Finite Group Databasebeta

← #13080754

Subgroups — #13080754

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
1#10623226C211yesmaximal, characteristic, complemented
2D4×D44C211yesmaximal, characteristic, complemented
3C11×#478C211yesmaximal, characteristic, complemented
4#10622680C211yesmaximal, characteristic, complemented
5#10622627C211yesmaximal, characteristic, complemented
6#10622498C211yesmaximal, characteristic, complemented
7#10622496C211yesmaximal, characteristic, complemented
8#10622478C211yesmaximal, characteristic, complemented
9#10622476C211yesmaximal, characteristic, complemented
10#10622456C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622383C211yesmaximal, characteristic, complemented
15D11×#102C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C22×D44—21no—
19C11×#125C2211yescharacteristic, complemented
20C4×D4×C11C2211yescharacteristic
21C2×#4323C2211yescharacteristic
22#66983—21no—
23C2×D88C2211yescharacteristic, complemented
24C2×D88C2211yescharacteristic, complemented
25C2×#4313C2211yescharacteristic, complemented
26C2×C8×D11C2211yescharacteristic, complemented
27#66951—21no—
28#66948—21no—
29#66948C2211yescharacteristic
30#66948C2211yescharacteristic
31#66948C2211yescharacteristic, complemented
32#66948C2211yescharacteristic, complemented
33#66947—21no—
34#66946—21no—
35#66945C2211yescharacteristic, complemented
36C4⋊C4×D11C2211yescharacteristic, complemented
37#66935—21no—
38#66935—21no—
39#66927C2211yescharacteristic
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic, complemented
42C11×#107C2211yescharacteristic, complemented
43C11×#106C2211yescharacteristic, complemented
44C11×C4⋊C8C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic
46C11×#102C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic, complemented
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51(C2×D11)⋊C8C2211yescharacteristic, complemented
52#66873C2211yescharacteristic, complemented
53#66873C2211yescharacteristic, complemented
54#66873C2211yescharacteristic, complemented
55#66873C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65D4×D11—22no—
66D4×D11—22no—
67D4×D11—41no—
68D4×D11—41no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—44no—
76C2×D44D411yescharacteristic
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11C2311yescharacteristic
83C2×C4×D11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C42×C11C2311yescharacteristic
93#4323—22no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4D411yescharacteristic
101(C2×D11)⋊C4D411yescharacteristic
102C4⋊Dic11D411yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—41no—
109D88—41no—
110#4313—41no—
111C8×D11—41no—
112#3318—111nomaximal, Sylow
113C23×C11—21no—
114C22×D11—21no—
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
124C22×D11C2×D411yescharacteristic
125D4×C11—21no—
126D4×C11#4112yes—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—21no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139D44—22no—
140D44—21no—
141D44—21no—
142D44—21no—
143D44—21no—
144D44—21no—
145D44—21no—
146D44—42no—
147D44—42no—
148D44—42no—
149D44—42no—
150D44—81no—
151D44—81no—
152C4×D11—21no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—81no—
157C4×D11—81no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#553—111no—
163D42—111no—
164#490—111no—
165#482—111no—
166#481—111no—
167#478D1111yescharacteristic, complemented
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—22no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—84no—
196C2×D11—84no—
197C2×D11AGL(1,ℤ/8)12yes—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11C2×#4111yescharacteristic
204C4×C11H(5,𝔽2)11yescharacteristic
205Dic11—21no—
206Dic11—21no—
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—221no—
218#125C2×D1111yescharacteristic, complemented
219#123—221no—
220#121—111no—
221#121—111no—
222#121—111no—
223#121—111no—
224#121—221no—
225#121—221no—
226#120—221no—
227#120—221no—
228C4×D4—111no—
229C4×D4—111no—
230C4×D4—221no—
231C4×D4C2×D1111yescharacteristic
232#117—111no—
233C2×C4⋊C4—111no—
234#107C2×D1111yescharacteristic, complemented
235#106—111no—
236#106C2×D1111yescharacteristic, complemented
237C4⋊C8C2×D1111yescharacteristic, complemented
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#102C2×D1111yescharacteristic
247#102C2×D1111yescharacteristic
248C22⋊C8—111no—
249C22⋊C8—111no—
250#97—111no—
251C2×C11—42no—
252C2×C11#54611yescharacteristic
253C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
254C2×C11#57611yescharacteristic
255D11—22no—
256D11—41no—
257D11—81no—
258D11—81no—
259D11—81no—
260C24—221no—
261C24—221no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—111no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—222no—
273C2×D4—222no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—444no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4C22×D1111yescharacteristic
280C22×C4—21no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—221no—
284C22×C4—221no—
285D8—222no—
286D8—441no—
287D8—441no—
288M16—441no—
289C2×C8—111no—
290C2×C8—111no—
291C2×C8—441no—
292C2×C8C22×D1111yescharacteristic
293C2×C8C22×D1111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—111no—
297C4⋊C4—111no—
298C4⋊C4—221no—
299C4⋊C4C22×D1111yescharacteristic
300C4⋊C4C22×D1111yescharacteristic
301C4⋊C4C22×D1111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—111no—
304C22⋊C4—111no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C42—221no—
312C42C22×D1111yescharacteristic
313C11#331811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—111no—
316C23—111no—
317C23—221no—
318C23—221no—
319C23—221no—
320C23—442no—
321C23—442no—
322C23—442no—
323C23—442no—
324C23—881no—
325C23—881no—
326D4—21no—
327D4—222no—
328D4—221no—
329D4—221no—
330D4—221no—
331D4—221no—
332D4—221no—
333D4—221no—
334D4—442no—
335D4—442no—
336D4—442no—
337D4—442no—
338D4—442no—
339D4—442no—
340D4—881no—
341D4—881no—
342D4#434312yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4D4×D1111yescharacteristic
357C2×C4D4×D1111yescharacteristic
358C2×C4C23×D1111yescharacteristic
359C8—21no—
360C8—21no—
361C8—221no—
362C8—221no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—112no—
367C22—221no—
368C22—221no—
369C22—221no—
370C22—221no—
371C22—221no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—884no—
382C22—884no—
383C22C2×D4×D1111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—221no—
390C4—221no—
391C4—441no—
392C4C2×#434311yescharacteristic
393C4#6704211yescharacteristic
394C2—42no—
395C2—222no—
396C2—441no—
397C2—881no—
398C2—881no—
399C2—881no—
400C2#1062316111yescharacteristic
401C2#1062330011yescharacteristic
402C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
hypercenter#478D11
hypocenterC11#3318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623226C2semidirect
2. D4×D44C2semidirect
3. C11×#478C2semidirect
4. #10622680C2semidirect
5. #10622627C2semidirect
6. #10622498C2semidirect
7. #10622496C2semidirect
8. #10622478C2semidirect
9. #10622476C2semidirect
10. #10622456C2semidirect
11. #10622449C2semidirect
12. #10622386C2semidirect
13. #10622386C2semidirect
14. #10622383C2semidirect
15. D11×#102C2semidirect
19. C11×#125C22semidirect
23. C2×D88C22semidirect
24. C2×D88C22semidirect
25. C2×#4313C22semidirect
26. C2×C8×D11C22semidirect
31. #66948C22semidirect
32. #66948C22semidirect
35. #66945C22semidirect
36. C4⋊C4×D11C22semidirect
41. C4×D44C22semidirect
42. C11×#107C22semidirect
43. C11×#106C22semidirect
44. C11×C4⋊C8C22semidirect
48. #66885C22semidirect
49. #66885C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. (C2×D11)⋊C8C22semidirect
52. #66873C22semidirect
53. #66873C22semidirect
54. #66873C22semidirect
55. #66873C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66867C22semidirect
167. #478D11semidirect
218. #125C2×D11semidirect
234. #107C2×D11semidirect
236. #106C2×D11semidirect
237. C4⋊C8C2×D11semidirect
313. C11#3318semidirect

Maximal subgroups

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

subgroupindex
#106232262
D4×D442
C11×#4782
#106226802
#106226272
#106224982
#106224962
#106224782
#106224762
#106224562
#106224492
#106223862
#106223832
D11×#1022
#331811