Finite Group Databasebeta

← D11×#463 #13078036

Subgroups — D11×#463 #13078036

Order 1408.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D11C211yesmaximal, characteristic, complemented
2C2×D8×D11C211yesmaximal, characteristic
3D11×#124C211yesmaximal, characteristic, complemented
4C4×D4×D11C211yesmaximal, characteristic, complemented
5C11×#463C211yesmaximal, characteristic, complemented
6#10622778C211yesmaximal, characteristic, complemented
7#10622766C211yesmaximal, characteristic, complemented
8#10622670C211yesmaximal, characteristic, complemented
9#10622629C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11D11×C4⋊C8C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13D11×#103C211yesmaximal, characteristic, complemented
14#10622400C211yesmaximal, characteristic, complemented
15D11×#102C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C22×C4×D11—21no—
20C2×C11×SD16C2211yescharacteristic, complemented
21C2×C11×D8C2211yescharacteristic
22C11×#124C2211yescharacteristic, complemented
23C4×D4×C11C2211yescharacteristic, complemented
24#67000C2211yescharacteristic, complemented
25C2×#4325C2211yescharacteristic, complemented
26#66989C2211yescharacteristic, complemented
27D4×Dic11C2211yescharacteristic, complemented
28C2×#4324C2211yescharacteristic, complemented
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31C4×C22⋊D11—21no—
32SD16×D11—24no—
33D8×D11—24no—
34C2×D88C2211yescharacteristic
35C2×#4314C2211yescharacteristic, complemented
36C2×C8×D11C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
38#66946C2211yescharacteristic, complemented
39C4⋊C4×D11C2211yescharacteristic
40#66938—21no—
41#66938—21no—
42(C22⋊D11)⋊C4—21no—
43C22⋊C4×D11—21no—
44C22⋊C4×D11—21no—
45C22⋊C4×D11—21no—
46#66928C2211yescharacteristic, complemented
47C4×D44C2211yescharacteristic, complemented
48C42×D11C2211yescharacteristic
49C11×C4⋊C8C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54#66885C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58#66874C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C23×D11—21no—
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C22×Dic11—21no—
70Q8×D11—22no—
71Q8×D11—22no—
72D4×D11—22no—
73D4×D11—22no—
74D4×D11—22no—
75D4×D11D414yes—
76C2×D44C2311yescharacteristic
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—44no—
83C2×C4×D11D411yescharacteristic
84C2×C4×D11D411yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×Dic22—21no—
87C2×Dic22C2311yescharacteristic
88C11×SD16—22no—
89C11×D8—22no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C42×C11C2311yescharacteristic
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100#4325—22no—
101#4324—22no—
102#4323—22no—
103#4323—22no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110C4⋊Dic11C2311yescharacteristic
111Dic11⋊C4—21no—
112C4×Dic11D411yescharacteristic
113C4×Dic11D411yescharacteristic
114C4×Dic11C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117D88—22no—
118#4314—22no—
119C8×D11—22no—
120C8×D11—22no—
121C2×#463—111nomaximal, Sylow
122C23×C11—21no—
123C23×C11—21no—
124C22×D11—21no—
125C22×D11—24no—
126C22×D11—21no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—42no—
132C22×D11C2×D411yescharacteristic
133Q8×C11—21no—
134Q8×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11C2×D412yes—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2411yescharacteristic
145C22⋊D11—24no—
146C22⋊D11—42no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—42no—
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152C2×Dic11C2×D411yescharacteristic
153D44—21no—
154D44—21no—
155D44—21no—
156D44C2×D412yes—
157C4×D11—22no—
158C4×D11—22no—
159C4×D11—42no—
160C4×D11—42no—
161C4×D11—42no—
162C4×D11—42no—
163C4×D11C2×D412yes—
164C4×D11#4112yes—
165Dic22—21no—
166Dic22—21no—
167Dic22—42no—
168C8×C11—21no—
169C8×C11—21no—
170C11⋊C8—21no—
171C11⋊C8—21no—
172C22×SD16—111no—
173C22×D8—111no—
174C2×#124—111no—
175C2×C4×D4—111no—
176#463—111no—
177#463—111no—
178#463—111no—
179#463—111no—
180#463—111no—
181#463—111no—
182#463—111no—
183#463D1111yescharacteristic, direct product factor
184C2×C4⋊C8—111no—
185C2×#103—111no—
186C2×#102—111no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11C22×D411yescharacteristic
194C2×D11—22no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—48no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—84no—
202C2×D11#12112yes—
203C2×D11#13512yes—
204C2×D11AGL(1,ℤ/8)12yes—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11C22×D411yescharacteristic
210C4×C11C2×#4111yescharacteristic
211Dic11—21no—
212Dic11—21no—
213Dic11—41no—
214Dic11—41no—
215Dic11#12112yes—
216C22×Q8—111no—
217C22×D4—111no—
218C22×D4—111no—
219C23×C4—221no—
220C2×SD16—111no—
221C2×SD16—111no—
222C2×SD16—111no—
223C2×SD16—224no—
224C2×SD16C2×D1111yescharacteristic, complemented
225C2×D8—111no—
226C2×D8—111no—
227C2×D8—111no—
228C2×D8—224no—
229C2×D8C2×D1111yescharacteristic
230C22×C8—111no—
231C22×C8—111no—
232#124—111no—
233#124—111no—
234#124—111no—
235#124—221no—
236#124—221no—
237#124C2×D1111yescharacteristic, complemented
238C4×D4—111no—
239C4×D4—111no—
240C4×D4—111no—
241C4×D4—221no—
242C4×D4—221no—
243C4×D4C2×D1111yescharacteristic, complemented
244C2×C4⋊C4—111no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C42—111no—
249C4⋊C8—111no—
250C4⋊C8—111no—
251C4⋊C8—111no—
252C4⋊C8C2×D1111yescharacteristic, complemented
253#103—111no—
254#103—111no—
255#103—111no—
256#103C2×D1111yescharacteristic, complemented
257#102—111no—
258#102—111no—
259#102—111no—
260#102C2×D1111yescharacteristic, complemented
261C2×C11—42no—
262C2×C11—81no—
263C2×C11C2×#12111yescharacteristic
264C2×C11C2×#13511yescharacteristic
265C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
266D11—42no—
267D11—81no—
268D11#46314yesdirect product factor
269C24—221no—
270C24—221no—
271C2×Q8—111no—
272C2×Q8—221no—
273C2×Q8—222no—
274C2×Q8—222no—
275C2×Q8C22×D1111yescharacteristic
276C2×D4—114no—
277C2×D4—111no—
278C2×D4—111no—
279C2×D4—222no—
280C2×D4—222no—
281C2×D4—222no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4C22×D1111yescharacteristic
285C2×D4C22×D1111yescharacteristic
286C22×C4—21no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—444no—
296SD16—22no—
297SD16—222no—
298SD16—222no—
299SD16—222no—
300D8—22no—
301D8—222no—
302D8—222no—
303D8—222no—
304C2×C8—111no—
305C2×C8—111no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8C22×D1111yescharacteristic
309C2×C8C22×D1111yescharacteristic
310C4⋊C4—111no—
311C4⋊C4—221no—
312C4⋊C4C22×D1111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C42—111no—
326C42—111no—
327C42—111no—
328C42C22×D1111yescharacteristic
329C11C2×#46311yescharacteristic, complemented, Sylow
330C23—21no—
331C23—21no—
332C23—111no—
333C23—224no—
334C23—221no—
335C23—221no—
336C23—442no—
337C23—442no—
338C23—442no—
339C23—442no—
340C23—442no—
341Q8—21no—
342Q8—21no—
343Q8—221no—
344Q8—221no—
345Q8—442no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—112no—
350D4—224no—
351D4—221no—
352D4—221no—
353D4—221no—
354D4—442no—
355D4D4×D1112yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—111no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—111no—
363C2×C4—111no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4D4×D1111yescharacteristic
374C2×C4D4×D1111yescharacteristic
375C2×C4C23×D1111yescharacteristic
376C8—21no—
377C8—21no—
378C8—221no—
379C8—221no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—112no—
387C22—112no—
388C22—112no—
389C22—222no—
390C22—448no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—112no—
403C4—221no—
404C4—221no—
405C4—441no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#41×D1111yescharacteristic
409C2—42no—
410C2—81no—
411C2—114no—
412C2—442no—
413C2—881no—
414C2D11×#12111yescharacteristic
415C2D11×#13511yescharacteristic
416C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radicalC2×D8×D11C2
hypercenter#463D11
hypocenterC11C2×#463
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D11C2semidirect
3. D11×#124C2semidirect
4. C4×D4×D11C2semidirect
5. C11×#463C2semidirect
6. #10622778C2semidirect
7. #10622766C2semidirect
8. #10622670C2semidirect
9. #10622629C2semidirect
10. #10622457C2semidirect
11. D11×C4⋊C8C2semidirect
12. #10622432C2semidirect
13. D11×#103C2semidirect
14. #10622400C2semidirect
15. D11×#102C2semidirect
20. C2×C11×SD16C22semidirect
22. C11×#124C22semidirect
23. C4×D4×C11C22semidirect
24. #67000C22semidirect
25. C2×#4325C22semidirect
26. #66989C22semidirect
27. D4×Dic11C22semidirect
28. C2×#4324C22semidirect
35. C2×#4314C22semidirect
38. #66946C22semidirect
46. #66928C22semidirect
47. C4×D44C22semidirect
49. C11×C4⋊C8C22semidirect
50. C11×#103C22semidirect
51. C11×#102C22semidirect
52. #66899C22semidirect
53. #66896C22semidirect
54. #66885C22semidirect
55. #66880C22semidirect
56. Dic11⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
58. #66874C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
183. #463D11direct (N × H)
224. C2×SD16C2×D11semidirect
237. #124C2×D11semidirect
243. C4×D4C2×D11semidirect
252. C4⋊C8C2×D11semidirect
256. #103C2×D11semidirect
260. #102C2×D11semidirect
268. D11#463direct (N × H)
329. C11C2×#463semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D112
C2×D8×D112
D11×#1242
C4×D4×D112
C11×#4632
#106227782
#106227662
#106226702
#106226292
#106224572
D11×C4⋊C82
#106224322
D11×#1032
#106224002
D11×#1022
C2×#46311