Finite Group Databasebeta

← #14647102

Subgroups — #14647102

Order 2816.

898 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 179 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#13068526C212yesmaximal
2#13066459C214yesmaximal, complemented
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
4C24×C4×C11C2211yescharacteristic
5C22×C11×C22⋊C4C411yescharacteristic
6C22×C11×C22⋊C4C411yescharacteristic
7C22×C42×C11C412yes—
8C4×C11×C22⋊C4—24no—
9C2×C11×#95C2212yes—
10C2×C22⋊(C11⋊C8)—24no—
11C2×C22⋊(C11⋊C8)C2214yes—
12C25×C11C2×C411yescharacteristic
13C23×C4×C11—24no—
14C23×C4×C11—44no—
15C23×C4×C11C2×C411yescharacteristic
16C23×C4×C11C2×C412yes—
17C23×C4×C11C2×C412yes—
18C23×C4×C11D414yes—
19C23×C4×C11C2311yescharacteristic
20C2×C11×C22⋊C4—22no—
21C2×C11×C22⋊C4—22no—
22C2×C11×C22⋊C4—22no—
23C2×C11×C22⋊C4—24no—
24C2×C11×C22⋊C4C814yescomplemented
25C2×C42×C11—22no—
26C2×C42×C11—22no—
27C2×C42×C11—44no—
28C22×C11⋊C8—24no—
29C11×#95—24no—
30C22⋊(C11⋊C8)—28no—
31C22⋊(C11⋊C8)—48no—
32#8700—111nomaximal, Sylow
33C24×C11—22no—
34C24×C11—22no—
35C24×C11—42no—
36C24×C11—42no—
37C24×C11C22⋊C412yes—
38C24×C11C2×C812yes—
39C24×C11M1612yes—
40C24×C11C22×C411yescharacteristic
41C22×C4×C11—22no—
42C22×C4×C11—24no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—28no—
48C22×C4×C11—28no—
49C22×C4×C11—44no—
50C22×C4×C11—42no—
51C22×C4×C11—416no—
52C22×C4×C11—42no—
53C22×C4×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11—42no—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C2×C814yes—
58C22×C4×C11M1614yes—
59C22×C4×C11C2×D412yes—
60C22×C4×C11#4114yes—
61C11×C22⋊C4—28no—
62C11×C22⋊C4—28no—
63C42×C11—44no—
64C42×C11—44no—
65C2×C11⋊C8—48no—
66C2×C11⋊C8—44no—
67C2×C4×C22⋊C4D1111yescharacteristic
68#1779—112no—
69#1280—114no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—24no—
75C23×C11—24no—
76C23×C11—24no—
77C23×C11—24no—
78C23×C11—44no—
79C23×C11—44no—
80C23×C11—44no—
81C23×C11—44no—
82C23×C11—44no—
83C23×C11—44no—
84C23×C11C22⋊C814yes—
85C23×C11C2×C22⋊C411yescharacteristic
86C23×C11#11712yes—
87C23×C11C22×C811yescharacteristic
88C23×C11C2×M1611yescharacteristic
89C23×C11C2×M1612yes—
90C2×C4×C11—28no—
91C2×C4×C11—22no—
92C2×C4×C11—24no—
93C2×C4×C11—22no—
94C2×C4×C11—24no—
95C2×C4×C11—24no—
96C2×C4×C11—44no—
97C2×C4×C11—416no—
98C2×C4×C11—44no—
99C2×C4×C11—44no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—44no—
105C2×C4×C11—44no—
106C2×C4×C11#9914yes—
107C2×C4×C11#12314yes—
108C11⋊C8—84no—
109C24×C4C2×D1111yescharacteristic
110C22×C22⋊C4Dic1111yescharacteristic
111C22×C22⋊C4Dic1111yescharacteristic
112C22×C42Dic1112yes—
113C2×C22⋊C8—114no—
114C2×C22⋊C8—224no—
115C4×C22⋊C4—24no—
116C2×#95C2×D1112yes—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—24no—
124C22×C11—28no—
125C22×C11—48no—
126C22×C11—48no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—44no—
130C22×C11#38111yescharacteristic
131C22×C11C2×C22⋊C811yescharacteristic
132C22×C11#40711yescharacteristic
133C22×C11C2×#9912yes—
134C22×C11#41312yes—
135C22×C11#43112yes—
136C22×C11#43212yes—
137C4×C11—24no—
138C4×C11—24no—
139C4×C11—44no—
140C4×C11—44no—
141C25C2×Dic1111yescharacteristic
142C23×C4—24no—
143C23×C4—44no—
144C23×C4C2×Dic1111yescharacteristic
145C23×C4C2×Dic1112yes—
146C23×C4C2×Dic1112yes—
147C23×C4C22⋊D1114yes—
148C23×C4C22×D1111yescharacteristic
149C22×C8—224no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—24no—
154C2×C22⋊C4C11⋊C814yescomplemented
155C2×C42—22no—
156C2×C42—22no—
157C2×C42—44no—
158C22⋊C8—228no—
159C22⋊C8—448no—
160#95—24no—
161C2×C11—22no—
162C2×C11—22no—
163C2×C11—44no—
164C2×C11#145912yes—
165C2×C11#146512yes—
166C2×C11#181711yescharacteristic
167C2×C11#181911yescharacteristic
168C2×C11#182211yescharacteristic
169C24—22no—
170C24—22no—
171C24—42no—
172C24—42no—
173C24C2×C11⋊C812yes—
174C24#431812yes—
175C24C22⋊Dic1112yes—
176C24C22×Dic1111yescharacteristic
177C22×C4—22no—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—28no—
184C22×C4—28no—
185C22×C4—42no—
186C22×C4—44no—
187C22×C4—416no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4C2×C11⋊C814yes—
193C22×C4#431814yes—
194C22×C4C22⋊Dic1112yes—
195C22×C4#433914yes—
196C22×C4C2×C22⋊D1112yes—
197C2×C8—448no—
198C2×C8—444no—
199C22⋊C4—28no—
200C22⋊C4—28no—
201C42—44no—
202C42—44no—
203C11#870011yescharacteristic, complemented, Sylow
204C23—22no—
205C23—22no—
206C23—24no—
207C23—24no—
208C23—22no—
209C23—22no—
210C23—24no—
211C23—24no—
212C23—44no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—44no—
217C23—44no—
218C23C22⋊(C11⋊C8)14yes—
219C23C22×C11⋊C811yescharacteristic
220C23C2×#431812yes—
221C23C2×#431811yescharacteristic
222C23#6697912yes—
223C23C2×C22⋊Dic1111yescharacteristic
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—44no—
231C2×C4—416no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—44no—
240C2×C4#6689814yes—
241C2×C4#6698214yes—
242C8—884no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—24no—
250C22—28no—
251C22—48no—
252C22—48no—
253C22—42no—
254C22—42no—
255C22—44no—
256C22#1062253812yes—
257C22#1062253912yes—
258C22C2×C22⋊(C11⋊C8)11yescharacteristic
259C22#1062282011yescharacteristic
260C22#1062282411yescharacteristic
261C22C2×#6689812yes—
262C22#1062285012yes—
263C4—24no—
264C4—24no—
265C4—44no—
266C4—44no—
267C2—22no—
268C2—22no—
269C2—44no—
270C2#1306693412yes—
271C2#1306695412yes—
272C2#1306868411yescharacteristic
273C2#1306869011yescharacteristic
274C2#1306869911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C22×C8
FrattiniC23×C4C22×D11
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#8700
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13066459C2semidirect
24. C2×C11×C22⋊C4C8semidirect
154. C2×C22⋊C4C11⋊C8semidirect
203. C11#8700semidirect

Maximal subgroups

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

subgroupindex
#130685262
#130664592
C2×C4×C11×C22⋊C42
#870011