Finite Group Databasebeta

← #14752010

Subgroups — #14752010

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622613C211yesmaximal, characteristic
2#13071114C211yesmaximal, characteristic
3#13068488C212yesmaximal, complemented
4#13068483C212yesmaximal, complemented
5#13068397C212yesmaximal
6#13068392C212yesmaximal
7#13068369C211yesmaximal, characteristic, complemented
8#13068364C211yesmaximal, characteristic, complemented
9#13068302C211yesmaximal, characteristic, complemented
10C4×#66879C211yesmaximal, characteristic, complemented
11C2×C11×#405C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#405C418yescomplemented
16C2×C11×#97C2211yescharacteristic
17C2×C11×#97C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C4×C22⋊Dic11C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×#66879C2212yes—
23C2×#66879C2212yes—
24C2×#66879C2212yes—
25C2×C8×Dic11C2212yes—
26#10622613C418yescomplemented
27#10622594C414yes—
28#10622564C414yes—
29C4×C4⋊Dic11C2212yes—
30#10622545C2211yescharacteristic
31C42×Dic11C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2212yes—
33C2×#66867C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622188C2212yes—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622188C2212yes—
39C23×C4×C11C2311yescharacteristic
40C2×C11×M16—24no—
41C2×C11×M16C2×C414yes—
42C22×C8×C11—24no—
43C22×C8×C11C2×C414yes—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#117C2×C414yes—
49C11×#117C2×C414yes—
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C22⋊C4C2×C412yes—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11C2×C414yes—
55C2×C4⋊Dic11C2×C414yes—
56C2×C4×Dic11C2×C414yes—
57C2×C4×Dic11C2312yes—
58C2×C4×Dic11C2312yes—
59C22×C11⋊C8C2312yes—
60C22×C11⋊C8C2312yes—
61C11×#97C2×C414yes—
62C11×#97C2×C414yes—
63C4×C8×C11C2×C414yes—
64C4×C8×C11C2×C414yes—
65C11⋊#95C2×C414yes—
66C11⋊#95C2×C414yes—
67C11⋊#95C2×C414yes—
68C22⋊(C11⋊C8)C2×C418yes—
69#66879—24no—
70#66879—24no—
71#66879—24no—
72C8×Dic11—24no—
73C4⋊(C11⋊C8)C2×C418yes—
74#66867C2×C414yes—
75C4×C11⋊C8C2×C414yes—
76#20475—111nomaximal, Sylow
77C24×C11C22×C411yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2411yescharacteristic
86C22×Dic11C22×C414yes—
87C22×Dic11C22×C414yes—
88C11×M16—28no—
89C2×C8×C11—28no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11C22×C412yes—
93C2×C8×C11C22×C412yes—
94C2×C8×C11C22×C412yes—
95C2×C8×C11C22×C412yes—
96C2×C8×C11#4114yes—
97C2×C8×C11#4114yes—
98C11×C4⋊C4C4218yes—
99C11×C22⋊C4C4218yes—
100C42×C11C22×C412yes—
101C42×C11C22×C412yes—
102C42×C11C22×C412yes—
103C42×C11C22×C412yes—
104C22⋊Dic11—44no—
105C4⋊Dic11—44no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11—44no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8C22×C414yes—
116C2×C11⋊C8C22×C414yes—
117C2×#433—111no—
118C2×#405D1111yescharacteristic
119#2298—111no—
120#1771—112no—
121#1770—112no—
122#1753—112no—
123#1752—112no—
124#1746—111no—
125#1745—111no—
126#1726—111no—
127C4×#97—111no—
128C23×C11—22no—
129C23×C11—24no—
130C23×C11C2×C4212yes—
131C23×C11C23×C411yescharacteristic
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11C2×C4214yes—
139C2×C4×C11C2×C4214yes—
140C2×C4×C11C2×C4212yes—
141C2×C4×C11C23×C411yescharacteristic
142C2×C4×C11C23×C411yescharacteristic
143C2×C4×C11C2×#4112yes—
144C2×C4×C11C2×#4112yes—
145C2×Dic11—24no—
146C2×Dic11—24no—
147C2×Dic11—24no—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—24no—
151C8×C11—22no—
152C8×C11—22no—
153C8×C11#11714yes—
154C8×C11#11714yes—
155C11⋊C8—24no—
156C11⋊C8—24no—
157C22×M16C2×D1111yescharacteristic
158C23×C8C2×D1111yescharacteristic
159C2×#117C2×D1111yescharacteristic
160#433—118no—
161C2×C4⋊C8—112no—
162C2×C22⋊C8—112no—
163#405Dic1118yescomplemented
164C2×#97—111no—
165C2×#97—112no—
166C2×#97—112no—
167C2×#97—112no—
168C2×#97C2×D1111yescharacteristic
169C2×#97C2×D1111yescharacteristic
170C2×C4×C8—111no—
171C2×C4×C8—112no—
172C2×C4×C8C2×D1111yescharacteristic
173C2×C4×C8C2×D1111yescharacteristic
174#388—114no—
175#387—114no—
176C4×C4⋊C4—112no—
177C4×C22⋊C4—112no—
178#376—111no—
179C43—111no—
180#336—112no—
181#336—112no—
182#336—112no—
183#336—112no—
184C22×C11—24no—
185C22×C11—22no—
186C22×C11—44no—
187C22×C11C22×C4211yescharacteristic
188C22×C11C4×#4112yes—
189C22×C11#56814yes—
190C4×C11—24no—
191C4×C11—24no—
192C4×C11—22no—
193C4×C11C2×#11711yescharacteristic
194C4×C11C2×#11711yescharacteristic
195C4×C11C4×#4112yes—
196Dic11—44no—
197Dic11—44no—
198C23×C4C22×D1111yescharacteristic
199C2×M16—24no—
200C2×M16C2×Dic1114yes—
201C22×C8—24no—
202C22×C8—112no—
203C22×C8—112no—
204C22×C8C2×Dic1114yes—
205C22×C8C22×D1111yescharacteristic
206C22×C8C22×D1111yescharacteristic
207C22×C8C22×D1111yescharacteristic
208C22×C8C22×D1111yescharacteristic
209#117C4×D1114yes—
210#117C2×Dic1114yes—
211C2×C4⋊C4—114no—
212C2×C4⋊C4C4×D1112yes—
213C2×C22⋊C4—114no—
214C2×C22⋊C4C4×D1112yes—
215C2×C42—112no—
216C2×C42—112no—
217C2×C42—114no—
218C2×C42C22×D1111yescharacteristic
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—118no—
221C22⋊C8—118no—
222#97—114no—
223#97—224no—
224#97—224no—
225#97—224no—
226#97C2×Dic1114yes—
227#97C2×Dic1114yes—
228C4×C8—114no—
229C4×C8—224no—
230C4×C8C2×Dic1114yes—
231C4×C8C2×Dic1114yes—
232#95—114no—
233#95—114no—
234#95—114no—
235C2×C11—42no—
236C2×C11C4×#11711yescharacteristic
237C2×C11#287512yes—
238C2×C11#296714yes—
239C24C2×C4×D1111yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—114no—
243C22×C4—114no—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4C2×C4×D1112yes—
246C22×C4C2×C4×D1112yes—
247C22×C4C2×C4×D1112yes—
248C22×C4C22×Dic1112yes—
249C22×C4C23×D1111yescharacteristic
250M16—28no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—28no—
254C2×C8—114no—
255C2×C8—114no—
256C2×C8—222no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8#433914yes—
261C2×C8#433914yes—
262C2×C8C22×Dic1112yes—
263C2×C8C22×Dic1112yes—
264C2×C8C22×Dic1112yes—
265C2×C8C22×Dic1112yes—
266C4⋊C4—444no—
267C4⋊C4C4×Dic1118yes—
268C22⋊C4—444no—
269C22⋊C4C4×Dic1118yes—
270C42—222no—
271C42—222no—
272C42—222no—
273C42—222no—
274C42—444no—
275C42C2×C4×D1112yes—
276C42C2×C4×D1112yes—
277C42C22×Dic1112yes—
278C42C22×Dic1112yes—
279C11#2047511yescharacteristic, complemented, Sylow
280C23—22no—
281C23—24no—
282C23C2×C4×Dic1112yes—
283C23C22×C4×D1111yescharacteristic
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—224no—
291C2×C4—224no—
292C2×C4—224no—
293C2×C4—224no—
294C2×C4—224no—
295C2×C4—224no—
296C2×C4C2×C4×Dic1114yes—
297C2×C4C2×C4×Dic1114yes—
298C2×C4C2×C4×Dic1112yes—
299C2×C4C22×C4×D1111yescharacteristic
300C2×C4C2×#433912yes—
301C2×C4C2×#433912yes—
302C2×C4C23×Dic1111yescharacteristic
303C8—22no—
304C8—22no—
305C8—224no—
306C8—224no—
307C8#6697914yes—
308C8#6697914yes—
309C22—24no—
310C22—22no—
311C22—44no—
312C22C4×#433912yes—
313C22#1062328114yes—
314C22C22×C4×Dic1111yescharacteristic
315C4—24no—
316C4—24no—
317C4—22no—
318C4—444no—
319C4—444no—
320C4C4×#433912yes—
321C4C2×#6697911yescharacteristic
322C4C2×#6697911yescharacteristic
323C2—42no—
324C2C4×#6697911yescharacteristic
325C2#1307704212yes—
326C2#1307759714yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#405C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#405D11
hypocenterC11#20475
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
3. #13068488C2semidirect
4. #13068483C2semidirect
7. #13068369C2semidirect
8. #13068364C2semidirect
9. #13068302C2semidirect
10. C4×#66879C2semidirect
15. C11×#405C4semidirect
26. #10622613C4semidirect
163. #405Dic11semidirect
279. C11#20475semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130711142
#130684882
#130684832
#130683972
#130683922
#130683692
#130683642
#130683022
C4×#668792
C2×C11×#4052
#2047511