Finite Group Databasebeta

← #14763248

Subgroups — #14763248

Order 2816.

914 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 235 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
1C2×#10623031C211yesmaximal, characteristic
2#13077251C212yesmaximal
3#13069607C214yesmaximal, complemented
4#13069603C214yesmaximal, complemented
5#13068697C212yesmaximal
6#13068696C211yesmaximal, characteristic
7C11×#1821C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C2×#66979C2211yescharacteristic
11C2×#66977C414yes—
12#10623031—28no—
13C2×#66943C412yes—
14C2×#66943C2212yes—
15C2×#66941C412yes—
16C2×#66941C2212yes—
17C11×#407C2212yes—
18#10622820C2212yes—
19#10622731C2214yes—
20M16×Dic11C2214yes—
21#10622333—28no—
22C11×#343C2214yes—
23#10622192C2214yes—
24#10622192C2214yes—
25#10622168C2214yes—
26C23×C4×C11C2×C412yes—
27C23×C4×C11C2311yescharacteristic
28C22×Dic22C2×C414yes—
29C2×C11×M16C2314yes—
30C2×C11×C4⋊C4—24no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2312yes—
33C2×C22⋊Dic11C2×C412yes—
34C2×C22⋊Dic11C2×C412yes—
35#66979—24no—
36#66979D418yes—
37C2×C4⋊Dic11C2×C414yes—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2311yescharacteristic
41C2×C4⋊Dic11C2311yescharacteristic
42#66977—216no—
43C2×Dic11⋊C4C2×C414yes—
44C2×Dic11⋊C4C2×C414yes—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11C2312yes—
47C2×#4318C2314yes—
48#66943—28no—
49#66943—24no—
50#66943—24no—
51#66941—28no—
52#66941—24no—
53#66941—24no—
54C11×C22⋊C8—24no—
55C22⋊(C11⋊C8)—24no—
56#66879—24no—
57Dic11⋊C8—28no—
58C8×Dic11—24no—
59#21832—111nomaximal, Sylow
60C24×C11C22×C411yescharacteristic
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—82no—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C22×C414yes—
66C22×C4×C11C2×D414yes—
67C22×C4×C11C2411yescharacteristic
68C22×Dic11C22×C412yes—
69C22×Dic11C22×C412yes—
70C22×Dic11C22×C412yes—
71C22×Dic11C22×C412yes—
72C2×Dic22—28no—
73C2×Dic22—84no—
74C11×M16—28no—
75C2×C8×C11—24no—
76C11×C4⋊C4—24no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C22⋊Dic11—24no—
80C22⋊Dic11C22⋊C418yes—
81C4⋊Dic11—28no—
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84C4⋊Dic11C22⋊C414yes—
85C4⋊Dic11C22⋊C414yes—
86Dic11⋊C4—28no—
87Dic11⋊C4—28no—
88C4×Dic11—24no—
89C4×Dic11C2×D414yes—
90C4×Dic11C2×D414yes—
91#4318—28no—
92C2×C11⋊C8—24no—
93C2×#544—111no—
94#2921—112no—
95#1998—114no—
96#1997—114no—
97#1822—112no—
98#1821—111no—
99#1821D1111yescharacteristic
100C23×C11—22no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11C2×C22⋊C412yes—
104C23×C11C23×C411yescharacteristic
105C2×C4×C11—22no—
106C2×C4×C11—28no—
107C2×C4×C11—24no—
108C2×C4×C11—44no—
109C2×C4×C11—84no—
110C2×C4×C11C2×C22⋊C412yes—
111C2×C4×C11C22×D412yes—
112C2×C4×C112−1+414yes—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11C2×C22⋊C414yes—
120C2×Dic11C2×C22⋊C414yes—
121Dic22—88no—
122C8×C11—44no—
123C11⋊C8—44no—
124#544—228no—
125C2×C4⋊Q8—112no—
126C2×C4⋊Q8—112no—
127C2×#125—112no—
128C2×#125—112no—
129C2×C22⋊Q8—114no—
130C2×#117—111no—
131C2×#117—111no—
132C22×C4⋊C4C2×D1111yescharacteristic
133#433—228no—
134#423—114no—
135#407—112no—
136#407C2×D1112yes—
137C4×M16—114no—
138#343—114no—
139#343—114no—
140#343—114no—
141#343C2×D1114yes—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—44no—
148C22×C11C22×C22⋊C411yescharacteristic
149C22×C11#51912yes—
150C4×C11—22no—
151C4×C11—44no—
152C4×C11#53614yes—
153Dic11—24no—
154Dic11—24no—
155Dic11—42no—
156Dic11—42no—
157C22×Q8—114no—
158C23×C4C4×D1112yes—
159C23×C4C22×D1111yescharacteristic
160C2×M16—114no—
161C2×M16C22×D1114yes—
162C4⋊Q8—224no—
163C4⋊Q8—224no—
164C4⋊Q8—228no—
165#125—224no—
166#125—224no—
167#125—228no—
168C22⋊Q8—2216no—
169#117—118no—
170#117—224no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—111no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—114no—
175C2×C4⋊C4—114no—
176C2×C4⋊C4—114no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4C4×D1112yes—
180C2×C4⋊C4C22×D1112yes—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C42—112no—
184C2×C42—112no—
185C4⋊C8—228no—
186C22⋊C8—24no—
187C22⋊C8—224no—
188#97—224no—
189C4×C8—224no—
190C2×C11—22no—
191C2×C11—42no—
192C2×C11#231011yescharacteristic
193C2×C11#288811yescharacteristic
194C2×C11#288911yescharacteristic
195C24C2×C4×D1111yescharacteristic
196C2×Q8—228no—
197C2×Q8—884no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—82no—
201C22×C4—112no—
202C22×C4—112no—
203C22×C4—112no—
204C22×C4—112no—
205C22×C4C2×C4×D1111yescharacteristic
206C22×C4C2×C4×D1114yes—
207C22×C4D4×D1114yes—
208C22×C4C23×D1111yescharacteristic
209M16—28no—
210M16—228no—
211C2×C8—24no—
212C2×C8—224no—
213C4⋊C4—24no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—114no—
217C4⋊C4—114no—
218C4⋊C4—228no—
219C4⋊C4—228no—
220C4⋊C4—228no—
221C4⋊C4—222no—
222C4⋊C4—222no—
223C22⋊C4—118no—
224C22⋊C4—224no—
225C42—114no—
226C42—114no—
227C42—224no—
228C11#2183211yescharacteristic, complemented, Sylow
229C23—22no—
230C23—41no—
231C23—41no—
232C23C22⋊C4×D1112yes—
233C23C22×C4×D1111yescharacteristic
234Q8—888no—
235C2×C4—22no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—44no—
239C2×C4—84no—
240C2×C4—114no—
241C2×C4—114no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4C22⋊C4×D1112yes—
249C2×C4C2×D4×D1112yes—
250C2×C4#6704314yes—
251C8—44no—
252C8—444no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—44no—
259C22C2×C22⋊C4×D1111yescharacteristic
260C22#1062304712yes—
261C4—22no—
262C4—44no—
263C4—224no—
264C4—224no—
265C4—442no—
266C4—442no—
267C4#1062317914yes—
268C2—22no—
269C2—42no—
270C2#1307120111yescharacteristic
271C2#1307709211yescharacteristic
272C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1821C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1821D11
hypocenterC11#21832
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13069607C2semidirect
4. #13069603C2semidirect
228. C11#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130772512
#130696072
#130696032
#130686972
#130686962
C11×#18212
#2183211