Finite Group Databasebeta

← #14719137

Subgroups — #14719137

Order 2816.

1034 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 243 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#13066887C212yesmaximal
2#13066882C214yesmaximal
3#13066877C214yesmaximal
4#13066867C214yesmaximal
5C11×#1446C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C22×Dic11⋊C4C2214yes—
8C2×C11×#95C2214yes—
9C2×C11×#95C2212yes—
10C2×C11⋊#95C2214yes—
11C2×C11⋊#95C2212yes—
12C2×C11⋊#95C2214yes—
13C2×C11⋊#95C2214yes—
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2212yes—
16C2×C11⋊#95C2214yes—
17C22×Q8×C11—42no—
18C22×Q8×C11—44no—
19C22×Q8×C11Q814yes—
20C23×C4×C11C2314yes—
21C23×C4×C11C2312yes—
22C23×C4×C11C2311yescharacteristic
23C23×Dic11C2314yes—
24C23×Dic11C2314yes—
25C2×Dic11⋊C4—28no—
26C2×Dic11⋊C4—28no—
27C2×Dic11⋊C4—44no—
28C11×#95—42no—
29C11×#95—44no—
30C11⋊#95—28no—
31C11⋊#95—42no—
32C11⋊#95—44no—
33C11⋊#95—44no—
34C11⋊#95—44no—
35C11⋊#95—42no—
36C11⋊#95—44no—
37#17289—111nomaximal, Sylow
38C24×C11C2411yescharacteristic
39C2×Q8×C11—48no—
40C2×Q8×C11—44no—
41C2×Q8×C11—416no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—24no—
45C22×C4×C11—24no—
46C22×C4×C11—22no—
47C22×C4×C11—24no—
48C22×C4×C11—24no—
49C22×C4×C11—24no—
50C22×C4×C11—24no—
51C22×C4×C11—24no—
52C22×C4×C11—24no—
53C22×C4×C11—24no—
54C22×C4×C11—24no—
55C22×C4×C11C2×Q812yes—
56C22×C4×C11C2×Q814yes—
57C22×Dic11—24no—
58C22×Dic11—24no—
59C22×Dic11—24no—
60C22×Dic11—24no—
61C22×Dic11—24no—
62C22×Dic11—24no—
63C22×Dic11—24no—
64C22×Dic11—24no—
65C22×Dic11—24no—
66C22×Dic11—24no—
67C22×Dic11—24no—
68C22×Dic11—24no—
69C22×Dic11—24no—
70C22×Dic11#4118yes—
71Dic11⋊C4—416no—
72#1446—112no—
73#1446D1111yescharacteristic
74#1445—114no—
75#1443—114no—
76#1441—114no—
77C23×C11C22×Q811yescharacteristic
78C23×C11C2×#4114yes—
79C23×C11H(5,𝔽2)12yes—
80C23×C11H(5,𝔽2)14yes—
81C23×C112−1+414yes—
82Q8×C11—416no—
83C2×C4×C11—24no—
84C2×C4×C11—24no—
85C2×C4×C11—24no—
86C2×C4×C11—24no—
87C2×C4×C11—22no—
88C2×C4×C11—44no—
89C2×C4×C11—44no—
90C2×C4×C11—44no—
91C2×C4×C11—44no—
92C2×C4×C11—44no—
93C2×C4×C11—44no—
94C2×C4×C11—44no—
95C2×C4×C11—44no—
96C2×C4×C11—44no—
97C2×C4×C11—44no—
98C2×Dic11—28no—
99C2×Dic11—28no—
100C2×Dic11—28no—
101C2×Dic11—44no—
102C2×Dic11—44no—
103C2×Dic11—44no—
104C2×Dic11—44no—
105C2×Dic11—44no—
106C2×Dic11—44no—
107C2×Dic11—44no—
108C2×Dic11—44no—
109C2×Dic11—44no—
110C2×Dic11—44no—
111C2×Dic11—44no—
112C23×Q8C2×D1111yescharacteristic
113C22×C4⋊C4—114no—
114C2×#95—114no—
115C2×#95—112no—
116C2×#95—114no—
117C2×#95—114no—
118C2×#95—114no—
119C2×#95—112no—
120C2×#95—114no—
121C2×#95C2×D1114yes—
122C2×#95C2×D1112yes—
123C22×C11#53914yes—
124C22×C11#54214yes—
125C22×C11#54214yes—
126C22×C11#54312yes—
127C22×C11#54311yescharacteristic
128C22×C11#55114yes—
129C22×C11#55512yes—
130C22×C11#55714yes—
131C22×C11#56014yes—
132C22×C11#56314yes—
133C22×C11#56312yes—
134C4×C11—42no—
135C4×C11—44no—
136C4×C11—84no—
137Dic11—48no—
138Dic11—84no—
139C22×Q8—42no—
140C22×Q8—44no—
141C22×Q8Dic2214yes—
142C23×C4—114no—
143C23×C4—114no—
144C23×C4C22×D1114yes—
145C23×C4C22×D1112yes—
146C23×C4C22×D1111yescharacteristic
147C2×C4⋊C4—228no—
148C2×C4⋊C4—228no—
149C2×C4⋊C4—444no—
150#95—42no—
151#95—44no—
152#95—228no—
153#95—442no—
154#95—444no—
155#95—444no—
156#95—442no—
157#95—444no—
158#95—444no—
159C2×C11#273714yes—
160C2×C11#279914yes—
161C2×C11#280912yes—
162C2×C11#283814yes—
163C2×C11#284211yescharacteristic
164C24C23×D1111yescharacteristic
165C2×Q8—48no—
166C2×Q8—44no—
167C2×Q8—416no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—24no—
173C22×C4—24no—
174C22×C4—24no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—24no—
179C22×C4—24no—
180C22×C4—24no—
181C22×C4—118no—
182C22×C4—224no—
183C22×C4—224no—
184C22×C4—224no—
185C22×C4—224no—
186C22×C4—224no—
187C22×C4—224no—
188C22×C4—224no—
189C22×C4—224no—
190C22×C4—224no—
191C22×C4—224no—
192C22×C4—224no—
193C22×C4—224no—
194C22×C4—224no—
195C22×C4C2×Dic2214yes—
196C22×C4C2×Dic2212yes—
197C4⋊C4—4416no—
198C11#1728911yescharacteristic, complemented, Sylow
199C23C22×Dic2211yescharacteristic
200C23#6703712yes—
201C23#6703714yes—
202C23#6704014yes—
203C23#41×D1114yes—
204Q8—416no—
205C2×C4—24no—
206C2×C4—24no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—44no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4—44no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—44no—
219C2×C4—44no—
220C2×C4—228no—
221C2×C4—228no—
222C2×C4—228no—
223C2×C4—444no—
224C2×C4—444no—
225C2×C4—444no—
226C2×C4—444no—
227C2×C4—444no—
228C2×C4—444no—
229C2×C4—444no—
230C2×C4—444no—
231C2×C4—444no—
232C2×C4—444no—
233C2×C4—444no—
234C22#1062301412yes—
235C22#1062301411yescharacteristic
236C22#1062310014yes—
237C22#1062312614yes—
238C22#1062316914yes—
239C22#1062317114yes—
240C22#1062317114yes—
241C22#1062320112yes—
242C22#1062321014yes—
243C22#1062326614yes—
244C22#1062326612yes—
245C4—44no—
246C4—42no—
247C4—84no—
248C4—448no—
249C4—884no—
250C2#1307566414yes—
251C2#1307650014yes—
252C2#1307660212yes—
253C2#1307684014yes—
254C2#1307688011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1446C2
hypercenter#1446D11
hypocenterC11#17289
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
198. C11#17289semidirect

Maximal subgroups

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

subgroupindex
#130668872
#130668822
#130668772
#130668672
C11×#14462
#1728911