Finite Group Databasebeta

← #20254873

Subgroups — #20254873

Order 6016.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094052C211yesmaximal, characteristic, complemented
2C22×D376C211yesmaximal, characteristic, complemented
3#15689769C211yesmaximal, characteristic, complemented
4D4×D188C211yesmaximal, characteristic, complemented
5#15689512C211yesmaximal, characteristic, complemented
6#15689376C211yesmaximal, characteristic, complemented
7#15689352C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689319C211yesmaximal, characteristic, complemented
10#15689276C211yesmaximal, characteristic, complemented
11#15689270C211yesmaximal, characteristic, complemented
12#15689259C211yesmaximal, characteristic, complemented
13#15689259C211yesmaximal, characteristic, complemented
14#15689236C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic, complemented
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic, complemented
19C22×D188C2211yescharacteristic, complemented
20C2×D4×D47—21no—
21#13094052—24no—
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625325C2211yescharacteristic, complemented
25C2×D376—24no—
26C2×D376C2211yescharacteristic
27C2×D376C2211yescharacteristic
28C2×D376C2211yescharacteristic, complemented
29C2×D376C2211yescharacteristic, complemented
30C2×D376C2211yescharacteristic, complemented
31C2×D376C2211yescharacteristic, complemented
32#13094021C2211yescharacteristic, complemented
33#13094012C2211yescharacteristic, complemented
34#13094009—21no—
35#13094003C2211yescharacteristic, complemented
36#13093999—21no—
37#13093998C2211yescharacteristic
38#13093998C2211yescharacteristic, complemented
39#13093998C2211yescharacteristic, complemented
40#13093997—21no—
41#13093994—21no—
42#13093994—21no—
43#13093992—21no—
44C4×D188C2211yescharacteristic, complemented
45C4×D188C2211yescharacteristic, complemented
46C22⋊C4×D47—21no—
47#13093956C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52#13093946C2211yescharacteristic, complemented
53#13093946C2211yescharacteristic, complemented
54C2×M16×C47C2211yescharacteristic, complemented
55C22×C8×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic
57C4⋊C8×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C22⋊C8×C47C2211yescharacteristic, complemented
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C23×D47—21no—
64C2×D4×C47D411yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71D4×D47—44no—
72#10625350—22no—
73#10625350—41no—
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—22no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188C2311yescharacteristic
86C2×D188C2311yescharacteristic
87C2×D188C2311yescharacteristic
88C2×D188C2311yescharacteristic
89C2×D188C2311yescharacteristic
90C2×C4×D47—21no—
91C2×C4×D47—21no—
92C2×C4×D47—21no—
93C2×Dic94C2311yescharacteristic
94M16×C47—22no—
95C2×C8×C47—22no—
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C2×C8×C47C2311yescharacteristic
99C2×C8×C47C2311yescharacteristic
100C4⋊C4×C47D411yescharacteristic
101C22⋊C4×C47D411yescharacteristic
102C22⋊C4×C47D411yescharacteristic
103C42×C47C2311yescharacteristic
104C22⋊Dic47—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112C4⋊Dic47C2311yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115D376—22no—
116D376—22no—
117D376—22no—
118D376—22no—
119D376—41no—
120D376D414yescomplemented
121#10625325—22no—
122#10625325—22no—
123#10625325—41no—
124C23×C47C2×D411yescharacteristic
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—42no—
135C22×D47—42no—
136C22×D47—42no—
137C22×D47—81no—
138C22×D47—81no—
139C22×D47—81no—
140D4×C47—22no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2411yescharacteristic
150C22⋊D47—42no—
151C22⋊D47—42no—
152C22⋊D47—42no—
153C22⋊D47—81no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157D188—21no—
158D188—21no—
159D188—21no—
160D188—21no—
161D188—21no—
162D188—21no—
163D188—21no—
164D188—21no—
165D188—42no—
166D188—42no—
167D188—42no—
168D188—42no—
169D188—81no—
170D188C2×D412yes—
171D188C2×D412yescomplemented
172C4×D47—42no—
173C4×D47—42no—
174C4×D47—81no—
175Dic94—21no—
176Dic94—21no—
177C8×C47—21no—
178C8×C47—21no—
179C8×C47—21no—
180C8×C47C2×D412yescomplemented
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47AGL(1,ℤ/8)12yescomplemented
187C22×C47C22×D411yescharacteristic
188C2×D47—22no—
189C2×D47—22no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47—84no—
204C2×D47—84no—
205C2×D47—84no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—21no—
210C4×C47C22×D411yescharacteristic
211C4×C47H(5,𝔽2)11yescharacteristic
212Dic47—41no—
213Dic47—41no—
214Dic47—41no—
215#3264—471nomaximal, Sylow
216C2×C47—22no—
217C2×C47—41no—
218C2×C47D4211yescharacteristic
219C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C47#57611yescharacteristic
221D47—42no—
222D47—42no—
223D47—81no—
224D47—81no—
225D47—81no—
226C2×AGL(1,ℤ/8)—471no—
227C22×D8—471no—
228#546—471no—
229D42—471no—
230#496—471no—
231#469—471no—
232#465—471no—
233#463—471no—
234#459—471no—
235#450—471no—
236#449—471no—
237#447—471no—
238#447—471no—
239#442—471no—
240#435D4711yescharacteristic, complemented
241C47#326411yescharacteristic, complemented, Sylow
242C2×#41—471no—
243C22×D4—471no—
244C22×D4—471no—
245C22×D4—471no—
246C22×D4—941no—
247AGL(1,ℤ/8)—944no—
248C2×SD16—471no—
249C2×SD16—471no—
250C2×SD16—471no—
251C2×D8—471no—
252C2×D8—471no—
253C2×D8—471no—
254C2×D8—471no—
255C2×D8—471no—
256C2×D8—471no—
257C2×D8—944no—
258C2×M16C2×D4711yescharacteristic, complemented
259C22×C8C2×D4711yescharacteristic, complemented
260#127—471no—
261#124—471no—
262#123—941no—
263C22⋊Q8—471no—
264#121—471no—
265#121—471no—
266#121—471no—
267#121—941no—
268#121—941no—
269#120—941no—
270#120—941no—
271#120—941no—
272C4×D4—471no—
273C4×D4—471no—
274C4×D4C2×D4711yescharacteristic
275C2×C22⋊C4—941no—
276#106—471no—
277C4⋊C8C2×D4711yescharacteristic, complemented
278#103—471no—
279#102—471no—
280#102—471no—
281#102—471no—
282#102—471no—
283#102—471no—
284C22⋊C8C2×D4711yescharacteristic, complemented
285C22⋊C8C2×D4711yescharacteristic, complemented
286#97C2×D4711yescharacteristic, complemented
287C24—941no—
288C24—941no—
289C24—941no—
290#41—942no—
291#41—1881no—
292C2×Q8—471no—
293C2×D4—471no—
294C2×D4—471no—
295C2×D4—471no—
296C2×D4—471no—
297C2×D4—471no—
298C2×D4—942no—
299C2×D4—942no—
300C2×D4—942no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—941no—
304C2×D4—941no—
305C2×D4—941no—
306C2×D4—941no—
307C2×D4—941no—
308C2×D4—941no—
309C2×D4—941no—
310C2×D4—1881no—
311C2×D4—1881no—
312C2×D4—1881no—
313C2×D4—1884no—
314C2×D4D18811yescharacteristic
315C22×C4—941no—
316C22×C4—941no—
317C22×C4—941no—
318C22×C4C22×D4711yescharacteristic
319C22×C4C22×D4711yescharacteristic
320SD16—942no—
321SD16—942no—
322SD16—1881no—
323D8—474no—
324D8—942no—
325D8—942no—
326D8—942no—
327D8—942no—
328D8—1881no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D4711yescharacteristic
332C2×C8C22×D4711yescharacteristic
333C2×C8C22×D4711yescharacteristic
334C2×C8C22×D4711yescharacteristic
335C4⋊C4—471no—
336C4⋊C4—471no—
337C4⋊C4—941no—
338C4⋊C4D18811yescharacteristic
339C22⋊C4—941no—
340C22⋊C4—941no—
341C22⋊C4—941no—
342C22⋊C4—941no—
343C22⋊C4—941no—
344C22⋊C4—941no—
345C22⋊C4—941no—
346C22⋊C4—941no—
347C22⋊C4D18811yescharacteristic
348C22⋊C4D18811yescharacteristic
349C42C22×D4711yescharacteristic
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—3761no—
356C23—3761no—
357C23—3761no—
358C23—1882no—
359C23—1882no—
360C23—1882no—
361C23—1882no—
362C23—1882no—
363C23—1882no—
364C23C2×D18811yescharacteristic
365C23C2×D18811yescharacteristic
366Q8—941no—
367Q8—941no—
368D4—22no—
369D4—472no—
370D4—472no—
371D4—941no—
372D4—941no—
373D4—941no—
374D4—941no—
375D4—941no—
376D4—941no—
377D4—941no—
378D4—941no—
379D4—3761no—
380D4—3761no—
381D4—1882no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4—1882no—
387D4—1882no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—3761no—
396C2×C4—1882no—
397C2×C4—1882no—
398C2×C4C2×D18811yescharacteristic
399C2×C4C2×D18811yescharacteristic
400C2×C4C2×D18811yescharacteristic
401C2×C4C2×D18811yescharacteristic
402C2×C4C23×D4711yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D4712yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—942no—
413C22—942no—
414C22—3764no—
415C22—3764no—
416C22—3764no—
417C22—1881no—
418C22—1881no—
419C22—1881no—
420C22—1881no—
421C22—1881no—
422C22—1881no—
423C22—1881no—
424C22—1881no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22#1309405212yescomplemented
431C22C22×D18811yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—1881no—
437C4—1881no—
438C4—1881no—
439C4C2×D4×D4711yescharacteristic
440C4#1309407011yescharacteristic
441C2—22no—
442C2—41no—
443C2—3761no—
444C2—3761no—
445C2—3761no—
446C2—1882no—
447C2—1882no—
448C2D4×D18811yescharacteristic
449C2C2×#1309405211yescharacteristic
450C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. C22×D376C2semidirect
3. #15689769C2semidirect
4. D4×D188C2semidirect
5. #15689512C2semidirect
6. #15689376C2semidirect
7. #15689352C2semidirect
8. #15689339C2semidirect
9. #15689319C2semidirect
10. #15689276C2semidirect
11. #15689270C2semidirect
12. #15689259C2semidirect
13. #15689259C2semidirect
14. #15689236C2semidirect
15. C47×#435C2semidirect
16. C2×#10625350C22semidirect
18. C22×D188C22semidirect
19. C22×D188C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625325C22semidirect
28. C2×D376C22semidirect
29. C2×D376C22semidirect
30. C2×D376C22semidirect
31. C2×D376C22semidirect
32. #13094021C22semidirect
33. #13094012C22semidirect
35. #13094003C22semidirect
38. #13093998C22semidirect
39. #13093998C22semidirect
44. C4×D188C22semidirect
45. C4×D188C22semidirect
47. #13093956C22semidirect
48. #13093949C22semidirect
49. #13093946C22semidirect
50. #13093946C22semidirect
51. #13093946C22semidirect
52. #13093946C22semidirect
53. #13093946C22semidirect
54. C2×M16×C47C22semidirect
55. C22×C8×C47C22semidirect
57. C4⋊C8×C47C22semidirect
58. C22⋊C8×C47C22semidirect
59. C22⋊C8×C47C22semidirect
60. #97×C47C22semidirect
120. D376D4semidirect
171. D188C2×D4semidirect
180. C8×C47C2×D4semidirect
186. C22×C47AGL(1,ℤ/8)semidirect
240. #435D47semidirect
241. C47#3264semidirect
258. C2×M16C2×D47semidirect
259. C22×C8C2×D47semidirect
277. C4⋊C8C2×D47semidirect
284. C22⋊C8C2×D47semidirect
285. C22⋊C8C2×D47semidirect
286. #97C2×D47semidirect
406. C8D4×D47semidirect
430. C22#13094052semidirect