11—24no—
69C2×C4×C11—28no—
70C2×C4×C11—24no—
71C2×C4×C11—28no—
72C2×C4×C11—28no—
73C2×C4×C11—216no—
74C2×C4×C11—44no—
75C2×C4×C11—44no—
76C2×C4×C11—48no—
77C2×C4×C11C2×C22⋊C414yes—
78C2×C4×C11C2×C22⋊C418yes—
79C2×Dic11—48no—
80C2×Dic11—48no—
81C2×Dic11—48no—
82C2×Dic11—416no—
83C2×Dic11—416no—
84C2×#125—28no—
85C2×#125Dic1118yescomplemented
86C22×C4⋊C4—114no—
87C22×C4⋊C4C2×D1114yes—
88C22×C4⋊C4C2×D1112yes—
89C22×C42C2×D1111yescharacteristic
90#382—228no—
91C2×#95—114no—
92C2×#95—114no—
93C2×#95—1116no—
94C22×C11C22×C22⋊C411yescharacteristic
95C22×C11#51912yes—
96C22×C11#52014yes—
97C22×C11#53512yes—
98C22×C11#53614yes—
99C22×C11#53612yes—
100C22×C11#53714yes—
101C22×C11#56214yes—
102C22×C11#56318yes—
103C22×C11#56414yes—
104C4×C11—24no—
105C4×C11—28no—
106C4×C11—48no—
107Dic11—88no—
108C23×C4—118no—
109C23×C4C22×D1114yes—
110C23×C4C22×D1112yes—
111C23×C4C22×D1111yescharacteristic
112#125—232no—
113C2×C4⋊C4—28no—
114C2×C4⋊C4—24no—
115C2×C4⋊C4—24no—
116C2×C4⋊C4—28no—
117C2×C4⋊C4—228no—
118C2×C4⋊C4—448no—
119C2×C4⋊C4C2×Dic11116yes—
120C2×C4⋊C4C2×Dic1118yes—
121C2×C42C2×Dic1114yes—
122C2×C42C22⋊D1118yes—
123#95—228no—
124#95—228no—
125#95—4416no—
126C2×C11#231011yescharacteristic
127C2×C11#231112yes—
128C2×C11#238214yes—
129C2×C11#282014yes—
130C2×C11#282214yes—
131C24C23×D1111yescharacteristic
132C22×C4—24no—
133C22×C4—24no—
134C22×C4—24no—
135C22×C4—28no—
136C22×C4—28no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—2216no—
140C22×C4—228no—
141C22×C4—2216no—
142C22×C4—228no—
143C22×C4—228no—
144C22×C4C22×Dic1118yes—
145C22×C4C22×Dic1112yes—
146C22×C4C22×Dic1114yes—
147C22×C4C2×C22⋊D1114yes—
148C22×C4C2×C22⋊D1114yes—
149C22×C4C2×C22⋊D1114yes—
150C4⋊C4—216no—
151C4⋊C4—232no—
152C4⋊C4—4416no—
153C42C22⋊Dic11116yes—
154C11#1466411yescharacteristic, complemented, Sylow
155C23#6704014yes—
156C23#6704214yes—
157C23#6704314yes—
158C23C23×Dic1111yescharacteristic
159C23C22×C22⋊D1112yes—
160C2×C4—24no—
161C2×C4—28no—
162C2×C4—24no—
163C2×C4—28no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—216no—
167C2×C4—28no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4—48no—
171C2×C4—448no—
172C2×C4—448no—
173C2×C4—448no—
174C2×C4—4416no—
175C2×C4—4416no—
176C2×C4C2×C22⋊Dic1114yes—
177C2×C4C2×C22⋊Dic1118yes—
178C22C11⋊#56414yes—
179C22#1062323018yes—
180C22#1062323114yes—
181C22#1062334312yes—
182C22#1062334714yes—
183C22#1062335612yes—
184C22#1062335814yes—
185C22#1062336112yes—
186C22#1062336414yes—
187C22C22×C22⋊Dic1111yescharacteristic
188C4—24no—
189C4—28no—
190C4—48no—
191C4—888no—
192C2#1307120211yescharacteristic
193C2#1307120812yes—
194C2#1307180214yes—
195C2#1307666614yes—
196C2#1307668314yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#125C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×#125D11
hypocenterC11#14664
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
6. C2×C11×#125C4semidirect
85. C2×#125Dic11semidirect
154. C11#14664semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
#130668842
#130668692
C22×C11×#1252
#1466411