Finite Group Databasebeta

← D11×#397 #13071839

Subgroups — D11×#397 #13071839

Order 1408.

820 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D11C212yesmaximal
3C2×C22⋊C4×D11C211yesmaximal, characteristic
4C11×#397C211yesmaximal, characteristic, complemented
5#10622606C211yesmaximal, characteristic, complemented
6#10622566C211yesmaximal, characteristic, complemented
7#10622565C212yesmaximal, complemented
8#10622288C212yesmaximal, complemented
9#10622287C211yesmaximal, characteristic, complemented
10D11×#95C212yesmaximal, complemented
11D11×#95C211yesmaximal, characteristic, complemented
12C24×D11C2211yescharacteristic
13C22×C4×D11C2212yes—
14C22×C4×D11C2212yes—
15C22×C4×D11C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic, complemented
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic, complemented
27C2×Dic11⋊C4C2212yescomplemented
28C4⋊C4×D11—24no—
29C22⋊C4×D11—28no—
30C22⋊C4×D11—24no—
31C11×#95C2211yescharacteristic, complemented
32C11×#95C2212yescomplemented
33C11⋊#95C2212yescomplemented
34C11⋊#95C2212yescomplemented
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C11⋊#95C2211yescharacteristic, complemented
38C24×C11C2311yescharacteristic
39C23×D11—22no—
40C23×D11—22no—
41C23×D11—24no—
42C23×D11—24no—
43C23×D11D414yes—
44C23×D11C2311yescharacteristic
45C23×D11C2311yescharacteristic
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C2×C4×D11—24no—
55C2×C4×D11—24no—
56C2×C4×D11—22no—
57C2×C4×D11—24no—
58C2×C4×D11—24no—
59C2×C4×D11—24no—
60C2×C4×D11—24no—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×C4×D11D414yes—
64C11×C4⋊C4—22no—
65C11×C22⋊C4—24no—
66C11×C22⋊C4—22no—
67C22⋊Dic11—22no—
68C22⋊Dic11—24no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—22no—
73C4⋊Dic11—22no—
74Dic11⋊C4—24no—
75C2×#397—111nomaximal, Sylow
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11C2×D412yes—
81C23×C11C2411yescharacteristic
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—28no—
87C22×D11—216no—
88C22×D11—44no—
89C22×D11—44no—
90C22×D11—48no—
91C22×D11C2×D412yes—
92C22×D11C2×D412yes—
93C22×D11C2×D412yes—
94C22×D11#4112yes—
95C22×D11#4114yes—
96C22×D11#4114yes—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11C2×D412yes—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11C2×D412yes—
117C4×D11—28no—
118C4×D11—48no—
119C4×D11—48no—
120C4×D11—44no—
121C22×C4⋊C4—111no—
122C22×C22⋊C4—111no—
123C22×C22⋊C4—112no—
124#397—111no—
125#397—112no—
126#397—111no—
127#397—111no—
128#397—112no—
129#397D1111yescharacteristic, direct product factor
130C2×#95—111no—
131C2×#95—112no—
132C22×C11—22no—
133C22×C11—24no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—42no—
137C22×C11C22×D411yescharacteristic
138C22×C11C22×D411yescharacteristic
139C22×C11C2×#4111yescharacteristic
140C22×C11C2×#4112yes—
141C22×C11C2×#4112yes—
142C2×D11—22no—
143C2×D11—24no—
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—42no—
147C2×D11—416no—
148C2×D11#12114yes—
149C2×D11#12318yes—
150C2×D11#12314yes—
151C2×D11#12414yes—
152C2×D11#12618yes—
153C4×C11—22no—
154C4×C11—42no—
155C4×C11—42no—
156C4×C11—41no—
157Dic11—22no—
158Dic11—42no—
159Dic11—42no—
160Dic11—41no—
161C25—111no—
162C23×C4—111no—
163C23×C4—112no—
164C23×C4—111no—
165C23×C4—112no—
166C2×C4⋊C4—112no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—224no—
169C2×C4⋊C4C2×D1111yescharacteristic, complemented
170C2×C22⋊C4—111no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—111no—
176C2×C22⋊C4—224no—
177C2×C22⋊C4—228no—
178C2×C22⋊C4C2×D1112yes—
179C2×C22⋊C4C2×D1111yescharacteristic
180#95—112no—
181#95—112no—
182#95—111no—
183#95—112no—
184#95—112no—
185#95C2×D1112yescomplemented
186#95C2×D1111yescharacteristic, complemented
187C2×C11—42no—
188C2×C11C2×#12111yescharacteristic
189C2×C11C2×#12311yescharacteristic
190C2×C11C2×#12312yes—
191C2×C11C2×#12411yescharacteristic
192C2×C11C2×#12612yes—
193D11—42no—
194D11#39718yesdirect product factor
195C24—111no—
196C24—114no—
197C24—111no—
198C24—222no—
199C24—222no—
200C24—224no—
201C24—224no—
202C24C22×D1111yescharacteristic
203C22×C4—111no—
204C22×C4—114no—
205C22×C4—112no—
206C22×C4—111no—
207C22×C4—112no—
208C22×C4—224no—
209C22×C4—222no—
210C22×C4—224no—
211C22×C4—224no—
212C22×C4—224no—
213C22×C4—224no—
214C22×C4—224no—
215C22×C4—224no—
216C22×C4—224no—
217C22×C4C22×D1112yes—
218C22×C4C22×D1111yescharacteristic
219C22×C4C22×D1112yes—
220C22×C4C22×D1111yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—224no—
223C4⋊C4—222no—
224C22⋊C4—24no—
225C22⋊C4—22no—
226C22⋊C4—222no—
227C22⋊C4—224no—
228C22⋊C4—224no—
229C22⋊C4—222no—
230C22⋊C4—224no—
231C22⋊C4—222no—
232C11C2×#39711yescharacteristic, complemented, Sylow
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—112no—
238C23—112no—
239C23—112no—
240C23—114no—
241C23—114no—
242C23—112no—
243C23—228no—
244C23—2216no—
245C23—221no—
246C23—221no—
247C23—222no—
248C23—222no—
249C23—448no—
250C23—444no—
251C23—444no—
252C23D4×D1112yes—
253C23C23×D1111yescharacteristic
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—112no—
264C2×C4—228no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—222no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—448no—
275C2×C4—448no—
276C2×C4—444no—
277C2×C4D4×D1112yes—
278C22—22no—
279C22—24no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—118no—
284C22—114no—
285C22—114no—
286C22—118no—
287C22—114no—
288C22—222no—
289C22—224no—
290C22—4416no—
291C22—442no—
292C22—441no—
293C22—441no—
294C22C2×D4×D1111yescharacteristic
295C22C2×D4×D1111yescharacteristic
296C22#41×D1111yescharacteristic
297C22#41×D1112yes—
298C22#41×D1112yes—
299C4—22no—
300C4—42no—
301C4—42no—
302C4—41no—
303C4—222no—
304C4—442no—
305C4—442no—
306C4—441no—
307C2—42no—
308C2—118no—
309C2—442no—
310C2D11×#12111yescharacteristic
311C2D11×#12311yescharacteristic
312C2D11×#12312yes—
313C2D11×#12411yescharacteristic
314C2D11×#12612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×D11C22
hypercenter#397D11
hypocenterC11C2×#397
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D11C2semidirect
4. C11×#397C2semidirect
5. #10622606C2semidirect
6. #10622566C2semidirect
7. #10622565C2semidirect
8. #10622288C2semidirect
9. #10622287C2semidirect
10. D11×#95C2semidirect
11. D11×#95C2semidirect
17. C2×C11×C4⋊C4C22semidirect
26. C2×C4⋊Dic11C22semidirect
27. C2×Dic11⋊C4C22semidirect
31. C11×#95C22semidirect
32. C11×#95C22semidirect
33. C11⋊#95C22semidirect
34. C11⋊#95C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
37. C11⋊#95C22semidirect
129. #397D11direct (N × H)
169. C2×C4⋊C4C2×D11semidirect
185. #95C2×D11semidirect
186. #95C2×D11semidirect
194. D11#397direct (N × H)
232. C11C2×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D112
C2×C22⋊C4×D112
C11×#3972
#106226062
#106225662
#106225652
#106222882
#106222872
D11×#952
C2×#39711