Finite Group Databasebeta

← #13080854

Subgroups — #13080854

Order 1408.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C22⋊D11C211yesmaximal, characteristic, complemented
2#10623063C211yesmaximal, characteristic, complemented
3C11×#418C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622748C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622616C211yesmaximal, characteristic, complemented
8#10622399C211yesmaximal, characteristic, complemented
9#10622395C211yesmaximal, characteristic, complemented
10#10622392C211yesmaximal, characteristic, complemented
11#10622386C211yesmaximal, characteristic, complemented
12#10622383C211yesmaximal, characteristic, complemented
13#10622374C211yesmaximal, characteristic, complemented
14#10622373C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×C22⋊D11—21no—
18C2×D4×D11C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic, complemented
20C11×#117C2211yescharacteristic, complemented
21#67006—21no—
22#66993C2211yescharacteristic
23#66992—21no—
24#66991C2211yescharacteristic
25#66990—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28C2×#4323C2211yescharacteristic, complemented
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic, complemented
31C4×C22⋊D11C2211yescharacteristic
32C2×D88C2211yescharacteristic, complemented
33C2×#4313C2211yescharacteristic, complemented
34#66948C2211yescharacteristic, complemented
35#66946C2211yescharacteristic, complemented
36#66945C2211yescharacteristic, complemented
37#66941C2211yescharacteristic, complemented
38#66938—21no—
39#66937—21no—
40#66928—21no—
41#66925—21no—
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic, complemented
48C22⋊(C11⋊C8)C2211yescharacteristic, complemented
49#66885C2211yescharacteristic, complemented
50#66885C2211yescharacteristic, complemented
51(C2×D11)⋊C8C2211yescharacteristic, complemented
52#66881C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55#66873C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C23×D11—21no—
61C2×D4×C11—22no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—44no—
74C2×C22⋊D11D411yescharacteristic
75C22×Dic11—21no—
76D4×D11—22no—
77D4×D11—41no—
78C2×D44—21no—
79C2×D44C2311yescharacteristic
80C2×D44C2311yescharacteristic
81C2×C4×D11—21no—
82C2×C4×D11C2311yescharacteristic
83C2×Dic22—21no—
84C11×M16—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C42×C11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11D411yescharacteristic
94#4323—22no—
95#4323—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4D411yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4D411yescharacteristic
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110D88—41no—
111#4313—41no—
112#3325—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—81no—
118C23×C11C2×D411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—42no—
122C22×D11—42no—
123C22×D11—81no—
124C22×D11C2×D411yescharacteristic
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—42no—
129D4×C11#4112yes—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C22⋊D11—22no—
137C22⋊D11—42no—
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—42no—
141C22⋊D11—81no—
142C22⋊D11—81no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149D44—21no—
150D44—21no—
151D44—21no—
152D44—21no—
153D44—81no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—42no—
157Dic22—81no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#555—111no—
163D42—111no—
164#486—111no—
165#482—111no—
166#482—111no—
167#476—111no—
168#469—111no—
169#469—111no—
170#459—111no—
171#447—111no—
172#447—111no—
173C4×D8—111no—
174#436—111no—
175#418—111no—
176#418D1111yescharacteristic, complemented
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—84no—
187C22×C11C22×D411yescharacteristic
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—84no—
198C4×C11—21no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11C2×#4111yescharacteristic
202C4×C11H(5,𝔽2)11yescharacteristic
203Dic11—21no—
204Dic11—21no—
205Dic11—41no—
206Dic11—41no—
207Dic11AGL(1,ℤ/8)12yes—
208C22×D4—111no—
209C22×D4—221no—
210C22×D4C2×D1111yescharacteristic
211C2×D8—111no—
212C2×D8—111no—
213C2×D8—111no—
214C2×M16—111no—
215C2×M16C2×D1111yescharacteristic, complemented
216C4⋊Q8—111no—
217#127—111no—
218#124—221no—
219#124—221no—
220#121—111no—
221#121—111no—
222#121—111no—
223#121—111no—
224#121—221no—
225#121—221no—
226#120—221no—
227#120—221no—
228C4×D4—111no—
229C4×D4—111no—
230C4×D4—111no—
231#117—111no—
232#117—221no—
233#117C2×D1111yescharacteristic, complemented
234#107—111no—
235#106—111no—
236#106—111no—
237C4⋊C8—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243#102—111no—
244#102C2×D1111yescharacteristic
245#102C2×D1111yescharacteristic
246#102C2×D1111yescharacteristic, complemented
247#102C2×D1111yescharacteristic, complemented
248C22⋊C8—111no—
249C22⋊C8—111no—
250C4×C8—111no—
251C2×C11—42no—
252C2×C11—41no—
253C2×C11—81no—
254C2×C11#54611yescharacteristic
255C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C2×C11#57611yescharacteristic
257D11—41no—
258D11—81no—
259D11—81no—
260C24—21no—
261C24—221no—
262C2×Q8—221no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—111no—
267C2×D4—111no—
268C2×D4—111no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—222no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C2×D4—444no—
279C2×D4C22×D1111yescharacteristic
280C2×D4C22×D1111yescharacteristic
281C22×C4—111no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4C22×D1111yescharacteristic
285D8—222no—
286D8—441no—
287D8—441no—
288M16—41no—
289M16—441no—
290C2×C8—111no—
291C2×C8—111no—
292C2×C8C22×D1111yescharacteristic
293C2×C8C22×D1111yescharacteristic
294C4⋊C4—111no—
295C4⋊C4—111no—
296C4⋊C4—111no—
297C4⋊C4—221no—
298C4⋊C4C22×D1111yescharacteristic
299C4⋊C4C22×D1111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—111no—
302C22⋊C4—111no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C42—21no—
311C42—111no—
312C42—221no—
313C11#332511yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—111no—
320C23—221no—
321C23—221no—
322C23—442no—
323C23—442no—
324C23—881no—
325C23D4×D1111yescharacteristic
326Q8—881no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—222no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—442no—
337D4—442no—
338D4—442no—
339D4—442no—
340D4—881no—
341D4—881no—
342D4—881no—
343D4#433912yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—111no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4D4×D1111yescharacteristic
358C2×C4C23×D1111yescharacteristic
359C8—21no—
360C8—21no—
361C8—221no—
362C8—221no—
363C22—21no—
364C22—22no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—84no—
373C22—221no—
374C22—221no—
375C22—221no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—884no—
383C22C2×D4×D1111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—112no—
388C4—221no—
389C4—221no—
390C4—441no—
391C4—441no—
392C4C2×#433911yescharacteristic
393C4#6703711yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—441no—
398C2—881no—
399C2—881no—
400C2#1062302111yescharacteristic
401C2D11×AGL(1,ℤ/8)11yescharacteristic
402C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
hypercenter#418D11
hypocenterC11#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. D4×C22⋊D11C2semidirect
2. #10623063C2semidirect
3. C11×#418C2semidirect
4. #10622830C2semidirect
5. #10622748C2semidirect
6. #10622741C2semidirect
7. #10622616C2semidirect
8. #10622399C2semidirect
9. #10622395C2semidirect
10. #10622392C2semidirect
11. #10622386C2semidirect
12. #10622383C2semidirect
13. #10622374C2semidirect
14. #10622373C2semidirect
15. #10622369C2semidirect
19. C2×C11×M16C22semidirect
20. C11×#117C22semidirect
28. C2×#4323C22semidirect
30. #66983C22semidirect
32. C2×D88C22semidirect
33. C2×#4313C22semidirect
34. #66948C22semidirect
35. #66946C22semidirect
36. #66945C22semidirect
37. #66941C22semidirect
44. C11×#102C22semidirect
45. C11×#102C22semidirect
47. #66896C22semidirect
48. C22⋊(C11⋊C8)C22semidirect
49. #66885C22semidirect
50. #66885C22semidirect
51. (C2×D11)⋊C8C22semidirect
52. #66881C22semidirect
53. Dic11⋊C8C22semidirect
54. C8×Dic11C22semidirect
55. #66873C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
176. #418D11semidirect
215. C2×M16C2×D11semidirect
233. #117C2×D11semidirect
246. #102C2×D11semidirect
247. #102C2×D11semidirect
313. C11#3325semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊D112
#106230632
C11×#4182
#106228302
#106227482
#106227412
#106226162
#106223992
#106223952
#106223922
#106223862
#106223832
#106223742
#106223732
#106223692
#332511