Finite Group Databasebeta

← #14751929

Subgroups — #14751929

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622613C211yesmaximal, characteristic
2#117×Dic11C211yesmaximal, characteristic
3#13068475C212yesmaximal, complemented
4#13068471C212yesmaximal, complemented
5#13068384C212yesmaximal
6#13068380C212yesmaximal
7#13068369C211yesmaximal, characteristic, complemented
8#13068367C211yesmaximal, characteristic, complemented
9C4×#66879C211yesmaximal, characteristic, complemented
10#97×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#433C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C11×#433C418yescomplemented
16C2×C11×C4⋊C8C2212yes—
17C2×C11×C22⋊C8C2212yes—
18C2×C11×#97C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66879C2212yes—
22C2×#66879C2212yes—
23C2×#66879C2212yes—
24C2×C8×Dic11C2212yes—
25#10622613C418yescomplemented
26C4⋊C4×Dic11C414yes—
27C22⋊C4×Dic11C414yes—
28#10622545C2211yescharacteristic
29#10622545C2211yescharacteristic
30C42×Dic11C2211yescharacteristic
31C42×Dic11C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2212yes—
33C2×#66867C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622188C2212yes—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622188C2212yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2×C412yes—
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C11×#117C2×C414yes—
44C11×#117C2×C414yes—
45C2×C11×C4⋊C4C2×C412yes—
46C2×C11×C22⋊C4C2×C412yes—
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11C2×C412yes—
50#66979—24no—
51C2×C4⋊Dic11C2×C412yes—
52C2×C4×Dic11—24no—
53C2×C4×Dic11C2×C412yes—
54C2×C4×Dic11C2×C414yes—
55C2×C4×Dic11C2×C414yes—
56C2×C4×Dic11C2311yescharacteristic
57C2×C4×Dic11C2311yescharacteristic
58C2×C4×Dic11C2311yescharacteristic
59C2×C4×Dic11C2311yescharacteristic
60C22×C11⋊C8C2312yes—
61C22×C11⋊C8C2312yes—
62C11×C4⋊C8C2×C418yescomplemented
63C11×C22⋊C8C2×C418yes—
64C11×#97C2×C414yescomplemented
65C4×C8×C11C2×C414yescomplemented
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×C418yescomplemented
74#66867C2×C414yescomplemented
75C4×C11⋊C8C2×C414yescomplemented
76#20465—111nomaximal, Sylow
77C24×C11C22×C411yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—24no—
87C22×Dic11—44no—
88C22×Dic11C22×C412yes—
89C22×Dic11C22×C412yes—
90C22×Dic11C22×C412yes—
91C22×Dic11C22×C412yes—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11C22×C414yes—
97C2×C8×C11C22×C414yes—
98C11×C4⋊C4C4218yes—
99C11×C22⋊C4C4218yes—
100C42×C11C22×C412yes—
101C42×C11C22×C412yes—
102C42×C11C22×C412yes—
103C42×C11C22×C412yes—
104C22⋊Dic11—24no—
105C4⋊Dic11—24no—
106C4×Dic11—24no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109C4×Dic11—44no—
110C4×Dic11—44no—
111C4×Dic11#4114yes—
112C4×Dic11#4114yes—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8C22×C414yes—
118C2×C11⋊C8C22×C414yes—
119C2×#433—111no—
120C2×#433D1111yescharacteristic
121C4×#117—111no—
122#1768—112no—
123#1767—112no—
124#1750—112no—
125#1749—112no—
126#1746—111no—
127#1746—111no—
128C4×#97—111no—
129C4×#97—111no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—24no—
133C23×C11C2×C4212yes—
134C23×C11C23×C411yescharacteristic
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11C2×C4214yes—
142C2×C4×C11C2×C4214yes—
143C2×C4×C11C2×C4212yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C2×#4112yes—
147C2×C4×C11C2×#4112yes—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—48no—
155C2×Dic11#11714yes—
156C2×Dic11#11714yes—
157C8×C11—24no—
158C8×C11—24no—
159C11⋊C8—24no—
160C11⋊C8—24no—
161C2×#117—111no—
162C2×#117C2×D1111yescharacteristic
163C22×C42—111no—
164#433—118no—
165#433Dic1118yescomplemented
166C2×C4⋊C8—112no—
167C2×C4⋊C8C2×D1112yes—
168C2×C22⋊C8—112no—
169C2×C22⋊C8C2×D1112yes—
170C2×#97—111no—
171C2×#97—112no—
172C2×#97—112no—
173C2×#97—112no—
174C2×#97C2×D1111yescharacteristic
175C2×C4×C8—111no—
176C2×C4×C8—112no—
177C2×C4×C8C2×D1111yescharacteristic
178C4×C4⋊C4—114no—
179C4×C22⋊C4—114no—
180#376—111no—
181#376—111no—
182C43—111no—
183C43—111no—
184#336—112no—
185#336—112no—
186#336—112no—
187#336—112no—
188C22×C11—24no—
189C22×C11—22no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11C22×C4211yescharacteristic
193C22×C11C2×#11711yescharacteristic
194C22×C11C2×#11711yescharacteristic
195C22×C11#56814yes—
196C4×C11—24no—
197C4×C11—24no—
198C4×C11—22no—
199C4×C11C4×#4112yes—
200C4×C11C4×#4112yes—
201Dic11—24no—
202Dic11—24no—
203Dic11—42no—
204Dic11—42no—
205C23×C4—112no—
206C23×C4C22×D1111yescharacteristic
207C22×C8—112no—
208C22×C8—112no—
209C22×C8C22×D1112yes—
210C22×C8C22×D1112yes—
211#117—224no—
212#117C4×D1114yes—
213#117C2×Dic1114yes—
214C2×C4⋊C4—112no—
215C2×C4⋊C4C4×D1112yes—
216C2×C22⋊C4—112no—
217C2×C22⋊C4C4×D1112yes—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42—112no—
221C2×C42—111no—
222C2×C42—111no—
223C2×C42—114no—
224C2×C42—114no—
225C2×C42—224no—
226C2×C42C22×D1111yescharacteristic
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—118no—
229C4⋊C8C2×Dic1118yescomplemented
230C22⋊C8—118no—
231C22⋊C8C2×Dic1118yes—
232#97—114no—
233#97—224no—
234#97—224no—
235#97—224no—
236#97C2×Dic1114yescomplemented
237C4×C8—114no—
238C4×C8—224no—
239C4×C8C2×Dic1114yescomplemented
240#95—114no—
241#95—114no—
242C2×C11—42no—
243C2×C11C4×#11711yescharacteristic
244C2×C11#287512yes—
245C2×C11#292112yes—
246C2×C11#292312yes—
247C24C2×C4×D1111yescharacteristic
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—112no—
251C22×C4—112no—
252C22×C4—112no—
253C22×C4—112no—
254C22×C4—224no—
255C22×C4—444no—
256C22×C4C2×C4×D1112yes—
257C22×C4C2×C4×D1112yes—
258C22×C4C2×C4×D1111yescharacteristic
259C22×C4C2×C4×D1112yes—
260C22×C4C22×Dic1112yes—
261C22×C4C23×D1111yescharacteristic
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—114no—
267C2×C8—114no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8C22×Dic1114yes—
273C2×C8C22×Dic1114yes—
274C4⋊C4—224no—
275C4⋊C4C4×Dic1118yes—
276C22⋊C4—224no—
277C22⋊C4C4×Dic1118yes—
278C42—114no—
279C42—114no—
280C42—224no—
281C42—222no—
282C42—222no—
283C42—444no—
284C42—444no—
285C42C2×C4×D1112yes—
286C42C2×C4×D1112yes—
287C42C22×Dic1112yes—
288C42C22×Dic1112yes—
289C11#2046511yescharacteristic, complemented, Sylow
290C23—24no—
291C23—21no—
292C23—21no—
293C23C2×C4×Dic1112yes—
294C23C22×C4×D1111yescharacteristic
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—114no—
302C2×C4—114no—
303C2×C4—224no—
304C2×C4—224no—
305C2×C4—224no—
306C2×C4—224no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—448no—
310C2×C4C2×C4×Dic1114yes—
311C2×C4C2×C4×Dic1114yes—
312C2×C4C2×C4×Dic1112yes—
313C2×C4C22×C4×D1111yescharacteristic
314C2×C4#41×D1112yes—
315C2×C4#41×D1112yes—
316C2×C4C23×Dic1111yescharacteristic
317C8—24no—
318C8—24no—
319C8—224no—
320C8—224no—
321C22—24no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22D11×#11711yescharacteristic
326C22D11×#11711yescharacteristic
327C22#1062328114yes—
328C22C22×C4×Dic1111yescharacteristic
329C4—24no—
330C4—24no—
331C4—22no—
332C4—224no—
333C4—224no—
334C4—442no—
335C4—442no—
336C4#1062305312yes—
337C4#41×Dic1112yes—
338C2—42no—
339C2#117×Dic1111yescharacteristic
340C2#1307704212yes—
341C2#1307725012yes—
342C2#1307726412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#433C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#433D11
hypocenterC11#20465
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #13068475C2semidirect
4. #13068471C2semidirect
7. #13068369C2semidirect
8. #13068367C2semidirect
9. C4×#66879C2semidirect
10. #97×Dic11C2semidirect
15. C11×#433C4semidirect
25. #10622613C4semidirect
62. C11×C4⋊C8C2×C4semidirect
64. C11×#97C2×C4semidirect
65. C4×C8×C11C2×C4semidirect
73. C4⋊(C11⋊C8)C2×C4semidirect
74. #66867C2×C4semidirect
75. C4×C11⋊C8C2×C4semidirect
165. #433Dic11semidirect
229. C4⋊C8C2×Dic11semidirect
236. #97C2×Dic11semidirect
239. C4×C8C2×Dic11semidirect
289. C11#20465semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#117×Dic112
#130684752
#130684712
#130683842
#130683802
#130683692
#130683672
C4×#668792
#97×Dic112
C2×C11×#4332
#2046511