Finite Group Databasebeta

← #13080843

Subgroups — #13080843

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
1D4×C22⋊D11C211yesmaximal, characteristic
2#10623064C211yesmaximal, characteristic, complemented
3C11×#418C211yesmaximal, characteristic, complemented
4#10622831C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622616C211yesmaximal, characteristic, complemented
8#10622397C211yesmaximal, characteristic, complemented
9#10622393C211yesmaximal, characteristic, complemented
10#10622389C211yesmaximal, characteristic, complemented
11#10622383C211yesmaximal, characteristic, complemented
12#10622375C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622372C211yesmaximal, characteristic, complemented
15#10622371C211yesmaximal, 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×#4324C2211yescharacteristic
28C2×#4324C2211yescharacteristic, complemented
29#66983C2211yescharacteristic
30C4×C22⋊D11C2211yescharacteristic
31#66977C2211yescharacteristic, complemented
32C2×#4314C2211yescharacteristic, complemented
33C2×#4313C2211yescharacteristic, complemented
34#66950C2211yescharacteristic, complemented
35#66945C2211yescharacteristic, complemented
36#66941C2211yescharacteristic, complemented
37#66940C2211yescharacteristic, complemented
38#66938—21no—
39#66932—21no—
40#66929—21no—
41C4×Dic22—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(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66882C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, 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—44no—
73C2×C22⋊D11D411yescharacteristic
74C22×Dic11—21no—
75D4×D11—22no—
76D4×D11—41no—
77C2×D44C2311yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×M16—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C42×C11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11D411yescharacteristic
92#4324—22no—
93#4324—41no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314—41no—
111#4313—41no—
112#3324—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—42no—
121C22×D11—42no—
122C22×D11—81no—
123C22×D11C2×D411yescharacteristic
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—42no—
128D4×C11#4112yes—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—22no—
136C22⋊D11—42no—
137C22⋊D11—42no—
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—81no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—42no—
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148D44—21no—
149D44—21no—
150C4×D11—21no—
151C4×D11—21no—
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#482—111no—
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#418D1111yescharacteristic, complemented
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—84no—
184C22×C11C22×D411yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—84no—
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11C2×#4111yescharacteristic
196C4×C11H(5,𝔽2)11yescharacteristic
197Dic11—21no—
198Dic11—21no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202Dic11AGL(1,ℤ/8)12yes—
203C22×D4—111no—
204C22×D4—221no—
205C22×D4C2×D1111yescharacteristic
206C2×SD16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×M16—111no—
210C2×M16C2×D1111yescharacteristic, complemented
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—111no—
220#121—221no—
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#107—111no—
231#106—111no—
232C4⋊C8—111no—
233#103—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102C2×D1111yescharacteristic
240#102C2×D1111yescharacteristic
241#102C2×D1111yescharacteristic, complemented
242#102C2×D1111yescharacteristic, complemented
243C22⋊C8—111no—
244C22⋊C8—111no—
245C4×C8—111no—
246C2×C11—42no—
247C2×C11—41no—
248C2×C11—81no—
249C2×C11#54611yescharacteristic
250C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C2×C11#57711yescharacteristic
252D11—41no—
253D11—81no—
254C24—21no—
255C24—221no—
256C2×Q8—111no—
257C2×Q8—221no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—222no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C2×D4—444no—
271C2×D4C22×D1111yescharacteristic
272C2×D4C22×D1111yescharacteristic
273C22×C4—111no—
274C22×C4—221no—
275C22×C4C22×D1111yescharacteristic
276SD16—222no—
277SD16—441no—
278SD16—441no—
279M16—41no—
280M16—441no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—111no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4C22×D1111yescharacteristic
293C4⋊C4C22×D1111yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—111no—
296C22⋊C4—111no—
297C22⋊C4—221no—
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—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—111no—
314C23—221no—
315C23—442no—
316C23—442no—
317C23—881no—
318C23D4×D1111yescharacteristic
319Q8—221no—
320Q8—221no—
321Q8—442no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—222no—
327D4—221no—
328D4—221no—
329D4—442no—
330D4—442no—
331D4—442no—
332D4—442no—
333D4—881no—
334D4#433912yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—111no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—221no—
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—22no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—221no—
365C22—221no—
366C22—221no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—884no—
371C22C2×D4×D1111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—112no—
376C4—221no—
377C4—221no—
378C4—441no—
379C4—441no—
380C4—441no—
381C4C2×#433911yescharacteristic
382C4#6703711yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—441no—
387C2—881no—
388C2#1062302111yescharacteristic
389C2D11×AGL(1,ℤ/8)11yescharacteristic
390C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
prime radicalD4×C22⋊D11C2
hypercenter#418D11
hypocenterC11#3324
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
2. #10623064C2semidirect
3. C11×#418C2semidirect
4. #10622831C2semidirect
5. #10622747C2semidirect
6. #10622741C2semidirect
7. #10622616C2semidirect
8. #10622397C2semidirect
9. #10622393C2semidirect
10. #10622389C2semidirect
11. #10622383C2semidirect
12. #10622375C2semidirect
13. #10622373C2semidirect
14. #10622372C2semidirect
15. #10622371C2semidirect
19. C2×C11×M16C22semidirect
20. C11×#117C22semidirect
28. C2×#4324C22semidirect
31. #66977C22semidirect
32. C2×#4314C22semidirect
33. C2×#4313C22semidirect
34. #66950C22semidirect
35. #66945C22semidirect
36. #66941C22semidirect
37. #66940C22semidirect
44. C11×#102C22semidirect
45. C11×#102C22semidirect
47. #66896C22semidirect
48. C22⋊(C11⋊C8)C22semidirect
49. #66885C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66882C22semidirect
52. #66880C22semidirect
53. Dic11⋊C8C22semidirect
54. C8×Dic11C22semidirect
55. #66873C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
173. #418D11semidirect
210. C2×M16C2×D11semidirect
228. #117C2×D11semidirect
241. #102C2×D11semidirect
242. #102C2×D11semidirect
307. C11#3324semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊D112
#106230642
C11×#4182
#106228312
#106227472
#106227412
#106226162
#106223972
#106223932
#106223892
#106223832
#106223752
#106223732
#106223722
#106223712
#332411