Finite Group Databasebeta

← #20255605

Subgroups — #20255605

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#15689808C211yesmaximal, characteristic, complemented
2#15689761C211yesmaximal, characteristic
3#15689479C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689441C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689380C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689348C211yesmaximal, characteristic, complemented
10#15689285C211yesmaximal, characteristic, complemented
11#15689275C211yesmaximal, characteristic, complemented
12#15689214C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689126C211yesmaximal, characteristic, complemented
15C47×#417C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625337C2211yescharacteristic, complemented
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094019—21no—
22#13094015C2211yescharacteristic, complemented
23#13094014—21no—
24#13094013C2211yescharacteristic
25#13094007—21no—
26#13094007—21no—
27#13094004C2211yescharacteristic
28#13094003C2211yescharacteristic, complemented
29#13094000C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093996—21no—
32#13093992—21no—
33#13093989C2211yescharacteristic, complemented
34D4×Dic47C2211yescharacteristic
35C4×C22⋊D47C2211yescharacteristic
36#13093983—21no—
37#13093982C2211yescharacteristic
38C2×(C2×D47)⋊C4—21no—
39#13093958C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54C2×C4⋊C4×C47C2211yescharacteristic, complemented
55#103×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47D411yescharacteristic
71C22×Dic47—21no—
72D4×D47—22no—
73D4×D47—41no—
74C2×D188C2311yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77M16×C47—41no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47D411yescharacteristic
86#10625337—41no—
87#10625335—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
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⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625325—41no—
110#10625324—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×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×C47—21no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—41no—
133C22⋊D47—42no—
134C22⋊D47—81no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—81no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142D188—21no—
143D188—21no—
144C4×D47—21no—
145C4×D47—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×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47C2×#4111yescharacteristic
171C4×C47H(5,𝔽2)11yescharacteristic
172Dic47—21no—
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3323—471nomaximal, Sylow
179C2×C47—42no—
180C2×C47—41no—
181C2×C47#54611yescharacteristic
182C2×C47#57511yescharacteristic
183C2×C47#57711yescharacteristic
184D47—41no—
185D47—81no—
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#418—471no—
200#417D4711yescharacteristic, complemented
201C47#332311yescharacteristic, complemented, Sylow
202C2×#41C2×D4711yescharacteristic
203C22×D4—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×M16—471no—
208C2×M16C2×D4711yescharacteristic, complemented
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—471no—
225#117—941no—
226C2×C4⋊C4C2×D4711yescharacteristic, complemented
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106—471no—
231C4⋊C8—471no—
232#103—471no—
233#103—471no—
234#103C2×D4711yescharacteristic, complemented
235#103C2×D4711yescharacteristic, complemented
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244C4×C8—471no—
245C24—941no—
246#41—22no—
247#41—41no—
248C2×Q8—471no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—21no—
251C2×D4—471no—
252C2×D4—471no—
253C2×D4—941no—
254C2×D4—942no—
255C2×D4—941no—
256C2×D4—1881no—
257C2×D4C22×D4711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—471no—
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—21no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
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—471no—
285C22⋊C4—471no—
286C22⋊C4—941no—
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—471no—
299C23—941no—
300C23—3761no—
301C23—1882no—
302C23—1882no—
303C23D4×D4711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—42no—
310D4—941no—
311D4—941no—
312D4—3761no—
313D4—1881no—
314D4—1882no—
315D4#1062535012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—471no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3761no—
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—941no—
345C22—941no—
346C22—941no—
347C22—3764no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—941no—
357C4—941no—
358C4—941no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4C2×#1062535011yescharacteristic
363C4#1309406911yescharacteristic
364C2—41no—
365C2—42no—
366C2—3761no—
367C2—1881no—
368C2#1568976311yescharacteristic
369C2#1568991911yescharacteristic
370C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #15689808C2semidirect
3. #15689479C2semidirect
4. #15689463C2semidirect
5. #15689441C2semidirect
6. #15689421C2semidirect
7. #15689380C2semidirect
8. #15689369C2semidirect
9. #15689348C2semidirect
10. #15689285C2semidirect
11. #15689275C2semidirect
12. #15689214C2semidirect
13. #15689199C2semidirect
14. #15689126C2semidirect
15. C47×#417C2semidirect
17. C2×#10625337C22semidirect
22. #13094015C22semidirect
28. #13094003C22semidirect
33. #13093989C22semidirect
39. #13093958C22semidirect
40. #13093955C22semidirect
41. #13093955C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093948C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
51. C8×Dic47C22semidirect
53. C2×M16×C47C22semidirect
54. C2×C4⋊C4×C47C22semidirect
55. #103×C47C22semidirect
56. #103×C47C22semidirect
200. #417D47semidirect
201. C47#3323semidirect
208. C2×M16C2×D47semidirect
226. C2×C4⋊C4C2×D47semidirect
234. #103C2×D47semidirect
235. #103C2×D47semidirect