Finite Group Databasebeta

← #20255174

Subgroups — #20255174

Order 6016.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689931C212yesmaximal, complemented
2#15689925C211yesmaximal, characteristic, complemented
3#15689508C211yesmaximal, characteristic, complemented
4#15689395C211yesmaximal, characteristic, complemented
5#15689393C211yesmaximal, characteristic, complemented
6#15689388C212yesmaximal, complemented
7#15689299C212yesmaximal, complemented
8#15689296C212yesmaximal, complemented
9#15689240C211yesmaximal, characteristic, complemented
10#15689238C211yesmaximal, characteristic, complemented
11C47×#578C211yesmaximal, characteristic, complemented
12#13094070C2212yes—
13#13094055—22no—
14#13094055C2212yes—
15#13094051—22no—
16#13094049—22no—
17#13094049C2212yes—
18#13094049C2212yescomplemented
19#13094047—21no—
20#13094044—22no—
21#13094044C2211yescharacteristic
22C2×#10625336—22no—
23C2×#10625336C2212yescomplemented
24C2×D376C2211yescharacteristic
25D8×D47—21no—
26#13094031C2212yescomplemented
27#13094030C2211yescharacteristic
28#13094013C2212yescomplemented
29#13093960C2211yescharacteristic, complemented
30#13093959C2211yescharacteristic, complemented
31#13093951C2211yescharacteristic, complemented
32#13093951C2212yescomplemented
33#13093950C2211yescharacteristic
34#13093943C2212yescomplemented
35#13093940C2212yescomplemented
36C8×Dic47C2211yescharacteristic, complemented
372−1+4×C47C2212yescomplemented
38#137×C47—22no—
39#137×C47C2212yescomplemented
40#135×C47—21no—
41#135×C47C2211yescharacteristic
42C2×Q16×C47—21no—
43C2×Q16×C47C2211yescharacteristic, complemented
44#131×C47C2211yescharacteristic, complemented
45#41×C47—22no—
46#41×C47—22no—
47#41×C47—42no—
48#41×C47C2311yescharacteristic
49#41×C47C2312yes—
50C2×Q8×C47—22no—
51C2×Q8×C47—22no—
52C2×Q8×C47C2312yes—
53#10625354—22no—
54D4×D47—22no—
55D4×D47—42no—
56#10625350—22no—
57#10625350C2311yescharacteristic
58C2×D188—22no—
59C2×D188C2312yes—
60Q16×C47—22no—
61Q16×C47—21no—
62Q16×C47—21no—
63Q16×C47D411yescharacteristic
64SD16×C47—22no—
65SD16×C47D412yes—
66D8×C47D411yescharacteristic
67M16×C47—21no—
68M16×C47C2311yescharacteristic
69C2×C8×C47—21no—
70C2×C8×C47C2311yescharacteristic
71#10625337—22no—
72#10625337D411yescharacteristic
73#10625336—22no—
74#10625336—22no—
75#10625336—22no—
76#10625336—22no—
77#10625336—22no—
78#10625336D411yescharacteristic
79#10625335D411yescharacteristic
80#10625334—22no—
81#10625334—22no—
82#10625334D411yescharacteristic
83(C2×D47)⋊C4—42no—
84C4×Dic47C2311yescharacteristic
85#10625329—22no—
86#10625329C2312yes—
87#10625329C2311yescharacteristic
88C2×C47⋊C8—22no—
89C2×C47⋊C8C2311yescharacteristic
90D376—21no—
91D376—21no—
92#10625324—21no—
93C8×D47—21no—
94C22×D47—22no—
95C22×D47—42no—
96Q8×C47—22no—
97Q8×C47—22no—
98Q8×C47—42no—
99Q8×C47C2×D411yescharacteristic
100Q8×C47C2×D412yes—
101D4×C47—22no—
102D4×C47—21no—
103D4×C47—42no—
104D4×C47C2×D411yescharacteristic
105D4×C47C2×D412yes—
106C2×C4×C47—22no—
107C2×C4×C47—21no—
108C2×C4×C47—22no—
109C2×C4×C47—42no—
110C2×C4×C47—42no—
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—21no—
113C22⋊D47—42no—
114C2×Dic47—21no—
115D188—22no—
116D188—22no—
117D188—42no—
118D188C2×D411yescharacteristic
119C4×D47—21no—
120C4×D47—42no—
121Dic94C2×D411yescharacteristic
122C8×C47—21no—
123C8×C47C2×D411yescharacteristic
124C8×C47C2×D411yescharacteristic
125C47⋊C8—21no—
126C47⋊C8—22no—
127C47⋊C8C2×D411yescharacteristic
128C47⋊C8C2×D411yescharacteristic
129C22×C47—22no—
130C22×C47—21no—
131C22×C47H(5,𝔽2)11yescharacteristic
132C2×D47—21no—
133C2×D47—42no—
134C2×D47—82no—
135C2×D47—162no—
136C4×C47—22no—
137C4×C47—21no—
138C4×C47—42no—
139C4×C47C22×D411yescharacteristic
140C4×C47C22×D411yescharacteristic
141Dic47—21no—
142Dic47—41no—
143#3290—471nomaximal, Sylow
144C2×C47—21no—
145C2×C47—42no—
146C2×C47—41no—
147C2×C47D4211yescharacteristic
148D47—41no—
149D47—82no—
150#578D4711yescharacteristic, complemented
151#577—472no—
152#576—471no—
153#495—471no—
154#473—471no—
155#472—471no—
156#471—472no—
157#455—472no—
158#454—472no—
159#443—471no—
160#443—471no—
161C47#329011yescharacteristic, complemented, Sylow
1622−1+4C2×D4712yescomplemented
163H(5,𝔽2)—472no—
164#137—22no—
165#137—472no—
166#137—942no—
167#137C2×D4712yescomplemented
168AGL(1,ℤ/8)—472no—
169AGL(1,ℤ/8)—472no—
170AGL(1,ℤ/8)—942no—
171AGL(1,ℤ/8)—942no—
172#135—21no—
173#135—471no—
174#135—942no—
175#135—941no—
176#135C2×D4711yescharacteristic
177C2×Q16—21no—
178C2×Q16C2×D4711yescharacteristic, complemented
179C2×SD16—472no—
180C2×SD16—942no—
181C2×D8—471no—
182C2×D8—941no—
183#131—472no—
184#131—471no—
185#131C2×D4711yescharacteristic, complemented
186#124—472no—
187#108—471no—
188#108—471no—
189#104—471no—
190#104—472no—
191#104—471no—
192#101—472no—
193#100—472no—
194C4×C8—471no—
195#41—22no—
196#41—22no—
197#41—42no—
198#41—471no—
199#41—942no—
200#41—942no—
201#41C22×D4711yescharacteristic
202#41C22×D4712yes—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8C22×D4712yes—
206C2×D4—472no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—1882no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—471no—
214Q16—942no—
215Q16C22⋊D4711yescharacteristic
216SD16—22no—
217SD16—471no—
218SD16—471no—
219SD16—942no—
220SD16—942no—
221SD16—942no—
222SD16—942no—
223SD16—942no—
224SD16C22⋊D4712yes—
225D8—471no—
226D8—942no—
227D8—942no—
228D8—941no—
229D8—941no—
230D8C22⋊D4711yescharacteristic
231M16—21no—
232M16—472no—
233M16—471no—
234M16—942no—
235M16—941no—
236M16C22×D4711yescharacteristic
237C2×C8—21no—
238C2×C8—471no—
239C2×C8—942no—
240C2×C8—941no—
241C2×C8C22×D4711yescharacteristic
242C22⋊C4—1882no—
243C42—471no—
244C23—942no—
245C23—1882no—
246Q8—22no—
247Q8—22no—
248Q8—42no—
249Q8—471no—
250Q8D4×D4711yescharacteristic
251Q8C2×C22⋊D4712yes—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—471no—
256D4—941no—
257D4—942no—
258D4—942no—
259D4—1882no—
260D4—1882no—
261D4D4×D4711yescharacteristic
262D4C2×C22⋊D4712yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—941no—
269C2×C4—941no—
270C2×C4—1882no—
271C2×C4C23×D4711yescharacteristic
272C8—21no—
273C8—471no—
274C8—471no—
275C8—942no—
276C8—941no—
277C8C2×C22⋊D4711yescharacteristic
278C8C2×C22⋊D4711yescharacteristic
279C22—21no—
280C22—22no—
281C22—941no—
282C22—3762no—
283C22—1882no—
284C22—7522no—
285C22#1309406911yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—941no—
290C4—1881no—
291C4C2×D4×D4711yescharacteristic
292C4C22×C22⋊D4711yescharacteristic
293C2—21no—
294C2—42no—
295C2—41no—
296C2—3762no—
297C2—1881no—
298C2D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#578C2
socleC2×C47D42
hypercenter#578D47
hypocenterC47#3290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #15689931C2semidirect
2. #15689925C2semidirect
3. #15689508C2semidirect
4. #15689395C2semidirect
5. #15689393C2semidirect
6. #15689388C2semidirect
7. #15689299C2semidirect
8. #15689296C2semidirect
9. #15689240C2semidirect
10. #15689238C2semidirect
11. C47×#578C2semidirect
18. #13094049C22semidirect
23. C2×#10625336C22semidirect
26. #13094031C22semidirect
28. #13094013C22semidirect
29. #13093960C22semidirect
30. #13093959C22semidirect
31. #13093951C22semidirect
32. #13093951C22semidirect
34. #13093943C22semidirect
35. #13093940C22semidirect
36. C8×Dic47C22semidirect
37. 2−1+4×C47C22semidirect
39. #137×C47C22semidirect
43. C2×Q16×C47C22semidirect
44. #131×C47C22semidirect
150. #578D47semidirect
161. C47#3290semidirect
162. 2−1+4C2×D47semidirect
167. #137C2×D47semidirect
178. C2×Q16C2×D47semidirect
185. #131C2×D47semidirect