Finite Group Databasebeta

← #14680963

Subgroups — #14680963

Order 2816.

1998 conjugacy classes of subgroups; only the 491 normal subgroups are shown.

normal subgroups only

This group has 1998 conjugacy classes of subgroups — too many to draw. Only its 491 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×#10622824C212yesmaximal
2#13066884C218yesmaximal, complemented
3#13066839C214yesmaximal
4C23×C11×C4⋊C4C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C24×C4×C11C2212yes—
7C22×C11×C4⋊C4—28no—
8C22×C11×C4⋊C4C418yescomplemented
9C22×C11×C4⋊C4C2214yes—
10C22×C22⋊Dic11C2214yes—
11#10622824—28no—
12C2×C11⋊#95C2218yes—
13C2×C11⋊#95C22116yes—
14C25×C11C2311yescharacteristic
15C23×C4×C11—28no—
16C23×C4×C11—28no—
17C23×C4×C11—48no—
18C23×C4×C11C2×C414yes—
19C23×C4×C11C2×C418yes—
20C23×C4×C11D418yes—
21C23×C4×C11C2314yes—
22C23×C4×C11C2312yes—
23C23×Dic11C2318yes—
24C2×C11×C4⋊C4—232no—
25C2×C11×C4⋊C4—216no—
26C2×C11×C4⋊C4C2×C4116yes—
27C2×C22⋊Dic11—28no—
28C2×C22⋊Dic11—216no—
29C11⋊#95—216no—
30C11⋊#95—416no—
31#14342—111nomaximal, Sylow
32C24×C11—24no—
33C24×C11—24no—
34C24×C11C22×C412yes—
35C24×C11C2×D414yes—
36C24×C11#4118yes—
37C24×C11C2411yescharacteristic
38C22×C4×C11—216no—
39C22×C4×C11—232no—
40C22×C4×C11—28no—
41C22×C4×C11—216no—
42C22×C4×C11—28no—
43C22×C4×C11—216no—
44C22×C4×C11—416no—
45C22×C4×C11—432no—
46C22×C4×C11C22⋊C4116yes—
47C22×C4×C11C22×C418yes—
48C22×C4×C11C22×C414yes—
49C22×C4×C11C2×D418yes—
50C22×Dic11—28no—
51C22×Dic11—216no—
52C22×Dic11—216no—
53C22×Dic11—216no—
54C11×C4⋊C4—232no—
55C22⋊Dic11—416no—
56C23×C4⋊C4D1111yescharacteristic
57C2×#381—112no—
58#1445—118no—
59C22⋊#95—114no—
60C23×C11—24no—
61C23×C11—24no—
62C23×C11—28no—
63C23×C11—28no—
64C23×C11—232no—
65C23×C11C2×C22⋊C414yes—
66C23×C11#11718yes—
67C23×C11#123116yes—
68C23×C11C23×C411yescharacteristic
69C23×C11C22×D412yes—
70C23×C11C2×#4114yes—
71C23×C11H(5,𝔽2)14yes—
72C23×C112−1+414yes—
73C2×C4×C11—28no—
74C2×C4×C11—216no—
75C2×C4×C11—232no—
76C2×C4×C11—28no—
77C2×C4×C11—216no—
78C2×C4×C11—432no—
79C2×C4×C11—416no—
80C2×C4×C11C2×C22⋊C418yes—
81C2×Dic11—48no—
82C2×Dic11—48no—
83C2×Dic11—48no—
84C2×Dic11—432no—
85C24×C4C2×D1111yescharacteristic
86C24×C4C2×D1112yes—
87C22×C4⋊C4—28no—
88C22×C4⋊C4Dic1118yescomplemented
89C22×C4⋊C4C2×D1114yes—
90C22×C22⋊C4—114no—
91#381—228no—
92C2×#95—118no—
93C2×#95—1116no—
94C22×C11—24no—
95C22×C11—24no—
96C22×C11—216no—
97C22×C11—232no—
98C22×C11#38118yes—
99C22×C11C22×C22⋊C411yescharacteristic
100C22×C11C2×#11712yes—
101C22×C11#51812yes—
102C22×C11#51912yes—
103C22×C11C2×#12314yes—
104C22×C11#53514yes—
105C22×C11#53614yes—
106C22×C11#539116yes—
107C4×C11—28no—
108C4×C11—48no—
109Dic11—88no—
110C25C22×D1111yescharacteristic
111C23×C4—28no—
112C23×C4—28no—
113C23×C4—48no—
114C23×C4—118no—
115C23×C4C2×Dic1114yes—
116C23×C4C2×Dic1118yes—
117C23×C4C22⋊D1118yes—
118C23×C4C22×D1114yes—
119C23×C4C22×D1112yes—
120C2×C4⋊C4—232no—
121C2×C4⋊C4—216no—
122C2×C4⋊C4C2×Dic11116yes—
123C2×C22⋊C4—2216no—
124C2×C22⋊C4—228no—
125#95—2216no—
126#95—4416no—
127C2×C11—28no—
128C2×C11C2×#38111yescharacteristic
129C2×C11#230911yescharacteristic
130C2×C11#231011yescharacteristic
131C2×C11#231314yes—
132C2×C11#262318yes—
133C24—24no—
134C24—24no—
135C24#433918yes—
136C24C22×Dic1112yes—
137C24C2×C22⋊D1114yes—
138C24C23×D1111yescharacteristic
139C22×C4—216no—
140C22×C4—232no—
141C22×C4—28no—
142C22×C4—216no—
143C22×C4—216no—
144C22×C4—28no—
145C22×C4—416no—
146C22×C4—432no—
147C22×C4—2216no—
148C22×C4—2216no—
149C22×C4—2216no—
150C22×C4—228no—
151C22×C4C22⋊Dic11116yes—
152C22×C4C22×Dic1118yes—
153C22×C4C22×Dic1114yes—
154C22×C4C2×C22⋊D1118yes—
155C4⋊C4—232no—
156C22⋊C4—4416no—
157C11#1434211yescharacteristic, complemented, Sylow
158C23—232no—
159C23—24no—
160C23—28no—
161C23—24no—
162C23—28no—
163C23#6697918yes—
164C23#66982116yes—
165C23C2×C22⋊Dic1114yes—
166C23C2×#433914yes—
167C23#6703714yes—
168C23#6704014yes—
169C23C23×Dic1111yescharacteristic
170C23C22×C22⋊D1112yes—
171C2×C4—28no—
172C2×C4—216no—
173C2×C4—232no—
174C2×C4—216no—
175C2×C4—28no—
176C2×C4—432no—
177C2×C4—416no—
178C2×C4—4432no—
179C2×C4—448no—
180C2×C4—448no—
181C2×C4—448no—
182C2×C4C2×C22⋊Dic1118yes—
183C22—24no—
184C22—24no—
185C22—216no—
186C22—232no—
187C22#1062282418yes—
188C22#10623046116yes—
189C22C2×#6697912yes—
190C22C2×#6698214yes—
191C22#1062332912yes—
192C22#1062333614yes—
193C22#1062334312yes—
194C22#1062334714yes—
195C22C22×C22⋊Dic1111yescharacteristic
196C4—28no—
197C4—48no—
198C4—888no—
199C2—28no—
200C2C2×#1062282411yescharacteristic
201C2#1307119811yescharacteristic
202C2#1307120211yescharacteristic
203C2#1307121914yes—
204C2#1307439618yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC23×C4⋊C4D11
hypocenterC11#14342
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13066884C2semidirect
8. C22×C11×C4⋊C4C4semidirect
88. C22×C4⋊C4Dic11semidirect
157. C11#14342semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
#130668842
#130668392
C23×C11×C4⋊C42
#1434211