Finite Group Databasebeta

← #14916664

Subgroups — #14916664

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071802C214yesmaximal, complemented
2#13071722C214yesmaximal, complemented
3#13071493C218yesmaximal
4#13071422C218yesmaximal, complemented
5#13071219C214yesmaximal
6#13071014C212yesmaximal
7C22×C11×#125C211yesmaximal, characteristic
8C2×C11×#125C4116yescomplemented
9C2×C11×#125C2214yes—
10C2×C11×#125C2212yes—
11C2×C11×#125C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15#10622825C2218yes—
16#10622825C2214yes—
17#10622824C2214yes—
18C4×C22⋊Dic11C2218yes—
19C4×C22⋊Dic11C2214yes—
20#10622598C22116yes—
21#10622594C22116yes—
22#10622594C22116yes—
23#10622594C22116yes—
24#10622594C22116yes—
25C4⋊C4×Dic11C22116yes—
26#10622550C2214yes—
27#10622549C2214yes—
28C4×C4⋊Dic11C2214yes—
29#10622545C2214yes—
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2312yes—
32C23×C4×C11C2314yes—
33C11×#125C2×C4132yes—
34C11×#125C2×C4116yes—
35C11×#125C2×C4116yes—
36C2×C11×C4⋊C4C2×C4116yes—
37C2×C11×C4⋊C4C2×C4132yes—
38C2×C11×C4⋊C4C2318yes—
39C2×C11×C4⋊C4C2314yes—
40C2×C11×C4⋊C4C2314yes—
41C2×C11×C4⋊C4C2318yes—
42C2×C42×C11C2×C418yes—
43C2×C42×C11C2311yescharacteristic
44C2×C42×C11C2312yes—
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11C2318yes—
47C2×C4⋊Dic11C2318yes—
48C2×C4⋊Dic11C23116yes—
49C2×C4×Dic11C2318yes—
50C2×C4×Dic11C23116yes—
51C11⋊#95C2318yes—
52C11⋊#95C2318yes—
53C11⋊#95C2318yes—
54C11⋊#95C2318yes—
55C11⋊#95C23116yes—
56C11⋊#95C23116yes—
57#34372—111nomaximal, Sylow
58C24×C11C2411yescharacteristic
59C22×C4×C11—24no—
60C22×C4×C11—44no—
61C22×C4×C11—48no—
62C22×C4×C11C22×C414yes—
63C22×C4×C11C22×C418yes—
64C22×C4×C11C22×C4116yes—
65C22×C4×C11C2411yescharacteristic
66C22×C4×C11C2411yescharacteristic
67C22×C4×C11C2412yes—
68C22×C4×C11C2418yes—
69C22×C4×C11C2412yes—
70C22×Dic11C24116yes—
71C11×C4⋊C4C22×C4132yes—
72C11×C4⋊C4C22×C4116yes—
73C11×C4⋊C4C22×C4116yes—
74C11×C4⋊C4C22×C4132yes—
75C42×C11C22×C414yes—
76C42×C11C22×C418yes—
77C42×C11C22×C414yes—
78C22⋊Dic11—216no—
79C4⋊Dic11—416no—
80C4⋊Dic11—48no—
81C4×Dic11—48no—
82C4×Dic11—416no—
83C22×#125D1111yescharacteristic
84#2382—114no—
85#2371—114no—
86#2345—118no—
87#2336—118no—
88#2313—114no—
89#2283—112no—
90C23×C11—24no—
91C23×C11C23×C412yes—
92C23×C112−1+414yes—
93C23×C11C2511yescharacteristic
94C2×C4×C11—28no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—24no—
98C2×C4×C11—216no—
99C2×C4×C11—24no—
100C2×C4×C11—48no—
101C2×C4×C11—416no—
102C2×C4×C11C23×C412yes—
103C2×C4×C11C23×C412yes—
104C2×C4×C11C23×C414yes—
105C2×C4×C11C23×C414yes—
106C2×C4×C11C23×C4116yes—
107C2×Dic11—216no—
108C2×Dic11—216no—
109C2×Dic11—216no—
110C2×#125Dic11116yescomplemented
111C2×#125C2×D1114yes—
112C2×#125C2×D1112yes—
113C2×#125C2×D1112yes—
114C22×C4⋊C4C2×D1112yes—
115C22×C4⋊C4C2×D1114yes—
116C22×C42C2×D1111yescharacteristic
117#389—1116no—
118#387—1116no—
119#387—1116no—
120#387—1116no—
121#387—1116no—
122#383—114no—
123#382—114no—
124#381—114no—
125#380—118no—
126#380—114no—
127C4×C4⋊C4—1116no—
128C4×C4⋊C4—114no—
129C4×C22⋊C4—118no—
130C4×C22⋊C4—114no—
131#376—114no—
132C22×C11—24no—
133C22×C11—28no—
134C22×C11#51914yes—
135C22×C11C24×C411yescharacteristic
136C22×C11C2×2−1+412yes—
137C22×C11#58514yes—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—24no—
141C4×C11—216no—
142C4×C11—24no—
143Dic11—416no—
144C23×C4C22×D1111yescharacteristic
145C23×C4C22×D1114yes—
146C23×C4C22×D1112yes—
147#125C2×Dic11132yes—
148#125C2×Dic11116yes—
149#125C2×Dic11116yes—
150C2×C4⋊C4—118no—
151C2×C4⋊C4—1116no—
152C2×C4⋊C4C2×Dic11116yes—
153C2×C4⋊C4C2×Dic11132yes—
154C2×C4⋊C4C22×D1118yes—
155C2×C4⋊C4C22×D1114yes—
156C2×C4⋊C4C22×D1114yes—
157C2×C4⋊C4C22×D1118yes—
158C2×C22⋊C4—118no—
159C2×C42—118no—
160C2×C42—1116no—
161C2×C42C2×Dic1118yes—
162C2×C42C22×D1111yescharacteristic
163C2×C42C22×D1112yes—
164C2×C42C22×D1111yescharacteristic
165#95—118no—
166#95—118no—
167#95—118no—
168#95—1116no—
169#95—1116no—
170#95—118no—
171C2×C11—24no—
172C2×C11C2×#51911yescharacteristic
173C2×C11#342812yes—
174C2×C11#355314yes—
175C24C23×D1111yescharacteristic
176C22×C4—24no—
177C22×C4—44no—
178C22×C4—48no—
179C22×C4—1116no—
180C22×C4C22×Dic1114yes—
181C22×C4C22×Dic1118yes—
182C22×C4C22×Dic11116yes—
183C22×C4C23×D1111yescharacteristic
184C22×C4C23×D1111yescharacteristic
185C22×C4C23×D1112yes—
186C22×C4C23×D1118yes—
187C22×C4C23×D1112yes—
188C4⋊C4—4416no—
189C4⋊C4—448no—
190C4⋊C4C22×Dic11132yes—
191C4⋊C4C22×Dic11116yes—
192C4⋊C4C22×Dic11116yes—
193C4⋊C4C22×Dic11132yes—
194C22⋊C4—2216no—
195C42—448no—
196C42—4416no—
197C42C22×Dic1114yes—
198C42C22×Dic1118yes—
199C42C22×Dic1114yes—
200C11#3437211yescharacteristic, complemented, Sylow
201C23—24no—
202C23#6704014yes—
203C23C23×Dic1112yes—
204C23C24×D1111yescharacteristic
205C2×C4—28no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—24no—
211C2×C4—48no—
212C2×C4—416no—
213C2×C4—2216no—
214C2×C4—2216no—
215C2×C4—2216no—
216C2×C4C23×Dic1112yes—
217C2×C4C23×Dic1112yes—
218C2×C4C23×Dic1114yes—
219C2×C4C23×Dic1114yes—
220C2×C4C23×Dic11116yes—
221C22—28no—
222C22—24no—
223C22#1062334314yes—
224C22C2×#6704012yes—
225C22#1062345314yes—
226C22C24×Dic1111yescharacteristic
227C4—22no—
228C4—22no—
229C4—24no—
230C4—216no—
231C4—24no—
232C4—4416no—
233C2—24no—
234C2C2×#1062334311yescharacteristic
235C2#1308181912yes—
236C2#1308307214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C11×#125C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC22×#125D11
hypocenterC11#34372
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #13071802C2semidirect
2. #13071722C2semidirect
4. #13071422C2semidirect
8. C2×C11×#125C4semidirect
110. C2×#125Dic11semidirect
200. C11#34372semidirect

Maximal subgroups

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

subgroupindex
#130718022
#130717222
#130714932
#130714222
#130712192
#130710142
C22×C11×#1252
#3437211