Finite Group Databasebeta

← #13080581

Subgroups — #13080581

Order 1408.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623337C211yesmaximal, characteristic, complemented
2#10623142C211yesmaximal, characteristic, complemented
3C11×#447C211yesmaximal, characteristic, complemented
4C2×#66896C211yesmaximal, characteristic, complemented
5#10622772C211yesmaximal, characteristic, complemented
6#10622771C211yesmaximal, characteristic, complemented
7#10622766C211yesmaximal, characteristic, complemented
8#10622765C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic, complemented
10#10622390C211yesmaximal, characteristic, complemented
11#10622384C211yesmaximal, characteristic, complemented
12#10622378C211yesmaximal, characteristic, complemented
13#10622374C211yesmaximal, characteristic, complemented
14#10622343C211yesmaximal, characteristic, complemented
15#10622334C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341—21no—
18C2×#4341C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22#67006—21no—
23C2×C22⋊Dic11—21no—
24#66992—21no—
25#66991C2211yescharacteristic
26#66991C2211yescharacteristic, complemented
27#66989C2211yescharacteristic
28#66988—21no—
29#66988—21no—
30D4×Dic11C2211yescharacteristic
31D4×Dic11C2211yescharacteristic, complemented
32C2×#4324C2211yescharacteristic, complemented
33C4×C22⋊D11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35#66977C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37C2×#4313C2211yescharacteristic, complemented
38C4⋊C4×D11C2211yescharacteristic, complemented
39#66941C2211yescharacteristic, complemented
40#66936—21no—
41#66931—21no—
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66881C2211yescharacteristic, complemented
52#66881C2211yescharacteristic, complemented
53#66880C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55#66879C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76#4341—22no—
77#4341—41no—
78#4341—44no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×Dic22—21no—
82C2×Dic22C2311yescharacteristic
83C11×D8—22no—
84C11×D8—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11D411yescharacteristic
97#4324—41no—
98(C2×D11)⋊C4D411yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8—41no—
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#4313—41no—
112#3306—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—81no—
119C23×C11C2×D411yescharacteristic
120C22×D11C2×D411yescharacteristic
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11#4112yescomplemented
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×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—81no—
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
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#547—111no—
160#546—111no—
161#489—111no—
162#483—111no—
163#481—111no—
164#476—111no—
165#469—111no—
166#465—111no—
167#463—111no—
168#449—111no—
169#447D1111yescharacteristic, complemented
170#442—111no—
171#435—111no—
172#417—111no—
173C2×#102—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—84no—
186C22×C11AGL(1,ℤ/8)12yes—
187C22×C11C22×D411yescharacteristic
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11C2×#4111yescharacteristic
194C4×C11H(5,𝔽2)11yescharacteristic
195Dic11—21no—
196Dic11—21no—
197Dic11—21no—
198Dic11—41no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202C2×#41—111no—
203C2×#41—221no—
204C22×D4C2×D1111yescharacteristic
205C2×SD16—111no—
206C2×D8C2×D1111yescharacteristic
207C2×D8C2×D1111yescharacteristic
208C2×M16—111no—
209C22×C8—111no—
210C4⋊Q8—111no—
211#124—111no—
212#123—221no—
213#123—221no—
214#123—221no—
215C22⋊Q8—111no—
216C22⋊Q8—221no—
217#121—111no—
218#121—111no—
219#121—221no—
220#121C2×D1111yescharacteristic
221#120—221no—
222C4×D4—111no—
223C4×D4—111no—
224C4×D4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C22⋊C4—221no—
228#106—111no—
229#106—111no—
230#106—111no—
231C4⋊C8—111no—
232#103—111no—
233#103—111no—
234#103—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102C2×D1111yescharacteristic
241#102C2×D1111yescharacteristic
242C22⋊C8—111no—
243C22⋊C8C2×D1111yescharacteristic
244#97—111no—
245C2×C11—22no—
246C2×C11—42no—
247C2×C11—81no—
248C2×C11—81no—
249C2×C11#54611yescharacteristic
250C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C2×C11#57711yescharacteristic
252D11—41no—
253C24—21no—
254#41—222no—
255#41—441no—
256#41—444no—
257C2×Q8—111no—
258C2×Q8—221no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4C22×D1111yescharacteristic
268C2×D4C22×D1111yescharacteristic
269C2×D4C22×D1111yescharacteristic
270C22×C4—111no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4C22×D1111yescharacteristic
277SD16—441no—
278D8—22no—
279D8—41no—
280M16—441no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8—441no—
284C2×C8C22×D1111yescharacteristic
285C2×C8C22×D1111yescharacteristic
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⋊C4C22×D1111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—111no—
297C22⋊C4—111no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C42—111no—
306C11#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—111no—
314C23D4×D1111yescharacteristic
315Q8—221no—
316Q8—221no—
317Q8—442no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—222no—
326D4—442no—
327D4—442no—
328D4—881no—
329D4#434112yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—111no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—881no—
347C2×C4D4×D1111yescharacteristic
348C2×C4C23×D1111yescharacteristic
349C8—21no—
350C8—21no—
351C8—221no—
352C8—221no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—221no—
366C22—221no—
367C22—221no—
368C22#6696412yes—
369C22C2×D4×D1111yescharacteristic
370C4—21no—
371C4—41no—
372C4—221no—
373C4—221no—
374C4—221no—
375C4—441no—
376C4—441no—
377C4—441no—
378C4—441no—
379C4C2×#434111yescharacteristic
380C4#6703711yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—441no—
386C2#1062312211yescharacteristic
387C2C2×#6696411yescharacteristic
388C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#447C2
socleC22×C11C22×D4
hypercenter#447D11
hypocenterC11#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #10623337C2semidirect
2. #10623142C2semidirect
3. C11×#447C2semidirect
4. C2×#66896C2semidirect
5. #10622772C2semidirect
6. #10622771C2semidirect
7. #10622766C2semidirect
8. #10622765C2semidirect
9. #10622654C2semidirect
10. #10622390C2semidirect
11. #10622384C2semidirect
12. #10622378C2semidirect
13. #10622374C2semidirect
14. #10622343C2semidirect
15. #10622334C2semidirect
26. #66991C22semidirect
31. D4×Dic11C22semidirect
32. C2×#4324C22semidirect
37. C2×#4313C22semidirect
38. C4⋊C4×D11C22semidirect
39. #66941C22semidirect
49. #66896C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66881C22semidirect
52. #66881C22semidirect
53. #66880C22semidirect
54. #66880C22semidirect
55. #66879C22semidirect
56. Dic11⋊C8C22semidirect
57. #66874C22semidirect
58. #66872C22semidirect
128. D4×C11#41semidirect
169. #447D11semidirect
306. C11#3306semidirect
329. D4#4341semidirect

Maximal subgroups

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

subgroupindex
#106233372
#106231422
C11×#4472
C2×#668962
#106227722
#106227712
#106227662
#106227652
#106226542
#106223902
#106223842
#106223782
#106223742
#106223432
#106223342
#330611