Finite Group Databasebeta

← #20255204

Subgroups — #20255204

Order 6016.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#15689778C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic, complemented
3#15689469C211yesmaximal, characteristic, complemented
4#15689435C212yesmaximal, complemented
5#15689404C211yesmaximal, characteristic, complemented
6#15689356C212yesmaximal, complemented
7#15689255C212yesmaximal, complemented
8C4×#10625334C211yesmaximal, characteristic, complemented
9#15689188C211yesmaximal, characteristic, complemented
10#102×D47C212yesmaximal, complemented
11C47×#459C211yesmaximal, characteristic, complemented
12C2×#10625350—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15C2×#10625334C2211yescharacteristic
16C2×C8×D47C2212yescomplemented
17#13094024C2211yescharacteristic, complemented
18#13094006—22no—
19#13094003—21no—
20#13093995—21no—
21#13093995C2212yes—
22#13093995C2212yescomplemented
23#13093992—22no—
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26C4⋊C4×D47C2212yescomplemented
27#13093958C2212yescomplemented
28#13093957C2211yescharacteristic, complemented
29#13093946C2212yes—
30#13093945C2212yescomplemented
31#13093945C2211yescharacteristic, complemented
32#13093945C2212yescomplemented
33#13093944C2211yescharacteristic
34(C2×D47)⋊C8C2212yescomplemented
35C4×C47⋊C8C2211yescharacteristic, complemented
36C2×D8×C47C2212yescomplemented
37#127×C47C2211yescharacteristic
38C4×D4×C47C2211yescharacteristic, complemented
39C4⋊C8×C47C2211yescharacteristic, complemented
40#102×C47C2212yescomplemented
41C23×D47—22no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C2×D4×C47C2312yes—
46C22×C4×C47—21no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50D4×D47—24no—
51D4×D47—42no—
52D4×D47—44no—
53#10625350—44no—
54C2×D188D411yescharacteristic
55C2×D188C2311yescharacteristic
56C2×C4×D47—22no—
57C2×C4×D47—21no—
58C2×C4×D47C2312yes—
59C2×Dic94—21no—
60D8×C47—42no—
61C2×C8×C47C2312yes—
62C4⋊C4×C47C2311yescharacteristic
63C22⋊C4×C47—21no—
64C42×C47C2311yescharacteristic
65C22⋊Dic47—22no—
66C22⋊Dic47—22no—
67#10625334—22no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4D412yes—
70C4⋊Dic47—21no—
71C4⋊Dic47D411yescharacteristic
72C4⋊Dic47C2312yes—
73C4⋊Dic47C2311yescharacteristic
74Dic47⋊C4—22no—
75C2×C47⋊C8C2311yescharacteristic
76C2×C47⋊C8C2311yescharacteristic
77C8×D47—42no—
78C23×C47—21no—
79C23×C47—22no—
80C22×D47—21no—
81C22×D47—44no—
82C22×D47—44no—
83C22×D47—82no—
84C22×D47C2×D412yes—
85D4×C47—21no—
86D4×C47—22no—
87D4×C47—21no—
88D4×C47—22no—
89D4×C47—42no—
90D4×C47—81no—
91C2×C4×C47—21no—
92C2×C4×C47—42no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—44no—
97C22⋊D47—44no—
98C22⋊D47—44no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47C2×D412yes—
102D188—21no—
103D188D814yescomplemented
104D188#4112yescomplemented
105C4×D47—22no—
106C4×D47—22no—
107C4×D47—44no—
108C4×D47—42no—
109Dic94—42no—
110C8×C47—22no—
111C47⋊C8—21no—
112C47⋊C8—21no—
113C22×C47—42no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47—41no—
119C22×C47C22×D411yescharacteristic
120C2×D47—22no—
121C2×D47—22no—
122C2×D47—22no—
123C2×D47—41no—
124C2×D47—41no—
125C2×D47—88no—
126C2×D47C2×D814yes—
127C4×C47—21no—
128C4×C47—41no—
129C4×C47C2×D812yes—
130C4×C47C2×#4111yescharacteristic
131C4×C47H(5,𝔽2)11yescharacteristic
132Dic47—22no—
133Dic47—42no—
134Dic47—41no—
135#3294—471nomaximal, Sylow
136C2×C47—82no—
137C2×C47—81no—
138C2×C47#54611yescharacteristic
139C2×C47C22×D811yescharacteristic
140C2×C47#57711yescharacteristic
141D47—24no—
142D47—42no—
143#547—471no—
144D42—471no—
145#486—471no—
146#480—472no—
147#474—471no—
148#466—472no—
149#459D4711yescharacteristic, complemented
150#447—472no—
151C4×D8—471no—
152C8×D4—471no—
153C2×#102—472no—
154C47#329411yescharacteristic, complemented, Sylow
155C2×#41—941no—
156C22×D4—472no—
157C22×D4—941no—
158C2×D8—471no—
159C2×D8C2×D4712yescomplemented
160C22×C8—472no—
161C4⋊Q8—471no—
162#127C2×D4711yescharacteristic
163#123—942no—
164C22⋊Q8—941no—
165#121—472no—
166#121—472no—
167#121—941no—
168#120—942no—
169C4×D4—471no—
170C4×D4—471no—
171C4×D4C2×D4711yescharacteristic, complemented
172C2×C4⋊C4—472no—
173#107—472no—
174#107—471no—
175C4⋊C8C2×D4711yescharacteristic, complemented
176#102—472no—
177#102—471no—
178#102—472no—
179#102—472no—
180#102—471no—
181#102C2×D4712yescomplemented
182C22⋊C8—472no—
183C4×C8—471no—
184C24—942no—
185#41—1884no—
186C2×Q8—941no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—471no—
190C2×D4—471no—
191C2×D4—942no—
192C2×D4—944no—
193C2×D4—942no—
194C2×D4—942no—
195C2×D4—1882no—
196C2×D4—1884no—
197C2×D4C22×D4712yes—
198C2×D4C22×D4711yescharacteristic
199C22×C4—21no—
200C22×C4—472no—
201C22×C4—942no—
202C22×C4—941no—
203D8—42no—
204D8—942no—
205C2×C8—471no—
206C2×C8—471no—
207C2×C8—1882no—
208C2×C8C22×D4712yes—
209C4⋊C4—471no—
210C4⋊C4—472no—
211C4⋊C4—471no—
212C4⋊C4—942no—
213C4⋊C4—941no—
214C4⋊C4C22×D4711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—472no—
217C22⋊C4—942no—
218C22⋊C4—942no—
219C22⋊C4—941no—
220C42C22×D4711yescharacteristic
221C23—21no—
222C23—22no—
223C23—472no—
224C23—941no—
225C23—3762no—
226C23—1884no—
227C23—1884no—
228Q8—1882no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—474no—
236D4—472no—
237D4—941no—
238D4—1884no—
239D4—1884no—
240D4—1884no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—472no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—941no—
247C2×C4—942no—
248C2×C4—1884no—
249C2×C4—1882no—
250C2×C4D4×D4711yescharacteristic
251C2×C4D4×D4711yescharacteristic
252C2×C4C23×D4711yescharacteristic
253C8—22no—
254C8—941no—
255C8—941no—
256C22—42no—
257C22—41no—
258C22—41no—
259C22—42no—
260C22—42no—
261C22—41no—
262C22—474no—
263C22—942no—
264C22—942no—
265C22—942no—
266C22—3768no—
267C22—1881no—
268C22—1881no—
269C22C2×D4×D4711yescharacteristic
270C4—21no—
271C4—41no—
272C4—942no—
273C4—1881no—
274C4—1882no—
275C4D8×D4712yes—
276C4#41×D4711yescharacteristic
277C4#1309406911yescharacteristic
278C2—82no—
279C2—81no—
280C2—944no—
281C2—1882no—
282C2#1568977011yescharacteristic
283C2C2×D8×D4711yescharacteristic
284C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3294
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. #15689778C2semidirect
2. #15689758C2semidirect
3. #15689469C2semidirect
4. #15689435C2semidirect
5. #15689404C2semidirect
6. #15689356C2semidirect
7. #15689255C2semidirect
8. C4×#10625334C2semidirect
9. #15689188C2semidirect
10. #102×D47C2semidirect
11. C47×#459C2semidirect
16. C2×C8×D47C22semidirect
17. #13094024C22semidirect
22. #13093995C22semidirect
26. C4⋊C4×D47C22semidirect
27. #13093958C22semidirect
28. #13093957C22semidirect
30. #13093945C22semidirect
31. #13093945C22semidirect
32. #13093945C22semidirect
34. (C2×D47)⋊C8C22semidirect
35. C4×C47⋊C8C22semidirect
36. C2×D8×C47C22semidirect
38. C4×D4×C47C22semidirect
39. C4⋊C8×C47C22semidirect
40. #102×C47C22semidirect
103. D188D8semidirect
104. D188#41semidirect
149. #459D47semidirect
154. C47#3294semidirect
159. C2×D8C2×D47semidirect
171. C4×D4C2×D47semidirect
175. C4⋊C8C2×D47semidirect
181. #102C2×D47semidirect