Finite Group Databasebeta

← #20255060

Subgroups — #20255060

Order 6016.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×D47C212yesmaximal, complemented
2D4×D188C211yesmaximal, characteristic, complemented
3#15689758C211yesmaximal, characteristic, complemented
4#15689499C211yesmaximal, characteristic, complemented
5#15689358C212yesmaximal, complemented
6#15689319C211yesmaximal, characteristic, complemented
7#15689258C212yesmaximal, complemented
8#15689255C212yesmaximal, complemented
9C4×#10625334C211yesmaximal, characteristic, complemented
10#15689188C211yesmaximal, characteristic, complemented
11C47×#459C211yesmaximal, characteristic, complemented
12C22×D188—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2212yescomplemented
15C2×D4×D47C2212yescomplemented
16C2×D376C2212yescomplemented
17C2×#10625334C2211yescharacteristic
18C2×#10625334C2212yescomplemented
19C2×#10625334C2212yescomplemented
20D8×D47—28no—
21C2×C8×D47C2212yescomplemented
22#13094021C2211yescharacteristic, complemented
23#13093999C2212yescomplemented
24#13093998—21no—
25#13093995—21no—
26#13093995C2212yescomplemented
27#13093994—22no—
28#13093992—22no—
29C4×D188C2211yescharacteristic
30C4×D188C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093946C2212yescomplemented
33#13093945C2211yescharacteristic, complemented
34#13093944C2211yescharacteristic, complemented
35(C2×D47)⋊C8C2212yescomplemented
36C4×C47⋊C8C2211yescharacteristic, complemented
37C2×D8×C47C2212yescomplemented
38#127×C47C2211yescharacteristic, complemented
39C4×D4×C47C2211yescharacteristic, complemented
40C4⋊C8×C47C2211yescharacteristic, complemented
41#102×C47C2212yescomplemented
42C23×D47—22no—
43C23×D47—22no—
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47C2312yes—
47C2×D4×C47C2311yescharacteristic
48C22×C4×C47—21no—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52D4×D47—24no—
53D4×D47—24no—
54D4×D47—42no—
55D4×D47—42no—
56D4×D47—44no—
57C2×D188—22no—
58C2×D188—21no—
59C2×D188—21no—
60C2×D188—44no—
61C2×D188D411yescharacteristic
62C2×D188C2312yes—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47C2312yes—
66D8×C47—24no—
67C2×C8×C47C2312yes—
68C4⋊C4×C47C2311yescharacteristic
69C22⋊C4×C47—21no—
70C42×C47C2311yescharacteristic
71C22⋊Dic47—22no—
72#10625334—24no—
73#10625334—42no—
74#10625334D414yescomplemented
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4D412yes—
78C4⋊Dic47D411yescharacteristic
79C4⋊Dic47C2311yescharacteristic
80C2×C47⋊C8C2311yescharacteristic
81C2×C47⋊C8C2311yescharacteristic
82D376—24no—
83C8×D47—24no—
84C23×C47—21no—
85C23×C47—22no—
86C22×D47—21no—
87C22×D47—22no—
88C22×D47—44no—
89C22×D47—44no—
90C22×D47—44no—
91C22×D47—44no—
92C22×D47—82no—
93C22×D47—82no—
94C22×D47C2×D412yes—
95D4×C47—22no—
96D4×C47—21no—
97D4×C47—22no—
98D4×C47—42no—
99D4×C47—81no—
100D4×C47C2×D412yescomplemented
101C2×C4×C47—21no—
102C2×C4×C47—42no—
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47C2411yescharacteristic
106C22⋊D47—44no—
107C22⋊D47—44no—
108C22⋊D47—44no—
109C2×Dic47—21no—
110C2×Dic47C2×D412yes—
111D188—22no—
112D188—21no—
113D188—22no—
114D188—44no—
115D188—42no—
116D188—81no—
117D188D814yescomplemented
118D188C2×D412yescomplemented
119C4×D47—22no—
120C4×D47—22no—
121C4×D47—42no—
122C8×C47—22no—
123C47⋊C8—21no—
124C47⋊C8C2×D412yescomplemented
125C22×C47—22no—
126C22×C47—41no—
127C22×C47—41no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47—42no—
131C22×C47C22×D411yescharacteristic
132C2×D47—22no—
133C2×D47—22no—
134C2×D47—22no—
135C2×D47—41no—
136C2×D47—41no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—42no—
140C2×D47—88no—
141C2×D47—88no—
142C2×D47C2×D814yescomplemented
143C4×C47—21no—
144C4×C47—41no—
145C4×C47C2×D812yescomplemented
146C4×C47C22×D411yescharacteristic
147C4×C47H(5,𝔽2)11yescharacteristic
148Dic47—22no—
149Dic47—41no—
150D4×D8—471nomaximal, Sylow
151C2×C47—42no—
152C2×C47—82no—
153C2×C47D4211yescharacteristic
154C2×C47C22×D811yescharacteristic
155C2×C47#57611yescharacteristic
156D47—24no—
157D47—42no—
158D47—82no—
159C22×D8—472no—
160D42—471no—
161D42—471no—
162#493—471no—
163#466—472no—
164#459—471no—
165#459D4711yescharacteristic, complemented
166#447—472no—
167#447—472no—
168C4×D8—471no—
169C8×D4—471no—
170C47D4×D811yescharacteristic, complemented, Sylow
171C22×D4—472no—
172C22×D4—472no—
173C22×D4—941no—
174C22×D4—941no—
175C2×D8—471no—
176C2×D8—472no—
177C2×D8—472no—
178C2×D8—472no—
179C2×D8—948no—
180C2×D8C2×D4712yescomplemented
181C22×C8—472no—
182#127—471no—
183#127C2×D4711yescharacteristic, complemented
184#121—472no—
185#121—472no—
186#121—941no—
187#121—941no—
188#120—942no—
189#120—942no—
190C4×D4—471no—
191C4×D4—471no—
192C4×D4C2×D4711yescharacteristic, complemented
193#107—471no—
194C4⋊C8C2×D4711yescharacteristic, complemented
195#102—471no—
196#102—472no—
197#102—471no—
198#102C2×D4712yescomplemented
199C22⋊C8—472no—
200C4×C8—471no—
201C24—942no—
202C24—942no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—471no—
206C2×D4—471no—
207C2×D4—472no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—942no—
211C2×D4—944no—
212C2×D4—944no—
213C2×D4—942no—
214C2×D4—941no—
215C2×D4—941no—
216C2×D4—1884no—
217C2×D4—1882no—
218C2×D4—1882no—
219C2×D4—1884no—
220C2×D4C22×D4712yes—
221C2×D4C22×D4711yescharacteristic
222C22×C4—21no—
223C22×C4—472no—
224C22×C4—941no—
225D8—24no—
226D8—474no—
227D8—944no—
228D8—944no—
229D8—1882no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—944no—
233C2×C8C22×D4712yes—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4C22×D4711yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—472no—
239C22⋊C4—942no—
240C22⋊C4—942no—
241C22⋊C4—941no—
242C42C22×D4711yescharacteristic
243C23—21no—
244C23—22no—
245C23—472no—
246C23—941no—
247C23—942no—
248C23—3762no—
249C23—3762no—
250C23—1884no—
251C23—1884no—
252C23—1884no—
253C23—1884no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—474no—
260D4—472no—
261D4—942no—
262D4—941no—
263D4—942no—
264D4—3761no—
265D4—1884no—
266D4—1884no—
267D4—1884no—
268D4—1884no—
269D4—1882no—
270D4D4×D4712yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—472no—
274C2×C4—942no—
275C2×C4—942no—
276C2×C4—941no—
277C2×C4—1882no—
278C2×C4D4×D4711yescharacteristic
279C2×C4D4×D4711yescharacteristic
280C2×C4C23×D4711yescharacteristic
281C8—22no—
282C8—472no—
283C8—941no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—474no—
291C22—942no—
292C22—942no—
293C22—942no—
294C22—3768no—
295C22—3768no—
296C22—1882no—
297C22—1882no—
298C22—1882no—
299C22—1881no—
300C22—1881no—
301C22C2×D4×D4711yescharacteristic
302C4—21no—
303C4—41no—
304C4—942no—
305C4—1881no—
306C4D8×D4712yescomplemented
307C4C2×D4×D4711yescharacteristic
308C4#1309407011yescharacteristic
309C2—42no—
310C2—82no—
311C2—944no—
312C2—3762no—
313C2—1882no—
314C2#1568975711yescharacteristic
315C2C2×D8×D4711yescharacteristic
316C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47D4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×D8×D47C2semidirect
2. D4×D188C2semidirect
3. #15689758C2semidirect
4. #15689499C2semidirect
5. #15689358C2semidirect
6. #15689319C2semidirect
7. #15689258C2semidirect
8. #15689255C2semidirect
9. C4×#10625334C2semidirect
10. #15689188C2semidirect
11. C47×#459C2semidirect
14. C2×D4×D47C22semidirect
15. C2×D4×D47C22semidirect
16. C2×D376C22semidirect
18. C2×#10625334C22semidirect
19. C2×#10625334C22semidirect
21. C2×C8×D47C22semidirect
22. #13094021C22semidirect
23. #13093999C22semidirect
26. #13093995C22semidirect
30. C4×D188C22semidirect
31. #13093957C22semidirect
32. #13093946C22semidirect
33. #13093945C22semidirect
34. #13093944C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4×C47⋊C8C22semidirect
37. C2×D8×C47C22semidirect
38. #127×C47C22semidirect
39. C4×D4×C47C22semidirect
40. C4⋊C8×C47C22semidirect
41. #102×C47C22semidirect
74. #10625334D4semidirect
100. D4×C47C2×D4semidirect
117. D188D8semidirect
118. D188C2×D4semidirect
124. C47⋊C8C2×D4semidirect
142. C2×D47C2×D8semidirect
145. C4×C47C2×D8semidirect
165. #459D47semidirect
170. C47D4×D8semidirect
180. C2×D8C2×D47semidirect
183. #127C2×D47semidirect
192. C4×D4C2×D47semidirect
194. C4⋊C8C2×D47semidirect
198. #102C2×D47semidirect
270. D4D4×D47semidirect
306. C4D8×D47semidirect