Finite Group Databasebeta

← #14763229

Subgroups — #14763229

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2#13071217C212yesmaximal
3#13069599C218yesmaximal
4#13068693C211yesmaximal, characteristic
5#13068691C212yesmaximal
6C11×#1820C211yesmaximal, characteristic
7C2×C11×#117C2211yescharacteristic
8C2×#66979C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10#10623050—24no—
11#10623050—24no—
12C2×#66943C412yescomplemented
13C2×#66941C412yescomplemented
14C2×#66931C2214yes—
15C2×#66923C412yescomplemented
16C2×#66922C412yescomplemented
17C11×#381C2212yes—
18#10622824C2212yes—
19#10622555C2214yes—
20C22⋊C4×Dic11C2214yes—
21#10622267—24no—
22#10622266—24no—
23C11×#342C2214yes—
24#10622165C2218yes—
25#10622164C2214yes—
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2312yes—
28C22×Dic22C2×C414yes—
29C11×#117—22no—
30C11×#117—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4C2314yes—
34C2×C11×C22⋊C4C2312yes—
35C2×C42×C11C2×C412yes—
36C2×C22⋊Dic11C2314yes—
37C2×C22⋊Dic11C2312yes—
38#66979—22no—
39#66979—22no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×C4⋊Dic11C2×C414yes—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11C2×C412yes—
44C2×C4⋊Dic11C2×C412yes—
45C2×C4⋊Dic11D414yes—
46C2×C4⋊Dic11D414yes—
47C2×Dic11⋊C4—24no—
48C2×Dic11⋊C4C2×C414yes—
49C2×Dic11⋊C4C2×C414yes—
50C2×C4×Dic11—24no—
51C2×C4×Dic11C2×C412yes—
52#66943—28no—
53#66941—28no—
54#66931—28no—
55#66931—28no—
56#66923—24no—
57#66923—24no—
58#66922—24no—
59#66922—24no—
60C11×#95—22no—
61C11×#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—24no—
65C11⋊#95—24no—
66#21828—111nomaximal, Sylow
67C24×C11C2411yescharacteristic
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C22×C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D412yes—
76C22×Dic11—24no—
77C22×Dic11—82no—
78C22×Dic11C22×C412yes—
79C22×Dic11C22×C412yes—
80C22×Dic11C22×C414yes—
81C22×Dic11C2×D414yes—
82C22×Dic11C2×D414yes—
83C2×Dic22—28no—
84C2×Dic22—84no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C22⋊C4—24no—
88C11×C22⋊C4—28no—
89C42×C11—22no—
90C42×C11—22no—
91C22⋊Dic11—24no—
92C22⋊Dic11—28no—
93C4⋊Dic11—28no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C22⋊C414yes—
99C4⋊Dic11C22⋊C414yes—
100C4⋊Dic11C22⋊C418yes—
101Dic11⋊C4—28no—
102Dic11⋊C4—28no—
103Dic11⋊C4—84no—
104C4×Dic11—24no—
105C4×Dic11—84no—
106C2×#544—111no—
107#2313—112no—
108#1996—118no—
109#1820—112no—
110#1820—111no—
111#1820D1111yescharacteristic
112C23×C11—41no—
113C23×C11—41no—
114C23×C11C23×C411yescharacteristic
115C23×C11C22×D412yes—
116C23×C112−1+414yes—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—44no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11C2×C22⋊C412yes—
129C2×C4×C11C2×C22⋊C411yescharacteristic
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—44no—
141C2×Dic11C2×C22⋊C418yes—
142Dic22—88no—
143#544—224no—
144#544—224no—
145C2×C4⋊Q8—112no—
146C2×C4⋊Q8—112no—
147C2×#125—112no—
148C2×#125—112no—
149C2×C22⋊Q8—114no—
150C2×#117—111no—
151C2×#117C2×D1111yescharacteristic
152C22×C4⋊C4—111no—
153#387—224no—
154#387—224no—
155#381—112no—
156#381C2×D1112yes—
157#380—114no—
158C4×C22⋊C4—114no—
159#342—114no—
160#342—118no—
161#342C2×D1114yes—
162C22×C11—21no—
163C22×C11—22no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—44no—
167C22×C11C22×C22⋊C411yescharacteristic
168C22×C11#51912yes—
169C22×C11#53614yes—
170C4×C11—22no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—42no—
175C4×C11—84no—
176Dic11—28no—
177Dic11—42no—
178Dic11—42no—
179Dic11—84no—
180C22×Q8—114no—
181C23×C4—112no—
182C23×C4C22×D1111yescharacteristic
183C4⋊Q8—224no—
184C4⋊Q8—224no—
185C4⋊Q8—228no—
186#125—224no—
187#125—224no—
188#125—228no—
189C22⋊Q8—228no—
190C22⋊Q8—228no—
191#117—22no—
192#117—22no—
193#117—222no—
194#117—222no—
195C2×C4⋊C4—112no—
196C2×C4⋊C4—112no—
197C2×C4⋊C4—114no—
198C2×C4⋊C4—114no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—114no—
202C2×C4⋊C4—114no—
203C2×C4⋊C4—114no—
204C2×C4⋊C4—224no—
205C2×C4⋊C4C4×D1111yescharacteristic
206C2×C4⋊C4C4×D1111yescharacteristic
207C2×C22⋊C4—112no—
208C2×C22⋊C4—114no—
209C2×C22⋊C4C22×D1114yes—
210C2×C22⋊C4C22×D1112yes—
211C2×C42—112no—
212C2×C42—224no—
213C2×C42C4×D1112yes—
214#95—22no—
215#95—22no—
216#95—224no—
217#95—224no—
218#95—222no—
219#95—222no—
220C2×C11—24no—
221C2×C11—22no—
222C2×C11#231011yescharacteristic
223C2×C11#288311yescharacteristic
224C2×C11#288411yescharacteristic
225C24C23×D1111yescharacteristic
226C2×Q8—228no—
227C2×Q8—884no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—114no—
231C22×C4—114no—
232C22×C4—114no—
233C22×C4—112no—
234C22×C4—112no—
235C22×C4—224no—
236C22×C4—882no—
237C22×C4C2×C4×D1111yescharacteristic
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4C2×C4×D1112yes—
240C22×C4C2×C4×D1112yes—
241C22×C4D4×D1112yes—
242C22×C4D4×D1112yes—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—114no—
246C4⋊C4—114no—
247C4⋊C4—118no—
248C4⋊C4—228no—
249C4⋊C4—228no—
250C4⋊C4—228no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—884no—
256C22⋊C4—24no—
257C22⋊C4—28no—
258C22⋊C4—224no—
259C22⋊C4—228no—
260C42—22no—
261C42—22no—
262C42—224no—
263C42—884no—
264C11#2182811yescharacteristic, complemented, Sylow
265C23—41no—
266C23—41no—
267C23C22×C4×D1111yescharacteristic
268C23C2×D4×D1112yes—
269C23#6704314yes—
270Q8—888no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—118no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—444no—
286C2×C4—444no—
287C2×C4—444no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—444no—
291C2×C4—444no—
292C2×C4—444no—
293C2×C4C22⋊C4×D1111yescharacteristic
294C2×C4C22⋊C4×D1111yescharacteristic
295C2×C4C22⋊C4×D1112yes—
296C22—21no—
297C22—22no—
298C22—21no—
299C22—22no—
300C22—44no—
301C22C2×C22⋊C4×D1111yescharacteristic
302C22#1062304712yes—
303C22#1062317914yes—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—42no—
308C4—42no—
309C4—84no—
310C4—228no—
311C4—442no—
312C4—442no—
313C4—884no—
314C2—24no—
315C2—22no—
316C2#1307120111yescharacteristic
317C2#1307707511yescharacteristic
318C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1820C2
socleC22×C11C22×C22⋊C4
prime radical, cosocleC24×C11C24
hypercenter#1820D11
hypocenterC11#21828
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
12. C2×#66943C4semidirect
13. C2×#66941C4semidirect
15. C2×#66923C4semidirect
16. C2×#66922C4semidirect
264. C11#21828semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
#130712172
#130695992
#130686932
#130686912
C11×#18202
#2182811