Finite Group Databasebeta

← #20255608

Subgroups — #20255608

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689807C211yesmaximal, characteristic, complemented
2#15689767C211yesmaximal, characteristic
3#15689476C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689440C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689379C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689343C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11SD16×Dic47C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689128C211yesmaximal, characteristic, complemented
14#15689121C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625337C2211yescharacteristic, complemented
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic, complemented
20#13094017—21no—
21#13094015C2211yescharacteristic, complemented
22#13094014—21no—
23#13094011C2211yescharacteristic
24#13094006—21no—
25#13094005—21no—
26#13094003C2211yescharacteristic
27#13094000C2211yescharacteristic, complemented
28#13093996—21no—
29#13093995C2211yescharacteristic
30#13093993—21no—
31Q8×Dic47C2211yescharacteristic, complemented
32D4×Dic47C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34#13093983C2211yescharacteristic
35#13093982—21no—
36C4⋊C4×D47C2211yescharacteristic, complemented
37C2×C22⋊Dic47—21no—
38#13093958C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—21no—
72#10625352—22no—
73#10625352—41no—
74C2×C4×D47—21no—
75C2×C4×D47C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77SD16×C47—22no—
78SD16×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625337—41no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107#10625329—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—42no—
124D4×C47#4112yes—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—41no—
132C22⋊D47—42no—
133C22⋊D47—81no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47—81no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—42no—
146Dic94—21no—
147Dic94—21no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—22no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—84no—
162C22×C47C22×D411yescharacteristic
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—21no—
172Dic47—21no—
173Dic47—21no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3323—471nomaximal, Sylow
179C2×C47—41no—
180C2×C47—42no—
181C2×C47—81no—
182C2×C47#54611yescharacteristic
183C2×C47#57511yescharacteristic
184C2×C47#57711yescharacteristic
185D47—41no—
186#552—471no—
187#546—471no—
188#488—471no—
189#485—471no—
190#481—471no—
191#478—471no—
192#470—471no—
193#468—471no—
194#464—471no—
195#452—471no—
196#450D4711yescharacteristic, complemented
197C4×SD16—471no—
198#436—471no—
199#418—471no—
200#417—471no—
201C47#332311yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4C2×D4711yescharacteristic
204C2×Q16—471no—
205C2×SD16C2×D4711yescharacteristic
206C2×SD16C2×D4711yescharacteristic
207C2×M16—471no—
208C2×M16—471no—
209#126—941no—
210#125—471no—
211#125—941no—
212#124—471no—
213#123—941no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8C2×D4711yescharacteristic
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8—471no—
222C4×D4—471no—
223C4×D4—471no—
224#117—471no—
225#117—941no—
226C2×C4⋊C4—471no—
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106—471no—
231C4⋊C8—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8C2×D4711yescharacteristic
244C4×C8—471no—
245C24—21no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—471no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4C22×D4711yescharacteristic
257C2×D4C22×D4711yescharacteristic
258C22×C4—471no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4C22×D4711yescharacteristic
263Q16—1881no—
264SD16—22no—
265SD16—41no—
266M16—1881no—
267M16—1881no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4C22×D4711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—471no—
286C22⋊C4—471no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C42—471no—
295C42—941no—
296C42—941no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—471no—
303C23D4×D4711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—3761no—
313D4—1881no—
314D4—1882no—
315D4#1062535212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—471no—
321C2×C4—471no—
322C2×C4—471no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—3761no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—941no—
349C22—941no—
350C22—941no—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—941no—
356C4—941no—
357C4—941no—
358C4—1881no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4C2×#1062535211yescharacteristic
363C4#1309406911yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—1881no—
368C2#1568976011yescharacteristic
369C2#1568991911yescharacteristic
370C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689807C2semidirect
3. #15689476C2semidirect
4. #15689465C2semidirect
5. #15689440C2semidirect
6. #15689421C2semidirect
7. #15689379C2semidirect
8. #15689366C2semidirect
9. #15689343C2semidirect
10. #15689282C2semidirect
11. SD16×Dic47C2semidirect
12. #15689198C2semidirect
13. #15689128C2semidirect
14. #15689121C2semidirect
15. C47×#450C2semidirect
17. C2×#10625337C22semidirect
19. C2×#10625324C22semidirect
21. #13094015C22semidirect
27. #13094000C22semidirect
31. Q8×Dic47C22semidirect
36. C4⋊C4×D47C22semidirect
38. #13093958C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093948C22semidirect
45. #13093947C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
196. #450D47semidirect
201. C47#3323semidirect