Finite Group Databasebeta

← D11×#385 #13071024

Subgroups — D11×#385 #13071024

Order 1408.

1232 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D11C211yesmaximal, characteristic
2C2×C4⋊C4×D11C212yesmaximal, complemented
3C2×C22⋊C4×D11C211yesmaximal, characteristic
4C2×C22⋊C4×D11C211yesmaximal, characteristic
5C11×#385C211yesmaximal, characteristic, complemented
6#10622823C211yesmaximal, characteristic, complemented
7#10622602C212yesmaximal, complemented
8#10622563C211yesmaximal, characteristic, complemented
9#10622559C211yesmaximal, characteristic, complemented
10#10622281C212yesmaximal, complemented
11D11×#95C212yesmaximal, complemented
12C24×D11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×C4×D11—24no—
16C22×C4×D11—28no—
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2212yes—
20C22×C4×D11C2212yes—
21C22×C4×D11C2212yes—
22C2×C11×C4⋊C4C2212yescomplemented
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2212yes—
30C2×C4⋊Dic11C2212yescomplemented
31C2×Dic11⋊C4C2212yescomplemented
32C2×Dic11⋊C4C2212yescomplemented
33C4⋊C4×D11—28no—
34C22⋊C4×D11—24no—
35C22⋊C4×D11C418yescomplemented
36C11×#95C2212yescomplemented
37C11⋊#95C2212yescomplemented
38C11⋊#95C2212yescomplemented
39C11⋊#95C2212yescomplemented
40C24×C11C2311yescharacteristic
41C23×D11—24no—
42C23×D11—24no—
43C23×D11C2×C414yes—
44C23×D11D414yes—
45C23×D11Q814yes—
46C23×D11C2311yescharacteristic
47C23×D11C2311yescharacteristic
48C22×C4×C11—22no—
49C22×C4×C11—24no—
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2312yes—
53C22×C4×C11C2312yes—
54C22×Dic11—24no—
55C22×Dic11—22no—
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2312yes—
59C22×Dic11C2312yes—
60C2×C4×D11—232no—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×C4×D11—24no—
64C2×C4×D11—24no—
65C2×C4×D11—24no—
66C2×C4×D11—22no—
67C2×C4×D11—22no—
68C2×C4×D11—24no—
69C2×C4×D11—24no—
70C2×C4×D11—24no—
71C2×C4×D11—24no—
72C2×C4×D11C2×C418yescomplemented
73C2×C4×D11D418yes—
74C11×C4⋊C4—24no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4C2×C414yescomplemented
77C22⋊Dic11—22no—
78C22⋊Dic11C2×C414yescomplemented
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4C2×C418yescomplemented
82C4⋊Dic11—24no—
83Dic11⋊C4—24no—
84Dic11⋊C4—24no—
85C2×#385—111nomaximal, Sylow
86C23×C11—22no—
87C23×C11—22no—
88C23×C11C22×C412yes—
89C23×C11C2×D412yes—
90C23×C11C2×Q812yes—
91C23×C11C2411yescharacteristic
92C22×D11—22no—
93C22×D11—22no—
94C22×D11—216no—
95C22×D11—28no—
96C22×D11—216no—
97C22×D11—28no—
98C22×D11C4⋊C4116yescomplemented
99C22×D11C22×C412yes—
100C22×D11C22×C412yes—
101C22×D11C2×D412yes—
102C22×D11C2×D412yes—
103C22×D11C2×D414yes—
104C22×D11C2×Q812yes—
105C22×D11C2×Q812yes—
106C22×D11#4114yes—
107C2×C4×C11—28no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11C22×C414yescomplemented
117C2×C4×C11C2×D414yes—
118C2×Dic11—28no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11C22×C414yescomplemented
128C2×Dic11C2×D414yes—
129C4×D11—216no—
130C4×D11—216no—
131C4×D11—216no—
132C4×D11—44no—
133C4×D11—44no—
134C24×C4—111no—
135C22×C4⋊C4—112no—
136C22×C22⋊C4—111no—
137C22×C22⋊C4—111no—
138#385—111no—
139#385—112no—
140#385—111no—
141#385—111no—
142#385—112no—
143#385D1111yescharacteristic, direct product factor
144C2×#95—112no—
145C22×C11—24no—
146C22×C11—22no—
147C22×C11—24no—
148C22×C11—22no—
149C22×C11C2×C4⋊C414yescomplemented
150C22×C11C23×C411yescharacteristic
151C22×C11C22×D411yescharacteristic
152C22×C11C22×D412yes—
153C22×C11C22×Q811yescharacteristic
154C22×C11C2×#4112yes—
155C2×D11—24no—
156C2×D11—22no—
157C2×D11—24no—
158C2×D11—22no—
159C2×D11—232no—
160C2×D11C2×C4⋊C414yes—
161C2×D11C2×C4⋊C414yescomplemented
162C2×D11C4×D418yes—
163C2×D11#12014yes—
164C2×D11C22⋊Q818yes—
165C2×D11#12314yes—
166C4×C11—24no—
167C4×C11—24no—
168C4×C11—41no—
169C4×C11—41no—
170Dic11—24no—
171Dic11—24no—
172Dic11—41no—
173Dic11—41no—
174C25—111no—
175C23×C4—112no—
176C23×C4—112no—
177C23×C4—111no—
178C23×C4—111no—
179C23×C4—111no—
180C23×C4—112no—
181C23×C4—228no—
182C23×C4—224no—
183C23×C4C2×D1111yescharacteristic
184C2×C4⋊C4—112no—
185C2×C4⋊C4—112no—
186C2×C4⋊C4—112no—
187C2×C4⋊C4—228no—
188C2×C4⋊C4C2×D1112yescomplemented
189C2×C22⋊C4—111no—
190C2×C22⋊C4—112no—
191C2×C22⋊C4—118no—
192C2×C22⋊C4—111no—
193C2×C22⋊C4—111no—
194C2×C22⋊C4—111no—
195C2×C22⋊C4—224no—
196C2×C22⋊C4C2×D1111yescharacteristic
197C2×C22⋊C4C2×D1111yescharacteristic
198#95—112no—
199#95—112no—
200#95—112no—
201#95C2×D1112yescomplemented
202C2×C11—24no—
203C2×C11C22×C4⋊C411yescharacteristic
204C2×C11C2×C4×D412yes—
205C2×C11C2×#12011yescharacteristic
206C2×C11C2×C22⋊Q812yes—
207C2×C11C2×#12311yescharacteristic
208D11—24no—
209D11#38518yesdirect product factor
210C24—111no—
211C24—114no—
212C24—114no—
213C24—114no—
214C24—111no—
215C24—224no—
216C24—224no—
217C24C22×D1111yescharacteristic
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—112no—
221C22×C4—112no—
222C22×C4—118no—
223C22×C4—118no—
224C22×C4—111no—
225C22×C4—111no—
226C22×C4—224no—
227C22×C4—224no—
228C22×C4—224no—
229C22×C4—224no—
230C22×C4—224no—
231C22×C4—224no—
232C22×C4—2232no—
233C22×C4—222no—
234C22×C4—222no—
235C22×C4—224no—
236C22×C4—224no—
237C22×C4—224no—
238C22×C4—222no—
239C22×C4—224no—
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1112yes—
243C22×C4C22×D1112yes—
244C4⋊C4—24no—
245C4⋊C4—224no—
246C4⋊C4—224no—
247C4⋊C4—224no—
248C22⋊C4—22no—
249C22⋊C4—114no—
250C22⋊C4—118no—
251C22⋊C4—222no—
252C22⋊C4—222no—
253C22⋊C4—222no—
254C22⋊C4C4×D1114yescomplemented
255C11C2×#38511yescharacteristic, complemented, Sylow
256C23—22no—
257C23—22no—
258C23—112no—
259C23—114no—
260C23—112no—
261C23—112no—
262C23—114no—
263C23—1116no—
264C23—112no—
265C23—112no—
266C23—112no—
267C23—228no—
268C23—2216no—
269C23—2216no—
270C23—228no—
271C23—222no—
272C23—222no—
273C23C2×C4×D1112yes—
274C23D4×D1112yes—
275C23Q8×D1112yes—
276C23C23×D1111yescharacteristic
277C2×C4—28no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—114no—
287C2×C4—114no—
288C2×C4—2216no—
289C2×C4—2216no—
290C2×C4—2216no—
291C2×C4—228no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4C2×C4×D1114yescomplemented
303C2×C4D4×D1114yes—
304C22—24no—
305C22—22no—
306C22—24no—
307C22—22no—
308C22—114no—
309C22—118no—
310C22—114no—
311C22—118no—
312C22—114no—
313C22—114no—
314C22—2232no—
315C22—224no—
316C22—222no—
317C22—224no—
318C22—222no—
319C22C4⋊C4×D1114yescomplemented
320C22C22×C4×D1111yescharacteristic
321C22C2×D4×D1111yescharacteristic
322C22C2×D4×D1112yes—
323C22C2×Q8×D1111yescharacteristic
324C22#41×D1112yes—
325C4—24no—
326C4—24no—
327C4—41no—
328C4—41no—
329C4—224no—
330C4—224no—
331C4—441no—
332C4—441no—
333C2—24no—
334C2—118no—
335C2—224no—
336C2C2×C4⋊C4×D1111yescharacteristic
337C2C4×D4×D1112yes—
338C2D11×#12011yescharacteristic
339C2D11×C22⋊Q812yes—
340C2D11×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#385C2
socle, cosocleC23×C11C24
prime radicalC24×D11C22
hypercenter#385D11
hypocenterC11C2×#385
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
5. C11×#385C2semidirect
6. #10622823C2semidirect
7. #10622602C2semidirect
8. #10622563C2semidirect
9. #10622559C2semidirect
10. #10622281C2semidirect
11. D11×#95C2semidirect
22. C2×C11×C4⋊C4C22semidirect
30. C2×C4⋊Dic11C22semidirect
31. C2×Dic11⋊C4C22semidirect
32. C2×Dic11⋊C4C22semidirect
35. C22⋊C4×D11C4semidirect
36. C11×#95C22semidirect
37. C11⋊#95C22semidirect
38. C11⋊#95C22semidirect
39. C11⋊#95C22semidirect
72. C2×C4×D11C2×C4semidirect
76. C11×C22⋊C4C2×C4semidirect
78. C22⋊Dic11C2×C4semidirect
81. (C2×D11)⋊C4C2×C4semidirect
98. C22×D11C4⋊C4semidirect
116. C2×C4×C11C22×C4semidirect
127. C2×Dic11C22×C4semidirect
143. #385D11direct (N × H)
149. C22×C11C2×C4⋊C4semidirect
161. C2×D11C2×C4⋊C4semidirect
188. C2×C4⋊C4C2×D11semidirect
201. #95C2×D11semidirect
209. D11#385direct (N × H)
254. C22⋊C4C4×D11semidirect
255. C11C2×#385semidirect
302. C2×C4C2×C4×D11semidirect
319. C22C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D112
C2×C4⋊C4×D112
C2×C22⋊C4×D112
C11×#3852
#106228232
#106226022
#106225632
#106225592
#106222812
D11×#952
C2×#38511