Finite Group Databasebeta

← #14675395

Subgroups — #14675395

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C212yesmaximal
2#13066853C214yesmaximal
3#13066850C218yesmaximal, complemented
4C2×C11×#381C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C11×C22⋊C4C2212yes—
7C22×C22⋊Dic11C2214yes—
8C22×C4⋊Dic11C2214yes—
9C22×C4×Dic11C2214yes—
10C11×#381C418yescomplemented
11C2×C11×#95C2214yes—
12#10622825C4116yescomplemented
13C2×C11⋊#95C2218yes—
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2214yes—
16C25×C11C2311yescharacteristic
17C23×C4×C11—44no—
18C23×C4×C11C2×C418yes—
19C23×C4×C11C2×C414yes—
20C23×C4×C11C2314yes—
21C23×C4×C11C2312yes—
22C23×Dic11C2318yes—
23C2×C11×C22⋊C4—44no—
24C2×C11×C22⋊C4C2×C418yes—
25C2×C22⋊Dic11—44no—
26C2×C22⋊Dic11—44no—
27C2×C22⋊Dic11C2×C4116yes—
28C2×C4⋊Dic11—48no—
29C2×C4⋊Dic11C2×C4116yes—
30C2×C4×Dic11—48no—
31C2×C4×Dic11—44no—
32C11×#95C2×C4116yes—
33C11⋊#95—48no—
34C11⋊#95—44no—
35C11⋊#95C2×C4116yes—
36#13828—111nomaximal, Sylow
37C24×C11—24no—
38C24×C11—24no—
39C24×C11—24no—
40C24×C11C22×C414yes—
41C24×C11C22×C412yes—
42C24×C11C2411yescharacteristic
43C22×C4×C11—28no—
44C22×C4×C11—28no—
45C22×C4×C11—24no—
46C22×C4×C11—24no—
47C22×C4×C11—28no—
48C22×C4×C11—416no—
49C22×C4×C11—48no—
50C22×C4×C11C42116yescomplemented
51C22×C4×C11C22×C418yes—
52C22×C4×C11C22×C414yes—
53C22×C4×C11C22×C414yes—
54C22×C4×C11C22×C414yes—
55C22×Dic11—28no—
56C22×Dic11—28no—
57C22×Dic11—28no—
58C22×Dic11—28no—
59C22×Dic11—28no—
60C22×Dic11—28no—
61C22×Dic11C22×C4116yes—
62C11×C22⋊C4—48no—
63C22⋊Dic11—416no—
64C4⋊Dic11—416no—
65C4×Dic11—416no—
66C2×#381D1111yescharacteristic
67C2×#380—112no—
68#1437—114no—
69#1436—118no—
70C23×C11—24no—
71C23×C11—24no—
72C23×C11—28no—
73C23×C11—24no—
74C23×C11—28no—
75C23×C11—28no—
76C23×C11—44no—
77C23×C11—48no—
78C23×C11—44no—
79C23×C11C2×C4214yes—
80C23×C11C23×C412yes—
81C23×C11C23×C411yescharacteristic
82C23×C11H(5,𝔽2)14yes—
83C23×C11H(5,𝔽2)14yes—
84C23×C112−1+414yes—
85C2×C4×C11—28no—
86C2×C4×C11—28no—
87C2×C4×C11—28no—
88C2×C4×C11—28no—
89C2×C4×C11—216no—
90C2×C4×C11—416no—
91C2×C4×C11—44no—
92C2×C4×C11—48no—
93C2×C4×C11—44no—
94C2×C4×C11C2×C4218yes—
95C2×Dic11—216no—
96C2×Dic11—216no—
97C2×Dic11—216no—
98C2×Dic11—48no—
99C2×Dic11—48no—
100C2×Dic11—48no—
101C2×Dic11—48no—
102C24×C4C2×D1111yescharacteristic
103C22×C4⋊C4—114no—
104C22×C22⋊C4—114no—
105C22×C22⋊C4C2×D1112yes—
106C22×C42—114no—
107#381Dic1118yescomplemented
108#380—1116no—
109C2×#95—114no—
110C2×#95—114no—
111C2×#95—118no—
112C2×#95C2×D1114yes—
113C22×C11—24no—
114C22×C11—28no—
115C22×C11—48no—
116C22×C11—48no—
117C22×C11—48no—
118C22×C11C22×C4211yescharacteristic
119C22×C11#51814yes—
120C22×C11#51812yes—
121C22×C11#51812yes—
122C22×C11#51912yes—
123C22×C11#52014yes—
124C22×C11#52014yes—
125C22×C11#56014yes—
126C22×C11#56218yes—
127C22×C11#56314yes—
128C4×C11—28no—
129C4×C11—48no—
130Dic11—416no—
131C25C22×D1111yescharacteristic
132C23×C4—44no—
133C23×C4—118no—
134C23×C4C4×D1118yes—
135C23×C4C2×Dic1114yes—
136C23×C4C22×D1114yes—
137C23×C4C22×D1112yes—
138C2×C4⋊C4—1116no—
139C2×C4⋊C4—448no—
140C2×C22⋊C4—44no—
141C2×C22⋊C4—1116no—
142C2×C22⋊C4—444no—
143C2×C22⋊C4—444no—
144C2×C22⋊C4C2×Dic1118yes—
145C2×C42—444no—
146C2×C42—448no—
147#95—1116no—
148#95—444no—
149#95—448no—
150#95C2×Dic11116yes—
151C2×C11—44no—
152C2×C11#227311yescharacteristic
153C2×C11#227412yes—
154C2×C11#237614yes—
155C2×C11#237714yes—
156C2×C11#237814yes—
157C24—24no—
158C24—24no—
159C24—24no—
160C24C2×C4×D1114yes—
161C24C22×Dic1112yes—
162C24C23×D1111yescharacteristic
163C22×C4—28no—
164C22×C4—24no—
165C22×C4—24no—
166C22×C4—28no—
167C22×C4—28no—
168C22×C4—416no—
169C22×C4—48no—
170C22×C4—1116no—
171C22×C4—228no—
172C22×C4—228no—
173C22×C4—228no—
174C22×C4—228no—
175C22×C4—228no—
176C22×C4—228no—
177C22×C4C4×Dic11116yescomplemented
178C22×C4C2×C4×D1114yes—
179C22×C4C2×C4×D1114yes—
180C22×C4C22×Dic1118yes—
181C22×C4C22×Dic1114yes—
182C4⋊C4—4416no—
183C22⋊C4—48no—
184C22⋊C4—4416no—
185C42—4416no—
186C11#1382811yescharacteristic, complemented, Sylow
187C23—28no—
188C23—24no—
189C23—24no—
190C23—28no—
191C23—24no—
192C23—28no—
193C23—44no—
194C23—44no—
195C23—48no—
196C23C2×C4×Dic1114yes—
197C23C22×C4×D1112yes—
198C23#6703714yes—
199C23#6704214yes—
200C23#6704314yes—
201C23C23×Dic1111yescharacteristic
202C2×C4—28no—
203C2×C4—28no—
204C2×C4—28no—
205C2×C4—28no—
206C2×C4—216no—
207C2×C4—416no—
208C2×C4—44no—
209C2×C4—44no—
210C2×C4—48no—
211C2×C4—2216no—
212C2×C4—2216no—
213C2×C4—2216no—
214C2×C4—448no—
215C2×C4—448no—
216C2×C4—448no—
217C2×C4—448no—
218C2×C4C2×C4×Dic1118yes—
219C22—24no—
220C22—28no—
221C22—48no—
222C22—48no—
223C22—48no—
224C22#1062301714yes—
225C22#1062304712yes—
226C22#1062305212yes—
227C22#1062305414yes—
228C22#1062318214yes—
229C22#1062319714yes—
230C22#1062319818yes—
231C22C22×C4×Dic1111yescharacteristic
232C22#1062332912yes—
233C22#1062335814yes—
234C4—28no—
235C4—48no—
236C4—4416no—
237C2—44no—
238C2#1307096911yescharacteristic
239C2#1307097212yes—
240C2#1307176414yes—
241C2#1307177514yes—
242C2#1307178414yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#13828
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #13066850C2semidirect
10. C11×#381C4semidirect
12. #10622825C4semidirect
50. C22×C4×C11C42semidirect
107. #381Dic11semidirect
177. C22×C4C4×Dic11semidirect
186. C11#13828semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
#130668532
#130668502
C2×C11×#3812
#1382811