Finite Group Databasebeta

← #13080435

Subgroups — #13080435

Order 1408.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623166C211yesmaximal, characteristic, complemented
2#10623140C211yesmaximal, characteristic
3C11×#465C211yesmaximal, characteristic, complemented
4#10622782C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic, complemented
6C2×#66885C211yesmaximal, characteristic, complemented
7C8×C22⋊D11C211yesmaximal, characteristic, complemented
8#10622659C211yesmaximal, characteristic, complemented
9#10622647C211yesmaximal, characteristic, complemented
10#10622483C211yesmaximal, characteristic, complemented
11#10622476C211yesmaximal, characteristic, complemented
12#10622420C211yesmaximal, characteristic, complemented
13#10622401C211yesmaximal, characteristic, complemented
14D11×#102C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C2×D4×D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic, complemented
20C22×C8×C11C2211yescharacteristic, complemented
21C11×C22⋊Q8C2211yescharacteristic, complemented
22C11×#121C2211yescharacteristic
23#66999C2211yescharacteristic, complemented
24Q8×Dic11C2211yescharacteristic, complemented
25C2×#4325C2211yescharacteristic
26C2×#4325C2211yescharacteristic, complemented
27#66993C2211yescharacteristic
28#66990—21no—
29C4×C22⋊D11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic, complemented
31C2×C8×D11C2211yescharacteristic, complemented
32#66950—21no—
33#66948C2211yescharacteristic
34#66946C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic, complemented
36#66942—21no—
37#66941C2211yescharacteristic, complemented
38#66937—21no—
39#66935—21no—
40(C22⋊D11)⋊C4—21no—
41#66931—21no—
42C11×#106C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45#66896C2211yescharacteristic, complemented
46#66896C2211yescharacteristic, complemented
47C22⋊(C11⋊C8)C2211yescharacteristic, complemented
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic, complemented
51#66885C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69C22×Dic11—21no—
70D4×D11—22no—
71D4×D11—41no—
72D4×D11—44no—
73C2×D44—21no—
74C2×D44—22no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11C2311yescharacteristic
82C2×Dic22—21no—
83C11×SD16—41no—
84C2×C8×C11—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C22⋊Dic11D411yescharacteristic
93#4325—22no—
94#4325—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107C4×Dic11—21no—
108C4×Dic11C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C8×D11—41no—
112#3295—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
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—42no—
129C2×C4×C11—21no—
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—42no—
137C22⋊D11—42no—
138C22⋊D11—81no—
139C22⋊D11SD1614yescomplemented
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—81no—
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146D44—21no—
147D44—21no—
148D44—21no—
149D44—42no—
150D44—42no—
151D44#4112yes—
152C4×D11—21no—
153C4×D11—21no—
154C4×D11—42no—
155C4×D11—81no—
156Dic22—81no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#554—111no—
162D42—111no—
163#486—111no—
164#481—111no—
165#481—111no—
166#476—111no—
167#465—111no—
168#465D1111yescharacteristic, complemented
169#460—111no—
170#450—111no—
171#450—111no—
172C4×SD16—111no—
173C8×D4—111no—
174C2×#102—111no—
175C2×#102—111no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11C2×SD1612yes—
182C22×C11C22×D411yescharacteristic
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—22no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—84no—
192C2×D11—84no—
193C2×D11C2×SD1612yes—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11C2×#4111yescharacteristic
199C4×C11H(5,𝔽2)11yescharacteristic
200Dic11—21no—
201Dic11—21no—
202Dic11—41no—
203Dic11—41no—
204Dic11C2×SD1612yes—
205C22×D4—111no—
206C22×D4—111no—
207C22×D4—221no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×SD16C2×D1111yescharacteristic, complemented
211C22×C8—111no—
212C22×C8C2×D1111yescharacteristic, complemented
213C4⋊Q8—111no—
214#127—111no—
215#125—221no—
216C22⋊Q8—111no—
217C22⋊Q8—221no—
218C22⋊Q8—221no—
219C22⋊Q8C2×D1111yescharacteristic, complemented
220#121—111no—
221#121—221no—
222#121C2×D1111yescharacteristic
223#120—221no—
224#120—221no—
225C4×Q8—111no—
226C4×D4—111no—
227C4×D4—111no—
228C4×D4—221no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231#106—111no—
232#106—111no—
233#106C2×D1111yescharacteristic, complemented
234C4⋊C8—111no—
235#103C2×D1111yescharacteristic, complemented
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243#102—111no—
244#102C2×D1111yescharacteristic, complemented
245C22⋊C8—111no—
246C22⋊C8—111no—
247C4×C8—111no—
248C2×C11—22no—
249C2×C11—81no—
250C2×C11#54611yescharacteristic
251C2×C11C22×SD1611yescharacteristic
252C2×C11#57611yescharacteristic
253D11—22no—
254D11—42no—
255D11—81no—
256C24—221no—
257C24—221no—
258C2×Q8—221no—
259C2×Q8C22×D1111yescharacteristic
260C2×D4—21no—
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—222no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—222no—
270C2×D4—221no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—444no—
274C2×D4C22×D1111yescharacteristic
275C22×C4—111no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4C22×D1111yescharacteristic
280SD16—41no—
281SD16—222no—
282SD16—441no—
283C2×C8—41no—
284C2×C8—111no—
285C2×C8—111no—
286C2×C8—441no—
287C2×C8C22×D1111yescharacteristic
288C2×C8C22×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—111no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4C22×D1111yescharacteristic
299C4⋊C4C22×D1111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—111no—
303C22⋊C4—111no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—111no—
308C42—221no—
309C11#329511yescharacteristic, complemented, Sylow
310C23—21no—
311C23—111no—
312C23—221no—
313C23—221no—
314C23—442no—
315C23—442no—
316C23—442no—
317C23—442no—
318C23—881no—
319C23—881no—
320C23D4×D1111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—881no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—114no—
328D4—112no—
329D4—221no—
330D4—221no—
331D4—221no—
332D4—442no—
333D4—442no—
334D4—442no—
335D4—442no—
336D4—881no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—111no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—442no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4D4×D1111yescharacteristic
353C2×C4C23×D1111yescharacteristic
354C8—21no—
355C8—21no—
356C8—221no—
357C8—221no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—112no—
364C22—221no—
365C22—221no—
366C22—222no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—884no—
373C22—884no—
374C22SD16×D1112yes—
375C22C2×D4×D1111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—112no—
381C4—221no—
382C4—221no—
383C4—441no—
384C4—441no—
385C4#6703711yescharacteristic
386C4#41×D1111yescharacteristic
387C2—22no—
388C2—81no—
389C2—222no—
390C2—442no—
391C2—881no—
392C2#1062314111yescharacteristic
393C2C2×SD16×D1111yescharacteristic
394C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
prime radical#10623140C2
hypercenter#465D11
hypocenterC11#3295
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10623166C2semidirect
3. C11×#465C2semidirect
4. #10622782C2semidirect
5. #10622776C2semidirect
6. C2×#66885C2semidirect
7. C8×C22⋊D11C2semidirect
8. #10622659C2semidirect
9. #10622647C2semidirect
10. #10622483C2semidirect
11. #10622476C2semidirect
12. #10622420C2semidirect
13. #10622401C2semidirect
14. D11×#102C2semidirect
15. #10622373C2semidirect
19. C2×C11×SD16C22semidirect
20. C22×C8×C11C22semidirect
21. C11×C22⋊Q8C22semidirect
23. #66999C22semidirect
24. Q8×Dic11C22semidirect
26. C2×#4325C22semidirect
30. C2×C4⋊Dic11C22semidirect
31. C2×C8×D11C22semidirect
35. C4⋊C4×D11C22semidirect
37. #66941C22semidirect
42. C11×#106C22semidirect
43. C11×#103C22semidirect
44. C11×#102C22semidirect
45. #66896C22semidirect
46. #66896C22semidirect
47. C22⋊(C11⋊C8)C22semidirect
50. #66885C22semidirect
51. #66885C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
54. C8×Dic11C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66872C22semidirect
139. C22⋊D11SD16semidirect
168. #465D11semidirect
210. C2×SD16C2×D11semidirect
212. C22×C8C2×D11semidirect
219. C22⋊Q8C2×D11semidirect
233. #106C2×D11semidirect
235. #103C2×D11semidirect
244. #102C2×D11semidirect
309. C11#3295semidirect

Maximal subgroups

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

subgroupindex
#106231662
#106231402
C11×#4652
#106227822
#106227762
C2×#668852
C8×C22⋊D112
#106226592
#106226472
#106224832
#106224762
#106224202
#106224012
D11×#1022
#106223732
#329511