Finite Group Databasebeta

← #20255228

Subgroups — #20255228

Order 6016.

408 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#15689814C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic
3#15689478C211yesmaximal, characteristic, complemented
4#15689455C211yesmaximal, characteristic, complemented
5#15689449C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689363C211yesmaximal, characteristic, complemented
8#15689355C211yesmaximal, characteristic, complemented
9#15689345C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12C8×D188C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625336C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic, complemented
22#13094018—21no—
23#13094016C2211yescharacteristic, complemented
24#13094014—21no—
25#13094012C2211yescharacteristic
26#13094009—21no—
27#13094008—21no—
28#13094004C2211yescharacteristic
29#13094000C2211yescharacteristic
30#13094000C2211yescharacteristic, complemented
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093994—21no—
34C4×D188C2211yescharacteristic
35#13093982C2211yescharacteristic, complemented
36#13093981—21no—
37C4⋊C4×D47C2211yescharacteristic
38C2×(C2×D47)⋊C4—21no—
39#13093957C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66#10625352—22no—
67#10625352—41no—
68D4×D47—22no—
69D4×D47—41no—
70C2×D188—21no—
71C2×D188D411yescharacteristic
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47C2311yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77SD16×C47—22no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86#10625337—41no—
87#10625336—41no—
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)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96(C2×D47)⋊C4D411yescharacteristic
97C4⋊Dic47—21no—
98C4⋊Dic47D411yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C8×D47—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47—81no—
116C22×D47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120D4×C47—21no—
121D4×C47#4112yes—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—81no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—42no—
130C22⋊D47—42no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—22no—
138D188—21no—
139D188—21no—
140D188—81no—
141C4×D47—21no—
142C4×D47—21no—
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—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—84no—
165C2×D47#13512yes—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3296—471nomaximal, Sylow
179C2×C47—42no—
180C2×C47#54611yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—22no—
184D47—41no—
185D47—81no—
186#552—471no—
187#546—471no—
188#488—471no—
189#483—471no—
190#482—471no—
191#478—471no—
192#467—471no—
193#465—471no—
194#464—471no—
195#452—471no—
196#450—471no—
197C4×SD16D4711yescharacteristic, complemented
198C8×D4—471no—
199#416—471no—
200C2×#102—471no—
201C47#329611yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16C2×D4711yescharacteristic
207C22×C8—471no—
208C22×C8—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⋊Q8—471no—
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8C2×D4711yescharacteristic, complemented
222C4×D4—471no—
223C4×D4C2×D4711yescharacteristic
224#117—471no—
225#117—941no—
226C2×C4⋊C4—471no—
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106C2×D4711yescharacteristic, complemented
231C4⋊C8—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103C2×D4711yescharacteristic, complemented
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244C4×C8C2×D4711yescharacteristic, complemented
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4—942no—
255C2×D4—941no—
256C2×D4—1881no—
257C2×D4C22×D4711yescharacteristic
258C22×C4—21no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—941no—
262C22×C4—941no—
263Q16—1881no—
264SD16—22no—
265SD16—1881no—
266C2×C8—471no—
267C2×C8—471no—
268C2×C8—1881no—
269C2×C8—1881no—
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—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—941no—
296C42C22×D4711yescharacteristic
297C23—21no—
298C23—471no—
299C23—471no—
300C23—941no—
301C23—3761no—
302C23—1882no—
303C23—1882no—
304Q8—21no—
305Q8—21no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—942no—
310D4—941no—
311D4—941no—
312D4—3761no—
313D4—1882no—
314D4—1882no—
315D4#1062535012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—471no—
321C2×C4—471no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—472no—
342C22—941no—
343C22—941no—
344C22—941no—
345C22—941no—
346C22—941no—
347C22—3764no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—941no—
358C4—941no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4C2×#1062535011yescharacteristic
363C4#1309407011yescharacteristic
364C2—42no—
365C2—942no—
366C2—3761no—
367C2—1881no—
368C2#1568976911yescharacteristic
369C2#135×D4711yescharacteristic
370C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#3296
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #15689814C2semidirect
3. #15689478C2semidirect
4. #15689455C2semidirect
5. #15689449C2semidirect
6. #15689423C2semidirect
7. #15689363C2semidirect
8. #15689355C2semidirect
9. #15689345C2semidirect
10. #15689282C2semidirect
11. #15689272C2semidirect
12. C8×D188C2semidirect
13. #15689116C2semidirect
14. #102×D47C2semidirect
15. C4×SD16×C47C2semidirect
18. C2×#10625337C22semidirect
21. C2×C8×D47C22semidirect
23. #13094016C22semidirect
30. #13094000C22semidirect
35. #13093982C22semidirect
39. #13093957C22semidirect
40. #13093955C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
51. (C2×D47)⋊C8C22semidirect
53. C4×Q8×C47C22semidirect
55. #106×C47C22semidirect
56. #103×C47C22semidirect
58. C4×C8×C47C22semidirect
197. C4×SD16D47semidirect
201. C47#3296semidirect
221. C4×Q8C2×D47semidirect
230. #106C2×D47semidirect
235. #103C2×D47semidirect
244. C4×C8C2×D47semidirect