Finite Group Databasebeta

← #464×D47 #20252828

Subgroups — #464×D47 #20252828

Order 6016.

500 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
1C2×Q16×D47C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic
3#124×D47C211yesmaximal, characteristic
4C4×Q8×D47C211yesmaximal, characteristic, complemented
5#15689348C211yesmaximal, characteristic, complemented
6#15689347C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689344C211yesmaximal, characteristic, complemented
10#15689343C211yesmaximal, characteristic, complemented
11#15689342C211yesmaximal, characteristic, complemented
12C4⋊C8×D47C211yesmaximal, characteristic, complemented
13#103×D47C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic
15C47×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×Dic188C2211yescharacteristic, complemented
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625337C2211yescharacteristic, complemented
22Q16×D47—24no—
23C2×#10625325C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26SD16×D47—24no—
27C2×C8×D47C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic
29#13094013C2211yescharacteristic
30#13094012C2211yescharacteristic
31#13094011C2211yescharacteristic
32#13094010—21no—
33#13094010—21no—
34Q8×Dic47C2211yescharacteristic, complemented
35C4×Dic94—21no—
36C4×Dic94C2211yescharacteristic, complemented
37#13093989—21no—
38#13093989C2211yescharacteristic, complemented
39C4⋊C4×D47—21no—
40C4⋊C4×D47C2211yescharacteristic
41C22⋊C4×D47—21no—
42C22⋊C4×D47—21no—
43C42×D47—21no—
44C42×D47C2211yescharacteristic
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46Dic47⋊C8C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic
52#13093945C2211yescharacteristic
53#13093944C2211yescharacteristic
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66Q8×D47—22no—
67Q8×D47—22no—
68Q8×D47—22no—
69Q8×D47D414yes—
70D4×D47—22no—
71D4×D47—22no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47D411yescharacteristic
77C2×C4×D47D411yescharacteristic
78C2×C4×D47C2311yescharacteristic
79C2×Dic94—21no—
80C2×Dic94—21no—
81C2×Dic94C2311yescharacteristic
82C2×Dic94C2311yescharacteristic
83Q16×C47—22no—
84SD16×C47—22no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47—21no—
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C42×C47—21no—
92C42×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95#10625337—22no—
96#10625337—22no—
97#10625336—22no—
98#10625335—22no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47—21no—
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C4×Dic47—21no—
109C4×Dic47—21no—
110C4×Dic47—21no—
111C4×Dic47D411yescharacteristic
112C4×Dic47D411yescharacteristic
113C4×Dic47C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116Dic188—22no—
117#10625325—22no—
118C8×D47—22no—
119C8×D47—22no—
120C23×C47—21no—
121C22×D47—21no—
122C22×D47—42no—
123C22×D47—42no—
124C22×D47—42no—
125C22×D47C2×D411yescharacteristic
126Q8×C47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47C2×D412yes—
130D4×C47—21no—
131D4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—42no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147C4×D47—24no—
148C4×D47—22no—
149C4×D47—22no—
150C4×D47—42no—
151C4×D47—42no—
152C4×D47C2×D412yes—
153C4×D47#4112yes—
154Dic94—21no—
155Dic94—24no—
156Dic94—21no—
157Dic94—21no—
158Dic94—42no—
159Dic94C2×D412yes—
160C8×C47—21no—
161C8×C47—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47C22×D411yescharacteristic
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—84no—
172C2×D47#12112yes—
173C2×D47#13512yes—
174C2×D47#13712yes—
175C4×C47—22no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47C22×D411yescharacteristic
181C4×C47C2×#4111yescharacteristic
182Dic47—22no—
183Dic47—21no—
184Dic47—21no—
185Dic47—41no—
186Dic47—41no—
187Dic47#12112yes—
188C2×#464—471nomaximal, Sylow
189C2×C47—81no—
190C2×C47C2×#12111yescharacteristic
191C2×C47C2×#13511yescharacteristic
192C2×C47C2×#13711yescharacteristic
193D47—81no—
194D47#46414yesdirect product factor
195C22×Q16—471no—
196C22×SD16—471no—
197C2×#124—471no—
198C2×C4×Q8—471no—
199#464—471no—
200#464—471no—
201#464—471no—
202#464—471no—
203#464—471no—
204#464—471no—
205#464—471no—
206#464D4711yescharacteristic, direct product factor
207C2×C4⋊C8—471no—
208C2×#103—471no—
209C2×#102—471no—
210C47C2×#46411yescharacteristic, complemented, Sylow
211C22×Q8—471no—
212C22×Q8—471no—
213C22×D4—471no—
214C2×Q16—471no—
215C2×Q16—471no—
216C2×Q16—471no—
217C2×Q16—944no—
218C2×Q16C2×D4711yescharacteristic, complemented
219C2×SD16—471no—
220C2×SD16—471no—
221C2×SD16—471no—
222C2×SD16—944no—
223C2×SD16C2×D4711yescharacteristic
224C22×C8—471no—
225C22×C8—471no—
226#124—471no—
227#124—471no—
228#124—471no—
229#124—941no—
230#124—941no—
231#124C2×D4711yescharacteristic
232C4×Q8—471no—
233C4×Q8—471no—
234C4×Q8—471no—
235C4×Q8—941no—
236C4×Q8—941no—
237C4×Q8C2×D4711yescharacteristic, complemented
238C2×C4⋊C4—471no—
239C2×C4⋊C4—941no—
240C2×C22⋊C4—941no—
241C2×C22⋊C4—941no—
242C2×C42—471no—
243C2×C42—941no—
244C4⋊C8—471no—
245C4⋊C8—471no—
246C4⋊C8—471no—
247C4⋊C8C2×D4711yescharacteristic, complemented
248#103—471no—
249#103—471no—
250#103—471no—
251#103C2×D4711yescharacteristic, complemented
252#102—471no—
253#102—471no—
254#102—471no—
255#102C2×D4711yescharacteristic
256C24—941no—
257C2×Q8—474no—
258C2×Q8—471no—
259C2×Q8—471no—
260C2×Q8—941no—
261C2×Q8—941no—
262C2×Q8—942no—
263C2×Q8—942no—
264C2×Q8—942no—
265C2×Q8C22×D4711yescharacteristic
266C2×Q8C22×D4711yescharacteristic
267C2×D4—471no—
268C2×D4—942no—
269C2×D4—942no—
270C2×D4—941no—
271C2×D4C22×D4711yescharacteristic
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4—941no—
278Q16—22no—
279Q16—942no—
280Q16—942no—
281Q16—942no—
282SD16—22no—
283SD16—942no—
284SD16—942no—
285SD16—942no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—942no—
289C2×C8—942no—
290C2×C8C22×D4711yescharacteristic
291C2×C8C22×D4711yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—471no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4C22×D4711yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C42—21no—
308C42—471no—
309C42—471no—
310C42—471no—
311C42—941no—
312C42—941no—
313C42—941no—
314C42C22×D4711yescharacteristic
315C23—21no—
316C23—471no—
317C23—941no—
318C23—1882no—
319C23—1882no—
320C23—1882no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—472no—
325Q8—944no—
326Q8—941no—
327Q8—941no—
328Q8—941no—
329Q8—1882no—
330Q8D4×D4712yes—
331D4—21no—
332D4—21no—
333D4—941no—
334D4—941no—
335D4—1882no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—471no—
340C2×C4—472no—
341C2×C4—472no—
342C2×C4—471no—
343C2×C4—471no—
344C2×C4—942no—
345C2×C4—942no—
346C2×C4—944no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—1882no—
351C2×C4—1882no—
352C2×C4D4×D4711yescharacteristic
353C2×C4D4×D4711yescharacteristic
354C2×C4C23×D4711yescharacteristic
355C8—21no—
356C8—21no—
357C8—941no—
358C8—941no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—472no—
363C22—472no—
364C22—472no—
365C22—3764no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22C2×D4×D4711yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—472no—
376C4—942no—
377C4—941no—
378C4—941no—
379C4—1881no—
380C4—1881no—
381C4C2×D4×D4711yescharacteristic
382C4#41×D4711yescharacteristic
383C2—81no—
384C2—474no—
385C2—3761no—
386C2#121×D4711yescharacteristic
387C2#135×D4711yescharacteristic
388C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47C2×#464
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D47C2semidirect
4. C4×Q8×D47C2semidirect
5. #15689348C2semidirect
6. #15689347C2semidirect
7. #15689346C2semidirect
8. #15689345C2semidirect
9. #15689344C2semidirect
10. #15689343C2semidirect
11. #15689342C2semidirect
12. C4⋊C8×D47C2semidirect
13. #103×D47C2semidirect
15. C47×#464C2semidirect
19. C2×Dic188C22semidirect
20. C2×#10625337C22semidirect
21. C2×#10625337C22semidirect
34. Q8×Dic47C22semidirect
36. C4×Dic94C22semidirect
38. #13093989C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093947C22semidirect
54. C2×Q16×C47C22semidirect
57. C4×Q8×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
194. D47#464direct (N × H)
206. #464D47direct (N × H)
210. C47C2×#464semidirect
218. C2×Q16C2×D47semidirect
237. C4×Q8C2×D47semidirect
247. C4⋊C8C2×D47semidirect
251. #103C2×D47semidirect