Finite Group Databasebeta

← #13080845

Subgroups — #13080845

Order 1408.

448 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#10623140C211yesmaximal, characteristic
2#10623064C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622655C211yesmaximal, characteristic, complemented
5#10622614C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622499C211yesmaximal, characteristic, complemented
8#10622479C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622389C211yesmaximal, characteristic, complemented
11#10622383C211yesmaximal, characteristic, complemented
12#10622375C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622344C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C2×D4×D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C11×#117C2211yescharacteristic, complemented
21#66993C2211yescharacteristic
22#66990—21no—
23C2×#4324C2211yescharacteristic, complemented
24C4×C22⋊D11C2211yescharacteristic
25#66977C2211yescharacteristic, complemented
26C2×#4318C2211yescharacteristic, complemented
27C2×#4314C2211yescharacteristic
28C2×#4314C2211yescharacteristic, complemented
29C2×#4313C2211yescharacteristic, complemented
30#66950C2211yescharacteristic, complemented
31#66948C2211yescharacteristic
32#66946C2211yescharacteristic
33#66945C2211yescharacteristic, complemented
34#66941C2211yescharacteristic, complemented
35#66940C2211yescharacteristic, complemented
36#66938—21no—
37#66937—21no—
38#66935—21no—
39#66932—21no—
40#66929—21no—
41C4×Dic22—21no—
42C11×#107C2211yescharacteristic, complemented
43C11×#106C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic, complemented
46C11×C22⋊C8C2211yescharacteristic, complemented
47#66896C2211yescharacteristic, complemented
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51Dic11⋊C8C2211yescharacteristic, complemented
52C8×Dic11C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic, complemented
57#66873C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11D411yescharacteristic
68D4×D11—22no—
69D4×D11—41no—
70D4×D11—44no—
71C2×D44—21no—
72C2×D44—22no—
73C2×D44—21no—
74C2×D44—41no—
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C42×C11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11D411yescharacteristic
91#4324—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106#4318—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4314—22no—
110#4314—41no—
111#4313—41no—
112#3324—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—81no—
122C22×D11—81no—
123C22×D11C2×D411yescharacteristic
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—42no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—22no—
135C22⋊D11—42no—
136C22⋊D11—42no—
137C22⋊D11—81no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145D44—21no—
146D44—42no—
147D44—42no—
148D44#4112yes—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—42no—
152Dic22—21no—
153Dic22—21no—
154Dic22—42no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#556—111no—
160D42—111no—
161#486—111no—
162#482—111no—
163#482D1111yescharacteristic, complemented
164#474—111no—
165#468—111no—
166#468—111no—
167#460—111no—
168#450—111no—
169#450—111no—
170C4×SD16—111no—
171#436—111no—
172#418—111no—
173#418—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—22no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—84no—
191C2×D11—84no—
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11C2×#4111yescharacteristic
197C4×C11H(5,𝔽2)11yescharacteristic
198Dic11—21no—
199Dic11—21no—
200Dic11—41no—
201Dic11—41no—
202Dic11AGL(1,ℤ/8)12yes—
203C22×D4—111no—
204C22×D4—111no—
205C22×D4—221no—
206C2×SD16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×M16—111no—
210C2×M16—111no—
211C4⋊Q8—111no—
212#127—111no—
213#126—221no—
214#126—221no—
215#124—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218#121—111no—
219#121—221no—
220#121C2×D1111yescharacteristic
221#120—221no—
222#120—221no—
223C4×Q8—111no—
224C4×Q8—221no—
225C4×D4—111no—
226C4×D4—111no—
227#117—111no—
228#117C2×D1111yescharacteristic, complemented
229#107—111no—
230#107C2×D1111yescharacteristic, complemented
231#106C2×D1111yescharacteristic, complemented
232C4⋊C8—111no—
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⋊C8C2×D1111yescharacteristic, complemented
245C4×C8—111no—
246C2×C11—41no—
247C2×C11—81no—
248C2×C11#54611yescharacteristic
249C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C11#57711yescharacteristic
251D11—41no—
252D11—42no—
253D11—81no—
254C24—221no—
255C24—221no—
256C2×Q8—111no—
257C2×Q8—221no—
258C2×D4—21no—
259C2×D4—111no—
260C2×D4—111no—
261C2×D4—111no—
262C2×D4—222no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4—444no—
272C2×D4C22×D1111yescharacteristic
273C22×C4—111no—
274C22×C4—221no—
275C22×C4C22×D1111yescharacteristic
276SD16—222no—
277SD16—441no—
278SD16—441no—
279M16—441no—
280M16—441no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4C22×D1111yescharacteristic
292C4⋊C4C22×D1111yescharacteristic
293C4⋊C4C22×D1111yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—111no—
297C22⋊C4—111no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C42—21no—
304C42—111no—
305C42—221no—
306C42—221no—
307C11#332411yescharacteristic, complemented, Sylow
308C23—21no—
309C23—111no—
310C23—221no—
311C23—221no—
312C23—442no—
313C23—442no—
314C23—442no—
315C23—442no—
316C23—881no—
317C23—881no—
318C23D4×D1111yescharacteristic
319Q8—221no—
320Q8—221no—
321Q8—442no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—112no—
326D4—222no—
327D4—221no—
328D4—221no—
329D4—221no—
330D4—442no—
331D4—442no—
332D4—442no—
333D4—442no—
334D4—881no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—442no—
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—221no—
361C22—221no—
362C22—221no—
363C22—222no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—884no—
370C22—884no—
371C22C2×D4×D1111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—112no—
377C4—221no—
378C4—221no—
379C4—441no—
380C4—441no—
381C4#41×D1111yescharacteristic
382C4#6704211yescharacteristic
383C2—41no—
384C2—81no—
385C2—441no—
386C2—442no—
387C2—881no—
388C2#1062318511yescharacteristic
389C2#1062330111yescharacteristic
390C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radical#10623140C2
hypercenter#482D11
hypocenterC11#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #10623064C2semidirect
3. C11×#482C2semidirect
4. #10622655C2semidirect
5. #10622614C2semidirect
6. #10622503C2semidirect
7. #10622499C2semidirect
8. #10622479C2semidirect
9. #10622465C2semidirect
10. #10622389C2semidirect
11. #10622383C2semidirect
12. #10622375C2semidirect
13. #10622373C2semidirect
14. #10622344C2semidirect
15. #10622342C2semidirect
20. C11×#117C22semidirect
23. C2×#4324C22semidirect
25. #66977C22semidirect
26. C2×#4318C22semidirect
28. C2×#4314C22semidirect
29. C2×#4313C22semidirect
30. #66950C22semidirect
33. #66945C22semidirect
34. #66941C22semidirect
35. #66940C22semidirect
42. C11×#107C22semidirect
43. C11×#106C22semidirect
44. C11×#102C22semidirect
45. C11×#102C22semidirect
46. C11×C22⋊C8C22semidirect
47. #66896C22semidirect
49. #66885C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. Dic11⋊C8C22semidirect
52. C8×Dic11C22semidirect
53. #66874C22semidirect
56. #66873C22semidirect
57. #66873C22semidirect
58. #66871C22semidirect
163. #482D11semidirect
228. #117C2×D11semidirect
230. #107C2×D11semidirect
231. #106C2×D11semidirect
241. #102C2×D11semidirect
242. #102C2×D11semidirect
244. C22⋊C8C2×D11semidirect
307. C11#3324semidirect

Maximal subgroups

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

subgroupindex
#106231402
#106230642
C11×#4822
#106226552
#106226142
#106225032
#106224992
#106224792
#106224652
#106223892
#106223832
#106223752
#106223732
#106223442
#106223422
#332411