Finite Group Databasebeta

← #14718925

Subgroups — #14718925

Order 2816.

1426 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 251 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
1#13066885C214yesmaximal, complemented
2#13066861C218yesmaximal, complemented
3#13066857C212yesmaximal
4C11×#1438C211yesmaximal, characteristic
5C23×D4×C11C2211yescharacteristic
6C22×C11×C22⋊C4C2214yes—
7C22×C22⋊Dic11C2214yes—
8C22×C22⋊Dic11C2214yes—
9C22×C4⋊Dic11C2214yes—
10C2×C11×#95C2212yes—
11C2×C11⋊#95C2214yes—
12C2×C11⋊#95C2218yes—
13C2×C11⋊#95C2214yes—
14C25×C11C2312yes—
15C22×D4×C11—44no—
16C22×D4×C11—42no—
17C22×D4×C11Q814yes—
18C23×C4×C11C2311yescharacteristic
19C23×C4×C11C2314yes—
20C23×Dic11C2318yes—
21C2×C11×C22⋊C4—216no—
22C2×C11×C22⋊C4—44no—
23C2×C22⋊Dic11—44no—
24C2×C22⋊Dic11—48no—
25C2×C22⋊Dic11—44no—
26C2×C22⋊Dic11—48no—
27C2×C4⋊Dic11—28no—
28C2×C4⋊Dic11—44no—
29C2×C4⋊Dic11—44no—
30C11×#95—42no—
31C11⋊#95—44no—
32C11⋊#95—48no—
33C11⋊#95—44no—
34#17273—111nomaximal, Sylow
35C24×C11—28no—
36C24×C11—28no—
37C24×C11—24no—
38C24×C11—24no—
39C24×C11—24no—
40C24×C11C2×Q814yes—
41C24×C11C2411yescharacteristic
42C2×D4×C11—48no—
43C2×D4×C11—44no—
44C2×D4×C11—416no—
45C22×C4×C11—28no—
46C22×C4×C11—24no—
47C22×C4×C11—28no—
48C22×C4×C11—24no—
49C22×C4×C11—24no—
50C22×C4×C11—22no—
51C22×C4×C11C2×Q812yes—
52C22×C4×C11#4118yes—
53C22×Dic11—28no—
54C22×Dic11—28no—
55C22×Dic11—28no—
56C22×Dic11—28no—
57C22×Dic11—28no—
58C22×Dic11—28no—
59C22×Dic11—28no—
60C11×C22⋊C4—416no—
61C22⋊Dic11—416no—
62C22⋊Dic11—416no—
63C4⋊Dic11—416no—
64#1445—114no—
65#1439—118no—
66#1438—112no—
67#1438D1111yescharacteristic
68C23×C11—24no—
69C23×C11—24no—
70C23×C11—24no—
71C23×C11—216no—
72C23×C11—48no—
73C23×C11—48no—
74C23×C11—48no—
75C23×C11—44no—
76C23×C11—44no—
77C23×C11—44no—
78C23×C11—44no—
79C23×C11—48no—
80C23×C11—44no—
81C23×C11—44no—
82C23×C11C22×Q811yescharacteristic
83C23×C11C2×#4114yes—
84C23×C11H(5,𝔽2)12yes—
85C23×C11H(5,𝔽2)14yes—
86C23×C11H(5,𝔽2)14yes—
87D4×C11—416no—
88C2×C4×C11—28no—
89C2×C4×C11—24no—
90C2×C4×C11—22no—
91C2×C4×C11—216no—
92C2×C4×C11—48no—
93C2×C4×C11—44no—
94C2×C4×C11—44no—
95C2×C4×C11—44no—
96C2×Dic11—48no—
97C2×Dic11—48no—
98C2×Dic11—48no—
99C2×Dic11—48no—
100C2×Dic11—48no—
101C2×Dic11—48no—
102C2×Dic11—48no—
103C23×D4C2×D1111yescharacteristic
104C22×C4⋊C4—114no—
105C22×C22⋊C4—114no—
106C22×C22⋊C4—114no—
107C22×C22⋊C4C2×D1114yes—
108C2×#95—114no—
109C2×#95—118no—
110C2×#95—114no—
111C2×#95C2×D1112yes—
112C22×C11—44no—
113C22×C11—48no—
114C22×C11—48no—
115C22×C11—48no—
116C22×C11—88no—
117C22×C11—88no—
118C22×C11#53814yes—
119C22×C11#54018yes—
120C22×C11#54312yes—
121C22×C11#54311yescharacteristic
122C22×C11#55114yes—
123C22×C11#55414yes—
124C22×C11#55912yes—
125C22×C11#56014yes—
126C22×C11#56014yes—
127C22×C11H(3,𝔽4)12yes—
128C4×C11—42no—
129C4×C11—48no—
130Dic11—88no—
131C25C22×D1112yes—
132C22×D4—42no—
133C22×D4—44no—
134C22×D4Dic2214yes—
135C23×C4—118no—
136C23×C4C22×D1111yescharacteristic
137C23×C4C22×D1114yes—
138C2×C4⋊C4—228no—
139C2×C4⋊C4—444no—
140C2×C4⋊C4—444no—
141C2×C22⋊C4—216no—
142C2×C22⋊C4—44no—
143C2×C22⋊C4—444no—
144C2×C22⋊C4—444no—
145C2×C22⋊C4—448no—
146C2×C22⋊C4—448no—
147#95—42no—
148#95—448no—
149#95—444no—
150#95—444no—
151C2×C11—84no—
152C2×C11#274814yes—
153C2×C11#275214yes—
154C2×C11#280412yes—
155C2×C11#282814yes—
156C2×C11#284211yescharacteristic
157C24—28no—
158C24—24no—
159C24—24no—
160C24—24no—
161C24—28no—
162C24C2×Dic2214yes—
163C24C23×D1111yescharacteristic
164C2×D4—44no—
165C2×D4—48no—
166C2×D4—416no—
167C22×C4—28no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—28no—
171C22×C4—24no—
172C22×C4—24no—
173C22×C4—228no—
174C22×C4—228no—
175C22×C4—228no—
176C22×C4—228no—
177C22×C4—228no—
178C22×C4—228no—
179C22×C4—228no—
180C22×C4C2×Dic2212yes—
181C22×C4#434118yes—
182C4⋊C4—4416no—
183C22⋊C4—416no—
184C22⋊C4—4416no—
185C22⋊C4—4416no—
186C11#1727311yescharacteristic, complemented, Sylow
187C23—24no—
188C23—24no—
189C23—24no—
190C23—216no—
191C23—44no—
192C23—44no—
193C23—44no—
194C23—48no—
195C23—48no—
196C23—48no—
197C23—48no—
198C23—44no—
199C23—44no—
200C23—44no—
201C23C22×Dic2211yescharacteristic
202C23C2×#434114yes—
203C23#6703712yes—
204C23#6703714yes—
205C23#6704214yes—
206D4—416no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—28no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4—44no—
214C2×C4—48no—
215C2×C4—448no—
216C2×C4—448no—
217C2×C4—448no—
218C2×C4—448no—
219C2×C4—448no—
220C2×C4—448no—
221C2×C4—448no—
222C22—48no—
223C22—48no—
224C22—48no—
225C22—44no—
226C22—88no—
227C22—88no—
228C22#1062301411yescharacteristic
229C22#1062301412yes—
230C22#1062307414yes—
231C22#1062311814yes—
232C22#1062312614yes—
233C22#1062314814yes—
234C22#1062315018yes—
235C22#1062319714yes—
236C22#1062321412yes—
237C22#1062324412yes—
238C4—42no—
239C4—48no—
240C4—888no—
241C2—84no—
242C2#1307583114yes—
243C2#1307588414yes—
244C2#1307656212yes—
245C2#1307673914yes—
246C2#1307688011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1438C2
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#17273
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13066885C2semidirect
2. #13066861C2semidirect
186. C11#17273semidirect

Maximal subgroups

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

subgroupindex
#130668852
#130668612
#130668572
C11×#14382
#1727311