Finite Group Databasebeta

← #20254328

Subgroups — #20254328

Order 6016.

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

normal subgroups only

This group has 488 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#15689677C211yesmaximal, characteristic, complemented
2#127×D47C211yesmaximal, characteristic
3#15689494C212yesmaximal, complemented
4#15689468C212yesmaximal, complemented
5#15689324C211yesmaximal, characteristic, complemented
6#15689323C211yesmaximal, characteristic, complemented
7#15689320C211yesmaximal, characteristic, complemented
8#15689275C212yesmaximal, complemented
9#15689272C212yesmaximal, complemented
10#15689175C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15C2×#10625325C2212yescomplemented
16C2×#10625335C2212yescomplemented
17C2×#10625336C2212yescomplemented
18#13094023C2211yescharacteristic, complemented
19#13094022C2211yescharacteristic, complemented
20#13094021C2211yescharacteristic
21#13094020—21no—
22#13094020—21no—
23#13094020C2212yes—
24#13094014—21no—
25#13094004C2211yescharacteristic
26#13094002—21no—
27#13094000C2211yescharacteristic
28C4×Dic94—21no—
29C4×Dic94C2211yescharacteristic, complemented
30#13093981—21no—
31C42×D47C2211yescharacteristic
32C4⋊(C47⋊C8)C2211yescharacteristic, complemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093944C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37C8×Dic47C2212yescomplemented
38C2×SD16×C47C2212yescomplemented
39#127×C47C2211yescharacteristic
40C4×Q8×C47C2211yescharacteristic, complemented
41C4⋊C8×C47C2211yescharacteristic, complemented
42#102×C47C2212yescomplemented
43C23×D47—22no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47—21no—
47C2×D4×C47C2312yes—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51D4×D47—42no—
52D4×D47—42no—
53D4×D47—44no—
54D4×D47—44no—
55C2×D188—21no—
56C2×D188—21no—
57C2×D188C2312yes—
58C2×C4×D47D411yescharacteristic
59C2×C4×D47D411yescharacteristic
60C2×C4×D47C2311yescharacteristic
61C2×Dic94—21no—
62C2×Dic94C2311yescharacteristic
63SD16×C47—42no—
64C2×C8×C47C2312yes—
65C4⋊C4×C47—21no—
66C4⋊C4×C47C2311yescharacteristic
67C42×C47—21no—
68C42×C47C2311yescharacteristic
69#10625336—42no—
70#10625335—42no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47—21no—
74C4⋊Dic47C2311yescharacteristic
75Dic47⋊C4—21no—
76Dic47⋊C4—21no—
77Dic47⋊C4—21no—
78Dic47⋊C4—21no—
79Dic47⋊C4—21no—
80C4×Dic47—21no—
81C4×Dic47D411yescharacteristic
82C4×Dic47D411yescharacteristic
83C4×Dic47C2311yescharacteristic
84C2×C47⋊C8C2312yes—
85#10625325—42no—
86C23×C47—22no—
87C22×D47—22no—
88C22×D47—44no—
89C22×D47—44no—
90C22×D47—44no—
91C22×D47C2×D411yescharacteristic
92Q8×C47—21no—
93Q8×C47—21no—
94D4×C47—22no—
95D4×C47—22no—
96D4×C47—42no—
97D4×C47—42no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2411yescharacteristic
103C22⋊D47—44no—
104C22⋊D47—44no—
105C22⋊D47—44no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108C2×Dic47C2×D411yescharacteristic
109C2×Dic47C2×D411yescharacteristic
110C2×Dic47C2×D411yescharacteristic
111D188—22no—
112D188—22no—
113D188—42no—
114D188—42no—
115C4×D47—21no—
116C4×D47—21no—
117C4×D47—22no—
118C4×D47SD1614yescomplemented
119Dic94—21no—
120Dic94—21no—
121Dic94—42no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47C22×D411yescharacteristic
128C2×D47—21no—
129C2×D47—21no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—88no—
134C2×D47C2×SD1612yes—
135C4×C47—21no—
136C4×C47—41no—
137C4×C47—41no—
138C4×C47C2×SD1612yes—
139C4×C47H(5,𝔽2)11yescharacteristic
140C4×C47H(5,𝔽2)11yescharacteristic
141Dic47—21no—
142Dic47—41no—
143Dic47—41no—
144Dic47C2×SD1612yes—
145Dic47AGL(1,ℤ/8)12yes—
146#3208—471nomaximal, Sylow
147C2×C47—82no—
148C2×C47#53511yescharacteristic
149C2×C47C22×SD1611yescharacteristic
150C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
151D47—22no—
152D47—82no—
153#533—471no—
154C2×#127—471no—
155#492—472no—
156#486—472no—
157#460—471no—
158#460—471no—
159#460—471no—
160#460D4711yescharacteristic, complemented
161#450—472no—
162#450—472no—
163#431—471no—
164C47#320811yescharacteristic, complemented, Sylow
165C22×D4—472no—
166C22×D4—941no—
167C22×D4—941no—
168C2×SD16—472no—
169C2×SD16—472no—
170C2×SD16—472no—
171C2×SD16C2×D4712yescomplemented
172C4⋊Q8—471no—
173C4⋊Q8—471no—
174#127—472no—
175#127—471no—
176#127—941no—
177#127—941no—
178#127C2×D4711yescharacteristic
179#125—941no—
180C22⋊Q8—471no—
181C22⋊Q8—471no—
182C22⋊Q8—941no—
183C4×Q8—471no—
184C4×Q8—941no—
185C4×Q8C2×D4711yescharacteristic, complemented
186#117—941no—
187C2×C42—471no—
188C4⋊C8—471no—
189C4⋊C8C2×D4711yescharacteristic, complemented
190#102—472no—
191#102—472no—
192#102—472no—
193#102C2×D4712yescomplemented
194C22⋊C8—472no—
195C4×C8—472no—
196C24—942no—
197C2×Q8—471no—
198C2×Q8—941no—
199C2×Q8C22×D4711yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—472no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—942no—
206C2×D4—941no—
207C2×D4—941no—
208C2×D4—1884no—
209C2×D4—1882no—
210C2×D4—1882no—
211C2×D4—1884no—
212C2×D4C22×D4712yes—
213C22×C4—471no—
214C22×C4—471no—
215C22×C4—471no—
216SD16—42no—
217SD16—1882no—
218SD16—1882no—
219SD16—1882no—
220C2×C8—472no—
221C2×C8C22×D4712yes—
222C4⋊C4—21no—
223C4⋊C4—471no—
224C4⋊C4—941no—
225C4⋊C4—941no—
226C4⋊C4—941no—
227C4⋊C4—941no—
228C4⋊C4—941no—
229C4⋊C4—941no—
230C4⋊C4C22×D4711yescharacteristic
231C22⋊C4—941no—
232C22⋊C4—941no—
233C42—21no—
234C42—471no—
235C42—471no—
236C42—471no—
237C42—941no—
238C42C22×D4711yescharacteristic
239C23—22no—
240C23—471no—
241C23—942no—
242C23—1884no—
243C23—1884no—
244C23—1884no—
245Q8—21no—
246Q8—21no—
247Q8—941no—
248Q8—941no—
249Q8—1882no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—942no—
255D4—942no—
256D4—1882no—
257D4—1884no—
258D4—1884no—
259D4—1884no—
260D4—1882no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—471no—
264C2×C4—471no—
265C2×C4—474no—
266C2×C4—471no—
267C2×C4—942no—
268C2×C4—941no—
269C2×C4—941no—
270C2×C4—941no—
271C2×C4—941no—
272C2×C4D4×D4711yescharacteristic
273C2×C4D4×D4711yescharacteristic
274C2×C4C23×D4711yescharacteristic
275C8—22no—
276C8—942no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—472no—
281C22—941no—
282C22—941no—
283C22—3768no—
284C22—1882no—
285C22—1882no—
286C22—1882no—
287C22C2×D4×D4711yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—472no—
292C4—472no—
293C4—941no—
294C4—1881no—
295C4—1881no—
296C4SD16×D4712yes—
297C4#1309406911yescharacteristic
298C4#1309407011yescharacteristic
299C2—82no—
300C2—942no—
301C2—3762no—
302C2#1568968911yescharacteristic
303C2C2×SD16×D4711yescharacteristic
304C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3208
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689494C2semidirect
4. #15689468C2semidirect
5. #15689324C2semidirect
6. #15689323C2semidirect
7. #15689320C2semidirect
8. #15689275C2semidirect
9. #15689272C2semidirect
10. #15689175C2semidirect
11. C47×#460C2semidirect
15. C2×#10625325C22semidirect
16. C2×#10625335C22semidirect
17. C2×#10625336C22semidirect
18. #13094023C22semidirect
19. #13094022C22semidirect
29. C4×Dic94C22semidirect
32. C4⋊(C47⋊C8)C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093944C22semidirect
37. C8×Dic47C22semidirect
38. C2×SD16×C47C22semidirect
40. C4×Q8×C47C22semidirect
41. C4⋊C8×C47C22semidirect
42. #102×C47C22semidirect
118. C4×D47SD16semidirect
160. #460D47semidirect
164. C47#3208semidirect
171. C2×SD16C2×D47semidirect
185. C4×Q8C2×D47semidirect
189. C4⋊C8C2×D47semidirect
193. #102C2×D47semidirect