Finite Group Databasebeta

← #20255600

Subgroups — #20255600

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#15689812C211yesmaximal, characteristic, complemented
2#15689767C211yesmaximal, characteristic
3#15689476C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689440C211yesmaximal, characteristic, complemented
6#15689425C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689368C211yesmaximal, characteristic, complemented
9#15689344C211yesmaximal, characteristic, complemented
10#15689286C211yesmaximal, characteristic, complemented
11#15689274C211yesmaximal, characteristic, complemented
12#15689214C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689121C211yesmaximal, characteristic, complemented
15C47×#418C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Dic188C2211yescharacteristic, complemented
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21#13094017—21no—
22#13094016—21no—
23#13094015C2211yescharacteristic, complemented
24#13094011C2211yescharacteristic
25#13094006—21no—
26#13094005—21no—
27#13094004C2211yescharacteristic, complemented
28#13094003C2211yescharacteristic
29#13094003C2211yescharacteristic
30#13093996—21no—
31#13093995C2211yescharacteristic
32#13093993—21no—
33#13093989C2211yescharacteristic, complemented
34D4×Dic47C2211yescharacteristic
35C4×C22⋊D47C2211yescharacteristic
36#13093981—21no—
37C4⋊C4×D47C2211yescharacteristic, complemented
38C2×C22⋊Dic47—21no—
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093947C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#102×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C24×C47—21no—
60C2×D4×C47—22no—
61C2×D4×C47—21no—
62C2×D4×C47—41no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—21no—
71#10625352—22no—
72#10625352—41no—
73C2×C4×D47—21no—
74C2×C4×D47C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77M16×C47—41no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C42×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625335—22no—
92#10625335—41no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109Dic188—41no—
110#10625324—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—42no—
122D4×C47#4112yes—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—41no—
130C22⋊D47—42no—
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—42no—
137C2×Dic47—81no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—42no—
144Dic94—21no—
145Dic94—21no—
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#450—471no—
197C4×SD16—471no—
198#436—471no—
199#418D4711yescharacteristic, complemented
200#417—471no—
201C47#332311yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4C2×D4711yescharacteristic
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×M16—471no—
208C2×M16C2×D4711yescharacteristic
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⋊Q8—471no—
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8—471no—
222C4×D4—471no—
223C4×D4—471no—
224#117—941no—
225#117C2×D4711yescharacteristic
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#102C2×D4711yescharacteristic
239#102C2×D4711yescharacteristic
240#102C2×D4711yescharacteristic
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244C4×C8—471no—
245C24—21no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8—471no—
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—942no—
265SD16—1881no—
266M16—41no—
267M16—1881no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4C22×D4711yescharacteristic
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—21no—
295C42—471no—
296C42—941no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—471no—
303C23D4×D4711yescharacteristic
304Q8—941no—
305Q8—941no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—3761no—
313D4—1881no—
314D4—1882no—
315D4#1062535012yes—
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×#1062535011yescharacteristic
363C4#1309406911yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—1881no—
368C2#1568976311yescharacteristic
369C2#1568991911yescharacteristic
370C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #15689812C2semidirect
3. #15689476C2semidirect
4. #15689464C2semidirect
5. #15689440C2semidirect
6. #15689425C2semidirect
7. #15689381C2semidirect
8. #15689368C2semidirect
9. #15689344C2semidirect
10. #15689286C2semidirect
11. #15689274C2semidirect
12. #15689214C2semidirect
13. #15689199C2semidirect
14. #15689121C2semidirect
15. C47×#418C2semidirect
17. C2×Dic188C22semidirect
20. C2×#10625324C22semidirect
23. #13094015C22semidirect
27. #13094004C22semidirect
33. #13093989C22semidirect
37. C4⋊C4×D47C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093947C22semidirect
46. #13093947C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
199. #418D47semidirect
201. C47#3323semidirect