Finite Group Databasebeta

← #13071271

Subgroups — #13071271

Order 1408.

808 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67006C211yesmaximal, characteristic
2C22×C22⋊Dic11C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C11×#379C211yesmaximal, characteristic, complemented
5#10622571C211yesmaximal, characteristic, complemented
6#10622570C212yesmaximal, complemented
7#10622569C212yesmaximal, complemented
8#10622559C211yesmaximal, characteristic, complemented
9#10622558C212yesmaximal, complemented
10#10622557C212yesmaximal, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C25×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C23×Dic11C2211yescharacteristic
16C23×Dic11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic, complemented
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2212yes—
21C2×C11×C22⋊C4C2212yes—
22#67006C418yescomplemented
23C2×C22⋊Dic11—24no—
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2212yes—
28C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
29C2×(C2×D11)⋊C4C2212yescomplemented
30C2×Dic11⋊C4C2211yescharacteristic, complemented
31C2×Dic11⋊C4C2212yescomplemented
32C2×C4×Dic11C2211yescharacteristic, complemented
33C2×C4×Dic11C2212yescomplemented
34(C22⋊D11)⋊C4—24no—
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C11⋊#95C2212yescomplemented
38C24×C11—22no—
39C24×C11—22no—
40C24×C11—42no—
41C24×C11—42no—
42C24×C11C2×C414yescomplemented
43C24×C11C2312yes—
44C24×C11C2311yescharacteristic
45C23×D11C2311yescharacteristic
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51C2×C22⋊D11—42no—
52C2×C22⋊D11—42no—
53C2×C22⋊D11C2×C414yes—
54C2×C22⋊D11C2×C418yescomplemented
55C22×Dic11—22no—
56C22×Dic11—42no—
57C22×Dic11—42no—
58C22×Dic11D414yescomplemented
59C22×Dic11C2312yes—
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2312yes—
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C2×C4×D11—22no—
65C2×C4×D11—42no—
66C11×C22⋊C4—22no—
67C11×C22⋊C4—22no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—42no—
70C22⋊Dic11—24no—
71C22⋊Dic11—24no—
72C22⋊Dic11C2×C418yescomplemented
73C22⋊Dic11C2×C414yescomplemented
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—42no—
76Dic11⋊C4—22no—
77Dic11⋊C4—42no—
78C4×Dic11—22no—
79C4×Dic11—42no—
80#2321—111nomaximal, Sylow
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—28no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—48no—
91C23×C11—44no—
92C23×C11—44no—
93C23×C11—48no—
94C23×C11C22×C414yes—
95C23×C11C22×C412yes—
96C23×C11C2×D412yes—
97C23×C11#4112yes—
98C23×C11C2411yescharacteristic
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—22no—
102C22×D11—22no—
103C22×D11C22×C412yes—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C22⋊D11—28no—
112C22⋊D11—48no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C2×Dic11C22×C412yes—
125C2×Dic11C22×C414yes—
126C2×Dic11C2×D412yes—
127C2×Dic11C2×D412yes—
128C4×D11—44no—
129C2×#120—111no—
130C2×C4×D4—111no—
131C22×C22⋊C4—111no—
132#390—112no—
133#388—112no—
134#388—112no—
135#386—112no—
136#386—111no—
137#385—111no—
138#379D1111yescharacteristic, complemented
139C4×C22⋊C4—111no—
140C22×C11—24no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—24no—
144C22×C11—24no—
145C22×C11—24no—
146C22×C11—24no—
147C22×C11—416no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11C4×D414yes—
153C22×C11C23×C411yescharacteristic
154C22×C11C22×D411yescharacteristic
155C22×C11C2×#4111yescharacteristic
156C22×C11H(5,𝔽2)12yes—
157C22×C11H(5,𝔽2)12yes—
158C2×D11—22no—
159C2×D11—24no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—42no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—42no—
166Dic11—22no—
167Dic11—24no—
168Dic11—22no—
169Dic11—22no—
170Dic11—42no—
171C25C2×D1111yescharacteristic
172C22×D4—111no—
173C22×D4—112no—
174C23×C4—111no—
175C23×C4—111no—
176C23×C4—111no—
177#120—118no—
178C4×D4—224no—
179C2×C4⋊C4—111no—
180C2×C4⋊C4—112no—
181C2×C22⋊C4—111no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—111no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—224no—
188C2×C22⋊C4C2×D1111yescharacteristic
189C2×C22⋊C4C2×D1111yescharacteristic
190C2×C22⋊C4C2×D1112yes—
191C2×C22⋊C4C2×D1112yes—
192C2×C42—111no—
193C2×C42—112no—
194#95—112no—
195#95—112no—
196#95—112no—
197C2×C11—24no—
198C2×C11—44no—
199C2×C11C2×C4×D411yescharacteristic
200C2×C11#51812yes—
201C2×C11#53411yescharacteristic
202C2×C11#53511yescharacteristic
203C2×C11#53812yes—
204D11—42no—
205C24—22no—
206C24—22no—
207C24—42no—
208C24—42no—
209C24—111no—
210C24C4×D1114yescomplemented
211C24C22×D1112yes—
212C24C22×D1111yescharacteristic
213C2×D4—114no—
214C2×D4—118no—
215C2×D4—222no—
216C2×D4—222no—
217C2×D4—442no—
218C2×D4—442no—
219C22×C4—111no—
220C22×C4—112no—
221C22×C4—111no—
222C22×C4—111no—
223C22×C4—114no—
224C22×C4—112no—
225C22×C4—222no—
226C22×C4—222no—
227C22×C4—442no—
228C22×C4—442no—
229C22×C4—442no—
230C22×C4C22×D1112yes—
231C22×C4C22×D1111yescharacteristic
232C22×C4C22×D1111yescharacteristic
233C4⋊C4—222no—
234C4⋊C4—442no—
235C22⋊C4—22no—
236C22⋊C4—22no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—118no—
240C22⋊C4—114no—
241C22⋊C4—222no—
242C22⋊C4—224no—
243C22⋊C4—224no—
244C22⋊C4—442no—
245C42—222no—
246C42—442no—
247C11#232111yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—28no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—48no—
258C23—44no—
259C23—44no—
260C23—48no—
261C23—112no—
262C23—221no—
263C23—221no—
264C23—222no—
265C23—222no—
266C23C2×C4×D1114yes—
267C23C2×C4×D1112yes—
268C23D4×D1112yes—
269C23#434112yes—
270C23C23×D1111yescharacteristic
271D4—228no—
272D4—448no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—112no—
281C2×C4—114no—
282C2×C4—112no—
283C2×C4—112no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—444no—
296C22—24no—
297C22—22no—
298C22—22no—
299C22—24no—
300C22—24no—
301C22—24no—
302C22—24no—
303C22—416no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—222no—
309C22—224no—
310C22—441no—
311C22—441no—
312C22—442no—
313C22(C22⋊D11)⋊C414yes—
314C22C22×C4×D1111yescharacteristic
315C22C2×D4×D1111yescharacteristic
316C22C2×#434111yescharacteristic
317C22#6703712yes—
318C22#6703712yes—
319C4—41no—
320C4—41no—
321C4—42no—
322C4—222no—
323C4—224no—
324C4—222no—
325C4—222no—
326C4—442no—
327C2—24no—
328C2—44no—
329C2—442no—
330C2C2×(C22⋊D11)⋊C411yescharacteristic
331C2#1062301712yes—
332C2#1062312011yescharacteristic
333C2#1062312311yescharacteristic
334C2#1062312412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#379C2
socle, cosocleC23×C11C24
prime radicalC2×#67006C2
hypercenter#379D11
hypocenterC11#2321
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Dic11C2semidirect
3. C2×(C22⋊D11)⋊C4C2semidirect
4. C11×#379C2semidirect
5. #10622571C2semidirect
6. #10622570C2semidirect
7. #10622569C2semidirect
8. #10622559C2semidirect
9. #10622558C2semidirect
10. #10622557C2semidirect
11. C22⋊C4×Dic11C2semidirect
17. C22×C4×D11C22semidirect
22. #67006C4semidirect
28. C2×(C2×D11)⋊C4C22semidirect
29. C2×(C2×D11)⋊C4C22semidirect
30. C2×Dic11⋊C4C22semidirect
31. C2×Dic11⋊C4C22semidirect
32. C2×C4×Dic11C22semidirect
33. C2×C4×Dic11C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
37. C11⋊#95C22semidirect
42. C24×C11C2×C4semidirect
54. C2×C22⋊D11C2×C4semidirect
58. C22×Dic11D4semidirect
72. C22⋊Dic11C2×C4semidirect
73. C22⋊Dic11C2×C4semidirect
138. #379D11semidirect
210. C24C4×D11semidirect
247. C11#2321semidirect

Maximal subgroups

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

subgroupindex
C2×#670062
C22×C22⋊Dic112
C2×(C22⋊D11)⋊C42
C11×#3792
#106225712
#106225702
#106225692
#106225592
#106225582
#106225572
C22⋊C4×Dic112
#232111