Finite Group Databasebeta

← #13080644

Subgroups — #13080644

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623248C211yesmaximal, characteristic
2#10623112C211yesmaximal, characteristic, complemented
3C11×#460C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622784C211yesmaximal, characteristic, complemented
6#10622782C211yesmaximal, characteristic, complemented
7#10622782C211yesmaximal, characteristic, complemented
8#10622684C211yesmaximal, characteristic, complemented
9#10622639C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622392C211yesmaximal, characteristic, complemented
13#10622387C211yesmaximal, characteristic, complemented
14#10622383C211yesmaximal, characteristic, complemented
15D11×#102C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C2×D4×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic, complemented
20C2×C11×SD16C2211yescharacteristic, complemented
21C11×#127C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic, complemented
23#66999C2211yescharacteristic, complemented
24#66999C2211yescharacteristic, complemented
25C2×#4325C2211yescharacteristic
26#66991—21no—
27#66991C2211yescharacteristic
28#66991C2211yescharacteristic
29#66990—21no—
30#66990—21no—
31C2×#4313C2211yescharacteristic, complemented
32C2×C8×D11C2211yescharacteristic, complemented
33#66947—21no—
34#66945C2211yescharacteristic, complemented
35C4⋊C4×D11C2211yescharacteristic, complemented
36#66942—21no—
37#66929—21no—
38C4×D44C2211yescharacteristic
39C4×D44C2211yescharacteristic
40#66925—21no—
41#66923C2211yescharacteristic, complemented
42C11×C4⋊C8C2211yescharacteristic, complemented
43C11×#102C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66896C2211yescharacteristic, complemented
47#66896C2211yescharacteristic, complemented
48#66896C2211yescharacteristic, complemented
49#66896C2211yescharacteristic, complemented
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53(C2×D11)⋊C8C2211yescharacteristic, complemented
54#66882C2211yescharacteristic, complemented
55#66881C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70D4×D11—22no—
71D4×D11—22no—
72D4×D11—41no—
73D4×D11—41no—
74D4×D11—44no—
75C2×D44D411yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11C2311yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C11×SD16—41no—
82C11×SD16—41no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C42×C11—21no—
88C42×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91#4325—22no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4D411yescharacteristic
97(C2×D11)⋊C4D411yescharacteristic
98C4⋊Dic11D411yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111C8×D11—41no—
112#3310—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—42no—
131D4×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—42no—
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—42no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146D44—22no—
147D44—21no—
148D44#4112yes—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—42no—
154C4×D11—42no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#552—111no—
160D42—111no—
161#490—111no—
162#482—111no—
163#480—111no—
164#478—111no—
165#468—111no—
166#465—111no—
167#460D1111yescharacteristic, complemented
168#450—111no—
169#450—111no—
170#440—111no—
171#435—111no—
172#418—111no—
173C2×#102—111no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—22no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—84no—
190C2×D11—84no—
191C2×D11AGL(1,ℤ/8)12yes—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11C2×#4111yescharacteristic
197C4×C11H(5,𝔽2)11yescharacteristic
198Dic11—21no—
199Dic11—21no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203C22×D4—111no—
204C22×D4—111no—
205C22×D4—221no—
206C2×SD16—111no—
207C2×SD16C2×D1111yescharacteristic, complemented
208C2×SD16C2×D1111yescharacteristic, complemented
209C2×M16—111no—
210C22×C8—111no—
211#127C2×D1111yescharacteristic
212#126—221no—
213#125—111no—
214#125—221no—
215#123—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218#121—111no—
219#121—111no—
220#121—221no—
221#120—221no—
222#120—221no—
223C4×Q8C2×D1111yescharacteristic, complemented
224C4×D4—111no—
225C4×D4—111no—
226#117—111no—
227#117—221no—
228C2×C4⋊C4—111no—
229#107—111no—
230#107—111no—
231#106—111no—
232C4⋊C8C2×D1111yescharacteristic, complemented
233#103—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102C2×D1111yescharacteristic, complemented
242#102C2×D1111yescharacteristic, complemented
243C22⋊C8—111no—
244C22⋊C8—111no—
245#97—111no—
246C2×C11—81no—
247C2×C11—81no—
248C2×C11#54611yescharacteristic
249C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C11#57711yescharacteristic
251D11—22no—
252D11—41no—
253D11—42no—
254C24—221no—
255C24—221no—
256C2×Q8C22×D1111yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—111no—
260C2×D4—111no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—222no—
264C2×D4—222no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—444no—
270C2×D4C22×D1111yescharacteristic
271C2×D4C22×D1111yescharacteristic
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276SD16—41no—
277SD16—41no—
278SD16—222no—
279M16—441no—
280C2×C8—111no—
281C2×C8—111no—
282C2×C8—441no—
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—111no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—111no—
297C22⋊C4—111no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C42—21no—
305C42—221no—
306C42C22×D1111yescharacteristic
307C11#331011yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—111no—
311C23—111no—
312C23—221no—
313C23—442no—
314C23—442no—
315C23—442no—
316C23—442no—
317C23—881no—
318C23—881no—
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—112no—
328D4—222no—
329D4—221no—
330D4—442no—
331D4—442no—
332D4—442no—
333D4—442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4D4×D1111yescharacteristic
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—112no—
361C22—221no—
362C22—221no—
363C22—221no—
364C22—221no—
365C22—221no—
366C22—222no—
367C22—441no—
368C22—441no—
369C22—884no—
370C22—884no—
371C22C2×D4×D1111yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—221no—
377C4—221no—
378C4—441no—
379C4—441no—
380C4—441no—
381C4#6703711yescharacteristic
382C4#41×D1111yescharacteristic
383C2—81no—
384C2—81no—
385C2—222no—
386C2—441no—
387C2—442no—
388C2#1062314311yescharacteristic
389C2#1062329311yescharacteristic
390C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#460C2
socleC22×C11C22×D4
prime radical#10623248C2
hypercenter#460D11
hypocenterC11#3310
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10623112C2semidirect
3. C11×#460C2semidirect
4. #10622787C2semidirect
5. #10622784C2semidirect
6. #10622782C2semidirect
7. #10622782C2semidirect
8. #10622684C2semidirect
9. #10622639C2semidirect
10. #10622460C2semidirect
11. #10622449C2semidirect
12. #10622392C2semidirect
13. #10622387C2semidirect
14. #10622383C2semidirect
15. D11×#102C2semidirect
19. C2×C11×SD16C22semidirect
20. C2×C11×SD16C22semidirect
22. C4×Q8×C11C22semidirect
23. #66999C22semidirect
24. #66999C22semidirect
31. C2×#4313C22semidirect
32. C2×C8×D11C22semidirect
34. #66945C22semidirect
35. C4⋊C4×D11C22semidirect
41. #66923C22semidirect
42. C11×C4⋊C8C22semidirect
43. C11×#102C22semidirect
44. C11×#102C22semidirect
45. #66899C22semidirect
46. #66896C22semidirect
47. #66896C22semidirect
48. #66896C22semidirect
49. #66896C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. (C2×D11)⋊C8C22semidirect
54. #66882C22semidirect
55. #66881C22semidirect
57. #66871C22semidirect
58. #66867C22semidirect
167. #460D11semidirect
207. C2×SD16C2×D11semidirect
208. C2×SD16C2×D11semidirect
223. C4×Q8C2×D11semidirect
232. C4⋊C8C2×D11semidirect
241. #102C2×D11semidirect
242. #102C2×D11semidirect
307. C11#3310semidirect

Maximal subgroups

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

subgroupindex
#106232482
#106231122
C11×#4602
#106227872
#106227842
#106227822
#106226842
#106226392
#106224602
#106224492
#106223922
#106223872
#106223832
D11×#1022
#331011