Finite Group Databasebeta

← #13071270

Subgroups — #13071270

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×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic
3C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#10622833C211yesmaximal, characteristic, complemented
5#10622826C212yesmaximal, complemented
6C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#10622603C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622559C211yesmaximal, characteristic, complemented
11#10622553C212yesmaximal, complemented
12C24×D11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C23×C4×C11C2211yescharacteristic, complemented
16C22×C22⋊D11C2212yes—
17C23×Dic11C2211yescharacteristic
18C4×D4×C11—24no—
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic, complemented
22C2×C42×C11C2211yescharacteristic, complemented
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2212yescomplemented
26#66990C418yescomplemented
27C2×(C2×D11)⋊C4—24no—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33C2×Dic11⋊C4C2212yescomplemented
34C2×C4×Dic11C2212yescomplemented
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C11⋊#95C2212yescomplemented
38C24×C11C2311yescharacteristic
39C24×C11C2311yescharacteristic
40C23×D11—22no—
41C23×D11—22no—
42C23×D11—42no—
43C23×D11—42no—
44C23×D11C2×C414yescomplemented
45C23×D11C2312yes—
46C2×D4×C11—22no—
47C2×D4×C11—22no—
48C2×D4×C11C2×C414yes—
49C22×C4×C11—22no—
50C22×C4×C11—42no—
51C22×C4×C11—42no—
52C22×C4×C11D414yescomplemented
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C2×C22⋊D11—42no—
59C2×C22⋊D11—42no—
60C2×C22⋊D11C2×C418yescomplemented
61C22×Dic11—22no—
62C22×Dic11—42no—
63C22×Dic11C2312yes—
64C22×Dic11C2312yes—
65C22×Dic11C2312yes—
66C11×C4⋊C4—22no—
67C11×C22⋊C4—22no—
68C11×C22⋊C4—22no—
69C42×C11—22no—
70C22⋊Dic11—22no—
71C22⋊Dic11—42no—
72C22⋊Dic11C2×C414yescomplemented
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—24no—
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—42no—
77(C2×D11)⋊C4C2×C418yescomplemented
78Dic11⋊C4—42no—
79C4×Dic11—42no—
80#2321—111nomaximal, Sylow
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—21no—
84C23×C11—21no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11C22×C412yes—
88C23×C11C22×C412yes—
89C23×C11C2×D412yes—
90C23×C11#4112yes—
91C23×C11C2411yescharacteristic
92C22×D11—28no—
93C22×D11—22no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—22no—
97C22×D11—22no—
98C22×D11—22no—
99C22×D11—48no—
100C22×D11—44no—
101C22×D11—44no—
102C22×D11—48no—
103C22×D11C22×C414yes—
104D4×C11—28no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11C22×C412yes—
116C2×C4×C11C2×D412yes—
117C2×C4×C11C2×D412yes—
118C22⋊D11—48no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—44no—
128C2×Dic11C22×C414yes—
129C2×#120—111no—
130C2×C4×D4D1111yescharacteristic, complemented
131C22×C22⋊C4—111no—
132#390—112no—
133#388—112no—
134#388—112no—
135#386—111no—
136#386—112no—
137#385—111no—
138#379—111no—
139C4×C22⋊C4—111no—
140C22×C11—24no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—24no—
144C22×C11—22no—
145C22×C11—24no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—42no—
149C22×C11C4×D414yes—
150C22×C11C23×C411yescharacteristic
151C22×C11C22×D411yescharacteristic
152C22×C11C2×#4111yescharacteristic
153C22×C11H(5,𝔽2)12yes—
154C22×C11H(5,𝔽2)12yes—
155C2×D11—24no—
156C2×D11—24no—
157C2×D11—24no—
158C2×D11—416no—
159C2×D11—42no—
160C2×D11—42no—
161C2×D11—42no—
162C2×D11—42no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—22no—
166C4×C11—41no—
167C4×C11—41no—
168Dic11—24no—
169Dic11—42no—
170Dic11—42no—
171C25—111no—
172C22×D4—112no—
173C22×D4C2×D1111yescharacteristic
174C23×C4—111no—
175C23×C4C2×D1111yescharacteristic
176C23×C4C2×D1111yescharacteristic, complemented
177#120—118no—
178C4×D4—24no—
179C2×C4⋊C4—112no—
180C2×C4⋊C4C2×D1111yescharacteristic, complemented
181C2×C22⋊C4—111no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—111no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4—224no—
190C2×C22⋊C4C2×D1111yescharacteristic
191C2×C22⋊C4C2×D1111yescharacteristic, complemented
192C2×C42—112no—
193C2×C42C2×D1111yescharacteristic, complemented
194#95—112no—
195#95—112no—
196#95—112no—
197C2×C11—24no—
198C2×C11—42no—
199C2×C11C2×C4×D411yescharacteristic
200C2×C11#51812yes—
201C2×C11#53411yescharacteristic
202C2×C11#53511yescharacteristic
203C2×C11#53812yes—
204D11—44no—
205C24—112no—
206C24—114no—
207C24—222no—
208C24—222no—
209C24—442no—
210C24—442no—
211C24C22×D1111yescharacteristic
212C24C22×D1111yescharacteristic
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—118no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4C4×D1114yes—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—112no—
223C22×C4—112no—
224C22×C4—112no—
225C22×C4—222no—
226C22×C4—442no—
227C22×C4C22⋊D1114yescomplemented
228C22×C4C22×D1111yescharacteristic
229C22×C4C22×D1111yescharacteristic
230C22×C4C22×D1111yescharacteristic
231C22×C4C22×D1111yescharacteristic
232C22×C4C22×D1111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—442no—
235C22⋊C4—22no—
236C22⋊C4—22no—
237C22⋊C4—114no—
238C22⋊C4—118no—
239C22⋊C4—222no—
240C22⋊C4—224no—
241C22⋊C4—224no—
242C22⋊C4—442no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C42—22no—
246C42—442no—
247C11#232111yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—21no—
251C23—22no—
252C23—22no—
253C23—21no—
254C23—114no—
255C23—228no—
256C23—222no—
257C23—222no—
258C23—222no—
259C23—222no—
260C23—222no—
261C23—222no—
262C23—448no—
263C23—444no—
264C23—448no—
265C23—444no—
266C23C2×C4×D1112yes—
267C23C2×C4×D1112yes—
268C23#433912yes—
269C23C2×C22⋊D1112yes—
270C23C23×D1111yescharacteristic
271D4—28no—
272D4—448no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—114no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—444no—
293C2×C4C2×C4×D1112yes—
294C2×C4C2×C22⋊D1112yes—
295C2×C4C2×C22⋊D1112yes—
296C22—24no—
297C22—22no—
298C22—24no—
299C22—22no—
300C22—22no—
301C22—24no—
302C22—41no—
303C22—42no—
304C22—41no—
305C22—224no—
306C22—224no—
307C22—224no—
308C22—4416no—
309C22—442no—
310C22—442no—
311C22—442no—
312C22—442no—
313C22C4×C22⋊D1114yes—
314C22C22×C4×D1111yescharacteristic
315C22C2×#433911yescharacteristic
316C22#6703712yes—
317C22#6704212yes—
318C22C22×C22⋊D1111yescharacteristic
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—41no—
324C4—224no—
325C4—442no—
326C4—442no—
327C2—24no—
328C2—42no—
329C2—444no—
330C2#1062307612yes—
331C2#1062309112yes—
332C2C2×C4×C22⋊D1111yescharacteristic
333C2#1062333511yescharacteristic
334C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC2×C4×D4×C11C2
socle, cosocleC23×C11C24
prime radicalC2×#66990C2
hypercenterC2×C4×D4D11
hypocenterC11#2321
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C11C2semidirect
3. C22×(C2×D11)⋊C4C2semidirect
4. #10622833C2semidirect
5. #10622826C2semidirect
6. C4×C22⋊Dic11C2semidirect
7. #10622603C2semidirect
8. #10622570C2semidirect
9. #10622568C2semidirect
10. #10622559C2semidirect
11. #10622553C2semidirect
15. C23×C4×C11C22semidirect
19. C2×C11×C4⋊C4C22semidirect
21. C2×C11×C22⋊C4C22semidirect
22. C2×C42×C11C22semidirect
25. C2×C22⋊Dic11C22semidirect
26. #66990C4semidirect
33. C2×Dic11⋊C4C22semidirect
34. C2×C4×Dic11C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
37. C11⋊#95C22semidirect
44. C23×D11C2×C4semidirect
52. C22×C4×C11D4semidirect
60. C2×C22⋊D11C2×C4semidirect
72. C22⋊Dic11C2×C4semidirect
77. (C2×D11)⋊C4C2×C4semidirect
130. C2×C4×D4D11semidirect
176. C23×C4C2×D11semidirect
180. C2×C4⋊C4C2×D11semidirect
191. C2×C22⋊C4C2×D11semidirect
193. C2×C42C2×D11semidirect
227. C22×C4C22⋊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×C4×D4×C112
C2×#669902
C22×(C2×D11)⋊C42
#106228332
#106228262
C4×C22⋊Dic112
#106226032
#106225702
#106225682
#106225592
#106225532
#232111