Finite Group Databasebeta

← #14680959

Subgroups — #14680959

Order 2816.

3246 conjugacy classes of subgroups; only the 491 normal subgroups are shown.

normal subgroups only

This group has 3246 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×#10622860C212yesmaximal
2#13066865C218yesmaximal, complemented
3#13066839C214yesmaximal, complemented
4C23×C11×C22⋊C4C211yesmaximal, characteristic
5C26×C11C2211yescharacteristic
6C24×C4×C11C2212yes—
7C22×C11×C22⋊C4—28no—
8C22×C11×C22⋊C4C418yescomplemented
9C22×C11×C22⋊C4C2214yes—
10C22×C22⋊Dic11C2214yes—
11C22×C22⋊Dic11C2218yes—
12#10622860—28no—
13C2×C11⋊#95C22116yescomplemented
14C25×C11—28no—
15C25×C11—48no—
16C25×C11C2×C414yes—
17C25×C11D418yes—
18C25×C11C2312yes—
19C25×C11C2311yescharacteristic
20C23×C4×C11—28no—
21C23×C4×C11—48no—
22C23×C4×C11C2×C418yes—
23C23×C4×C11C2314yes—
24C23×Dic11C2318yes—
25C2×C11×C22⋊C4—232no—
26C2×C11×C22⋊C4—216no—
27C2×C11×C22⋊C4C2×C4116yes—
28C2×C22⋊Dic11—216no—
29C2×C22⋊Dic11—28no—
30C2×C22⋊Dic11—216no—
31C2×C22⋊Dic11—416no—
32C11⋊#95—416no—
33#14341—111nomaximal, Sylow
34C24×C11—28no—
35C24×C11—216no—
36C24×C11—232no—
37C24×C11—28no—
38C24×C11—216no—
39C24×C11—416no—
40C24×C11—432no—
41C24×C11—464no—
42C24×C11C22⋊C4116yes—
43C24×C11C22×C414yes—
44C24×C11C22×C412yes—
45C24×C11C2×D418yes—
46C24×C11C2×D414yes—
47C24×C11#4118yes—
48C24×C11C2411yescharacteristic
49C22×C4×C11—216no—
50C22×C4×C11—28no—
51C22×C4×C11—216no—
52C22×C4×C11—416no—
53C22×C4×C11—432no—
54C22×C4×C11C22×C418yes—
55C22×Dic11—28no—
56C22×Dic11—216no—
57C22×Dic11—232no—
58C11×C22⋊C4—232no—
59C22⋊Dic11—432no—
60C22⋊Dic11—416no—
61C23×C22⋊C4D1111yescharacteristic
62C2×#379—112no—
63#1440—118no—
64C22⋊#95—114no—
65C23×C11—28no—
66C23×C11—216no—
67C23×C11—232no—
68C23×C11—28no—
69C23×C11—216no—
70C23×C11—216no—
71C23×C11—216no—
72C23×C11—216no—
73C23×C11—232no—
74C23×C11—432no—
75C23×C11—464no—
76C23×C11—4128no—
77C23×C11—432no—
78C23×C11C2×C22⋊C418yes—
79C23×C11C2×C22⋊C414yes—
80C23×C11#11718yes—
81C23×C11#123116yes—
82C23×C11C23×C411yescharacteristic
83C23×C11C22×D412yes—
84C23×C11C2×#4114yes—
85C23×C11H(5,𝔽2)18yes—
86C2×C4×C11—28no—
87C2×C4×C11—216no—
88C2×C4×C11—432no—
89C2×C4×C11—416no—
90C2×Dic11—48no—
91C2×Dic11—416no—
92C2×Dic11—432no—
93C26C2×D1111yescharacteristic
94C24×C4C2×D1112yes—
95C22×C22⋊C4—28no—
96C22×C22⋊C4—114no—
97C22×C22⋊C4—118no—
98C22×C22⋊C4Dic1118yescomplemented
99C22×C22⋊C4C2×D1114yes—
100#379—228no—
101C2×#95—1116no—
102C22×C11—28no—
103C22×C11—216no—
104C22×C11—232no—
105C22×C11—216no—
106C22×C11—28no—
107C22×C11—464no—
108C22×C11—416no—
109C22×C11—432no—
110C22×C11#38118yes—
111C22×C11C22×C22⋊C411yescharacteristic
112C22×C11C2×#11712yes—
113C22×C11#51814yes—
114C22×C11C2×#12314yes—
115C22×C11#53418yes—
116C22×C11#538116yes—
117C4×C11—48no—
118Dic11—88no—
119C25—28no—
120C25—48no—
121C25C2×Dic1114yes—
122C25C22⋊D1118yes—
123C25C22×D1112yes—
124C25C22×D1111yescharacteristic
125C23×C4—28no—
126C23×C4—48no—
127C23×C4—118no—
128C23×C4C2×Dic1118yes—
129C23×C4C22×D1114yes—
130C2×C22⋊C4—232no—
131C2×C22⋊C4—216no—
132C2×C22⋊C4—2216no—
133C2×C22⋊C4—2216no—
134C2×C22⋊C4—228no—
135C2×C22⋊C4—4416no—
136C2×C22⋊C4C2×Dic11116yes—
137#95—4416no—
138C2×C11—28no—
139C2×C11—48no—
140C2×C11C2×#38111yescharacteristic
141C2×C11#230812yes—
142C2×C11#231214yes—
143C2×C11#262218yes—
144C24—28no—
145C24—216no—
146C24—232no—
147C24—28no—
148C24—216no—
149C24—416no—
150C24—432no—
151C24—464no—
152C24C22⋊Dic11116yes—
153C24#433918yes—
154C24C22×Dic1114yes—
155C24C22×Dic1112yes—
156C24C2×C22⋊D1118yes—
157C24C2×C22⋊D1114yes—
158C24C23×D1111yescharacteristic
159C22×C4—216no—
160C22×C4—216no—
161C22×C4—28no—
162C22×C4—416no—
163C22×C4—432no—
164C22×C4—2216no—
165C22×C4—2232no—
166C22×C4—228no—
167C22×C4C22×Dic1118yes—
168C22⋊C4—232no—
169C22⋊C4—4432no—
170C22⋊C4—4416no—
171C11#1434111yescharacteristic, complemented, Sylow
172C23—232no—
173C23—28no—
174C23—216no—
175C23—28no—
176C23—216no—
177C23—216no—
178C23—216no—
179C23—216no—
180C23—232no—
181C23—432no—
182C23—464no—
183C23—4128no—
184C23—432no—
185C23#6697918yes—
186C23#66982116yes—
187C23C2×C22⋊Dic1118yes—
188C23C2×C22⋊Dic1114yes—
189C23C2×#433914yes—
190C23#6703718yes—
191C23C23×Dic1111yescharacteristic
192C23C22×C22⋊D1112yes—
193C2×C4—216no—
194C2×C4—28no—
195C2×C4—432no—
196C2×C4—416no—
197C2×C4—4432no—
198C2×C4—448no—
199C2×C4—4416no—
200C22—28no—
201C22—216no—
202C22—232no—
203C22—216no—
204C22—28no—
205C22—464no—
206C22—416no—
207C22—432no—
208C22#1062282418yes—
209C22#10623025116yes—
210C22C2×#6697912yes—
211C22C2×#6698214yes—
212C22#1062332914yes—
213C22#1062333518yes—
214C22C22×C22⋊Dic1111yescharacteristic
215C4—48no—
216C4—888no—
217C2—28no—
218C2—48no—
219C2C2×#1062282411yescharacteristic
220C2#1307119412yes—
221C2#1307121414yes—
222C2#1307438918yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#14341
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13066865C2semidirect
3. #13066839C2semidirect
8. C22×C11×C22⋊C4C4semidirect
13. C2×C11⋊#95C22semidirect
98. C22×C22⋊C4Dic11semidirect
171. C11#14341semidirect

Maximal subgroups

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

subgroupindex
C2×#106228602
#130668652
#130668392
C23×C11×C22⋊C42
#1434111