Finite Group Databasebeta

← #20254999

Subgroups — #20254999

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094050C211yesmaximal, characteristic, complemented
2C2×#13094048C211yesmaximal, characteristic, complemented
3#15689770C211yesmaximal, characteristic, complemented
4#15689767C211yesmaximal, characteristic, complemented
5#15689506C211yesmaximal, characteristic, complemented
6#15689368C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689337C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689286C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689198C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic, complemented
19#13094050—24no—
20#13094048—24no—
21C2×Dic188C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625335C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic, complemented
25C2×#10625335C2211yescharacteristic, complemented
26C2×#10625334C2211yescharacteristic
27C2×#10625334C2211yescharacteristic
28C2×#10625329C2211yescharacteristic, complemented
29C2×#10625324C2211yescharacteristic, complemented
30#13094011C2211yescharacteristic, complemented
31#13094011C2211yescharacteristic, complemented
32#13094006—21no—
33#13094005—21no—
34#13094004C2211yescharacteristic, complemented
35#13094003C2211yescharacteristic, complemented
36#13093996—21no—
37#13093995—21no—
38#13093995C2211yescharacteristic
39#13093993—21no—
40#13093992—21no—
41D4×Dic47C2211yescharacteristic, complemented
42#13093986C2211yescharacteristic, complemented
43C4×C22⋊D47C2211yescharacteristic
44C2×C22⋊Dic47—21no—
45C22⋊C4×D47—21no—
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56C2×D8×C47C2211yescharacteristic
57#121×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C23×D47—21no—
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—41no—
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47D411yescharacteristic
76C22×Dic47—21no—
77C22×Dic47—21no—
78#10625352—22no—
79#10625352—41no—
80D4×D47—22no—
81D4×D47—41no—
82#10625350—22no—
83#10625350—41no—
84C2×D188C2311yescharacteristic
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89C2×Dic94C2311yescharacteristic
90D8×C47—22no—
91D8×C47—41no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103C22⋊Dic47D411yescharacteristic
104#10625335—22no—
105#10625335—22no—
106#10625335—22no—
107#10625334—22no—
108#10625334D414yescomplemented
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47—21no—
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4D411yescharacteristic
116C4×Dic47C2311yescharacteristic
117#10625329—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120Dic188—41no—
121#10625325—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—42no—
127C23×C47—42no—
128C23×C47—81no—
129C23×C47C2×D411yescharacteristic
130C22×D47—21no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—81no—
134C22×D47C2×D411yescharacteristic
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—42no—
141D4×C47—81no—
142D4×C47C2×D412yes—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C22⋊D47—41no—
149C22⋊D47—42no—
150C22⋊D47—42no—
151C22⋊D47—42no—
152C22⋊D47—81no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—42no—
157C2×Dic47—81no—
158C2×Dic47C2×D411yescharacteristic
159C2×Dic47C2×D411yescharacteristic
160C2×Dic47C2×D411yescharacteristic
161D188—21no—
162D188C2×D412yes—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—42no—
166C4×D47—81no—
167Dic94—21no—
168Dic94—21no—
169Dic94—21no—
170Dic94—21no—
171C8×C47—21no—
172C8×C47—21no—
173C47⋊C8—21no—
174C47⋊C8C2×D412yes—
175C22×C47—22no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—84no—
188C22×C47C22×D411yescharacteristic
189C2×D47—21no—
190C2×D47—22no—
191C2×D47—21no—
192C2×D47—21no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—84no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47C22×D411yescharacteristic
199C4×C47H(5,𝔽2)11yescharacteristic
200Dic47—21no—
201Dic47—21no—
202Dic47—21no—
203Dic47—41no—
204Dic47—41no—
205Dic47—41no—
206#3273—471nomaximal, Sylow
207C2×C47—41no—
208C2×C47—42no—
209C2×C47—81no—
210C2×C47—81no—
211C2×C47D4211yescharacteristic
212C2×C47#57511yescharacteristic
213C2×C47#57611yescharacteristic
214D47—41no—
215D47—42no—
216C2×AGL(1,ℤ/8)—471no—
217C2×AGL(1,ℤ/8)—471no—
218#546—471no—
219#546—471no—
220#495—471no—
221#468—471no—
222#468—471no—
223#463—471no—
224#463—471no—
225#452—471no—
226#452—471no—
227#447—471no—
228#447D4711yescharacteristic, complemented
229C4×D8—471no—
230#436—471no—
231C47#327311yescharacteristic, complemented, Sylow
232C2×#41—471no—
233C2×#41—471no—
234C22×D4—471no—
235C22×D4C2×D4711yescharacteristic, complemented
236AGL(1,ℤ/8)—944no—
237AGL(1,ℤ/8)—944no—
238C2×Q16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×D8—471no—
244C2×D8—471no—
245C2×D8C2×D4711yescharacteristic
246C2×D8C2×D4711yescharacteristic
247C2×M16—471no—
248C2×M16—471no—
249#124—471no—
250#124—471no—
251#123—941no—
252#123—941no—
253C22⋊Q8—471no—
254C22⋊Q8—471no—
255#121—471no—
256#121—941no—
257#121—941no—
258#121C2×D4711yescharacteristic
259#120—941no—
260#120—941no—
261C4×D4—471no—
262C4×D4—471no—
263C4×D4—471no—
264C2×C22⋊C4—941no—
265C2×C22⋊C4—941no—
266#107—471no—
267C4⋊C8—471no—
268#103—471no—
269#103—471no—
270#102—471no—
271#102—471no—
272#102C2×D4711yescharacteristic, complemented
273#102C2×D4711yescharacteristic, complemented
274C22⋊C8—471no—
275C22⋊C8C2×D4711yescharacteristic, complemented
276C4×C8—471no—
277C24—21no—
278C24—941no—
279#41—942no—
280#41—942no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8—471no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—471no—
290C2×D4—471no—
291C2×D4—941no—
292C2×D4—942no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—1881no—
297C2×D4C22×D4711yescharacteristic
298C2×D4C22×D4711yescharacteristic
299C2×D4C22×D4711yescharacteristic
300C22×C4—471no—
301C22×C4—941no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4C22×D4711yescharacteristic
306Q16—1881no—
307SD16—942no—
308SD16—942no—
309SD16—942no—
310SD16—942no—
311D8—22no—
312D8—41no—
313D8—474no—
314D8—942no—
315M16—942no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8C22×D4711yescharacteristic
320C2×C8C22×D4711yescharacteristic
321C4⋊C4—471no—
322C4⋊C4—471no—
323C4⋊C4—941no—
324C4⋊C4—941no—
325C4⋊C4C22×D4711yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—471no—
328C22⋊C4—471no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C42—471no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—471no—
346C23—941no—
347C23—3761no—
348C23—1882no—
349C23—1882no—
350C23D4×D4711yescharacteristic
351Q8—941no—
352Q8—941no—
353Q8—941no—
354Q8—941no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—21no—
360D4—42no—
361D4—81no—
362D4—472no—
363D4—941no—
364D4—3761no—
365D4—1881no—
366D4—1882no—
367D4—1882no—
368D4—1882no—
369D4D4×D4712yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—471no—
374C2×C4—471no—
375C2×C4—471no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—3761no—
382C2×C4—3761no—
383C2×C4—1882no—
384C2×C4—1882no—
385C2×C4D4×D4711yescharacteristic
386C2×C4C23×D4711yescharacteristic
387C8—21no—
388C8—21no—
389C8—472no—
390C8—941no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—941no—
405C22—942no—
406C22—941no—
407C22—941no—
408C22—3764no—
409C22—1881no—
410C22—1881no—
411C22C2×D4×D4711yescharacteristic
412C4—21no—
413C4—41no—
414C4—941no—
415C4—941no—
416C4—941no—
417C4—1881no—
418C4—1881no—
419C4—1881no—
420C4C2×D4×D4711yescharacteristic
421C4#1309406911yescharacteristic
422C2—41no—
423C2—42no—
424C2—81no—
425C2—81no—
426C2—1881no—
427C2—1882no—
428C2#1568975511yescharacteristic
429C2#1568991911yescharacteristic
430C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#13094050C2semidirect
2. C2×#13094048C2semidirect
3. #15689770C2semidirect
4. #15689767C2semidirect
5. #15689506C2semidirect
6. #15689368C2semidirect
7. #15689367C2semidirect
8. #15689337C2semidirect
9. #15689336C2semidirect
10. #15689287C2semidirect
11. #15689286C2semidirect
12. #15689255C2semidirect
13. #15689203C2semidirect
14. #15689198C2semidirect
15. C47×#447C2semidirect
18. C2×D4×D47C22semidirect
21. C2×Dic188C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625335C22semidirect
25. C2×#10625335C22semidirect
28. C2×#10625329C22semidirect
29. C2×#10625324C22semidirect
30. #13094011C22semidirect
31. #13094011C22semidirect
34. #13094004C22semidirect
35. #13094003C22semidirect
41. D4×Dic47C22semidirect
42. #13093986C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093947C22semidirect
50. #13093946C22semidirect
51. #13093945C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
54. C22×D4×C47C22semidirect
58. #102×C47C22semidirect
59. #102×C47C22semidirect
60. C22⋊C8×C47C22semidirect
108. #10625334D4semidirect
228. #447D47semidirect
231. C47#3273semidirect
235. C22×D4C2×D47semidirect
272. #102C2×D47semidirect
273. #102C2×D47semidirect
275. C22⋊C8C2×D47semidirect