Finite Group Databasebeta

← #13080751

Subgroups — #13080751

Order 1408.

462 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
1C11×#553C211yesmaximal, characteristic, complemented
2D4×D44C211yesmaximal, characteristic, complemented
3#10622680C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622652C211yesmaximal, characteristic, complemented
6#10622651C211yesmaximal, characteristic, complemented
7#10622649C211yesmaximal, characteristic, complemented
8#10622649C211yesmaximal, characteristic, complemented
9#10622628C211yesmaximal, characteristic, complemented
10#10622627C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic, complemented
12#10622616C211yesmaximal, characteristic, complemented
13#10622614C211yesmaximal, characteristic, complemented
14#10622581C211yesmaximal, characteristic, complemented
15C2×#66873C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C22×D44C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C11×#126—21no—
20C11×#125C2211yescharacteristic, complemented
21C11×#123—21no—
22C11×#121—21no—
23C11×#121C2211yescharacteristic, complemented
24C11×#121C2211yescharacteristic, complemented
25C4×D4×C11—21no—
26C4×D4×C11C2211yescharacteristic
27C4×D4×C11C2211yescharacteristic, complemented
28C11×#117C2211yescharacteristic, complemented
29C2×C11×C4⋊C4C2211yescharacteristic, complemented
30C2×#4323C2211yescharacteristic
31C2×#4323C2211yescharacteristic, complemented
32C2×#4323C2211yescharacteristic, complemented
33#66983C2211yescharacteristic
34#66983C2211yescharacteristic
35C2×#4318C2211yescharacteristic, complemented
36C22×C11⋊C8C2211yescharacteristic, complemented
37#66948—21no—
38#66935—21no—
39#66935—21no—
40#66927C2211yescharacteristic
41C4×D44C2211yescharacteristic
42#66896C2211yescharacteristic, complemented
43C22⋊(C11⋊C8)C2211yescharacteristic, complemented
44C22⋊(C11⋊C8)C2211yescharacteristic, complemented
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66873C2211yescharacteristic, complemented
49#66873C2211yescharacteristic, complemented
50#66873C2211yescharacteristic, complemented
51#66873C2211yescharacteristic, complemented
52#66873C2211yescharacteristic, complemented
53#66873C2211yescharacteristic, complemented
54#66872C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66871C2211yescharacteristic, complemented
57C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11D411yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71D4×D11—44no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44C2311yescharacteristic
81C2×D44C2311yescharacteristic
82C2×D44C2311yescharacteristic
83C2×C4×D11—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4D411yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4D411yescharacteristic
96C11×C22⋊C4D411yescharacteristic
97C42×C11—21no—
98C42×C11C2311yescharacteristic
99#4323—22no—
100#4323—41no—
101#4323—41no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11C2311yescharacteristic
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#3318—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122C22×D11—42no—
123C22×D11—81no—
124C22×D11—81no—
125D4×C11—22no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—42no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2411yescharacteristic
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—21no—
147D44—21no—
148D44—21no—
149D44—21no—
150D44—21no—
151D44—21no—
152D44—42no—
153D44—42no—
154D44—42no—
155D44—81no—
156D44#4112yes—
157C4×D11—42no—
158C11⋊C8—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#553D1111yescharacteristic, complemented
163D42—111no—
164#490—111no—
165#482—111no—
166#481—111no—
167#478—111no—
168#469—111no—
169#466—111no—
170#459—111no—
171#447—111no—
172#447—111no—
173#442—111no—
174#435—111no—
175#418—111no—
176C2×#102—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11AGL(1,ℤ/8)12yes—
186C22×C11C22×D411yescharacteristic
187C2×D11—22no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—84no—
197C2×D11—84no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11C2×#4111yescharacteristic
206C4×C11H(5,𝔽2)11yescharacteristic
207Dic11—41no—
208C22×D4—111no—
209C22×D4—111no—
210C22×D4—221no—
211C2×D8—111no—
212C2×D8—111no—
213C2×D8—111no—
214C2×M16—111no—
215C22×C8—111no—
216#127—111no—
217#126—21no—
218#125C2×D1111yescharacteristic, complemented
219#123—21no—
220#121—21no—
221#121—111no—
222#121—111no—
223#121—221no—
224#121C2×D1111yescharacteristic, complemented
225#121C2×D1111yescharacteristic, complemented
226#120—221no—
227#120—221no—
228C4×D4—21no—
229C4×D4—111no—
230C4×D4C2×D1111yescharacteristic
231C4×D4C2×D1111yescharacteristic, complemented
232#117C2×D1111yescharacteristic, complemented
233C2×C4⋊C4C2×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#102—111no—
245#102—111no—
246#102—111no—
247#102—111no—
248C22⋊C8—111no—
249C22⋊C8—111no—
250#97—111no—
251C2×C11—22no—
252C2×C11—41no—
253C2×C11—81no—
254C2×C11#54611yescharacteristic
255C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C2×C11#57611yescharacteristic
257D11—42no—
258D11—81no—
259D11—81no—
260C24—221no—
261C24—221no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—111no—
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—444no—
278C2×D4C22⋊D1111yescharacteristic
279C2×D4C22×D1111yescharacteristic
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—221no—
283C22×C4C22×D1111yescharacteristic
284C22×C4C22×D1111yescharacteristic
285D8—222no—
286D8—441no—
287D8—441no—
288M16—441no—
289C2×C8—111no—
290C2×C8—111no—
291C2×C8—111no—
292C2×C8—111no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—111no—
298C4⋊C4C22⋊D1111yescharacteristic
299C4⋊C4C22×D1111yescharacteristic
300C4⋊C4C22×D1111yescharacteristic
301C4⋊C4C22×D1111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4C22⋊D1111yescharacteristic
310C22⋊C4C22⋊D1111yescharacteristic
311C42—21no—
312C42C22×D1111yescharacteristic
313C11#331811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—442no—
319C23—442no—
320C23—442no—
321C23—442no—
322C23—881no—
323C23—881no—
324C23C2×C22⋊D1111yescharacteristic
325C23C2×C22⋊D1111yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—81no—
331D4—112no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—221no—
337D4—442no—
338D4—442no—
339D4—442no—
340D4—442no—
341D4—442no—
342D4—881no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—221no—
353C2×C4—442no—
354C2×C4C2×C22⋊D1111yescharacteristic
355C2×C4C2×C22⋊D1111yescharacteristic
356C2×C4C2×C22⋊D1111yescharacteristic
357C2×C4C2×C22⋊D1111yescharacteristic
358C2×C4C23×D1111yescharacteristic
359C8—221no—
360C8—221no—
361C8—221no—
362C8—221no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—222no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—884no—
381C22—884no—
382C22#6700212yes—
383C22C22×C22⋊D1111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—441no—
392C4#41×D1111yescharacteristic
393C4#6704211yescharacteristic
394C2—22no—
395C2—41no—
396C2—81no—
397C2—442no—
398C2—881no—
399C2—881no—
400C2C2×#6700211yescharacteristic
401C2#1062336011yescharacteristic
402C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#553C2
socleC22×C11C22×D4
hypercenter#553D11
hypocenterC11#3318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C11×#553C2semidirect
2. D4×D44C2semidirect
3. #10622680C2semidirect
4. #10622679C2semidirect
5. #10622652C2semidirect
6. #10622651C2semidirect
7. #10622649C2semidirect
8. #10622649C2semidirect
9. #10622628C2semidirect
10. #10622627C2semidirect
11. #10622624C2semidirect
12. #10622616C2semidirect
13. #10622614C2semidirect
14. #10622581C2semidirect
15. C2×#66873C2semidirect
20. C11×#125C22semidirect
23. C11×#121C22semidirect
24. C11×#121C22semidirect
27. C4×D4×C11C22semidirect
28. C11×#117C22semidirect
29. C2×C11×C4⋊C4C22semidirect
31. C2×#4323C22semidirect
32. C2×#4323C22semidirect
35. C2×#4318C22semidirect
36. C22×C11⋊C8C22semidirect
42. #66896C22semidirect
43. C22⋊(C11⋊C8)C22semidirect
44. C22⋊(C11⋊C8)C22semidirect
48. #66873C22semidirect
49. #66873C22semidirect
50. #66873C22semidirect
51. #66873C22semidirect
52. #66873C22semidirect
53. #66873C22semidirect
54. #66872C22semidirect
55. #66872C22semidirect
56. #66871C22semidirect
57. C4⋊(C11⋊C8)C22semidirect
58. #66867C22semidirect
162. #553D11semidirect
218. #125C2×D11semidirect
224. #121C2×D11semidirect
225. #121C2×D11semidirect
231. C4×D4C2×D11semidirect
232. #117C2×D11semidirect
233. C2×C4⋊C4C2×D11semidirect
313. C11#3318semidirect

Maximal subgroups

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

subgroupindex
C11×#5532
D4×D442
#106226802
#106226792
#106226522
#106226512
#106226492
#106226282
#106226272
#106226242
#106226162
#106226142
#106225812
C2×#668732
#331811