Finite Group Databasebeta

← #20253855

Subgroups — #20253855

Order 6016.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094055C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic, complemented
3C2×#13094049C211yesmaximal, characteristic, complemented
4#15689669C211yesmaximal, characteristic, complemented
5C2×#13094013C211yesmaximal, characteristic, complemented
6#15689516C212yesmaximal, complemented
7#15689509C212yesmaximal, complemented
8#15689508C212yesmaximal, complemented
9#15689504C212yesmaximal, complemented
10M16×Dic47C211yesmaximal, characteristic, complemented
11C2×#137×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×D188C2211yescharacteristic
14#13094055—24no—
15#13094052—24no—
16#13094049—24no—
17C2×#10625337C2212yescomplemented
18C2×#10625325C2212yes—
19C2×#10625336C2212yes—
20C2×#10625336C2212yescomplemented
21C2×D376C2212yes—
22C2×#10625334C2212yes—
23C2×#10625329C2211yescharacteristic
24#13094022C2211yescharacteristic, complemented
25#13094020C2211yescharacteristic, complemented
26#13094013—22no—
27#13094013C2212yes—
28#13094013C2212yes—
29#13094013C2211yescharacteristic, complemented
30#13094011C2211yescharacteristic, complemented
31#13093996—22no—
32C4×C22⋊D47—22no—
33C2×(C2×D47)⋊C4—22no—
34C2×C4×Dic47C2211yescharacteristic
35#13093934C2212yescomplemented
36C8×Dic47C2212yescomplemented
37C2×#41×C47C2211yescharacteristic
38C22×Q8×C47C2211yescharacteristic
39#137×C47—24no—
40C2×Q16×C47C2212yescomplemented
41C2×SD16×C47C2212yescomplemented
42C2×M16×C47C2211yescharacteristic
43C23×D47—21no—
44#41×C47—22no—
45#41×C47—22no—
46C2×Q8×C47—21no—
47C2×Q8×C47—22no—
48C2×Q8×C47—22no—
49C2×Q8×C47C2312yes—
50C2×Q8×C47C2311yescharacteristic
51C2×D4×C47—21no—
52C2×D4×C47C2311yescharacteristic
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—21no—
57C2×C22⋊D47—22no—
58C22×Dic47D412yes—
59#10625350—22no—
60#10625350—22no—
61C2×D188—22no—
62C2×D188—22no—
63C2×D188—21no—
64C2×D188C2312yes—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×Dic94C2311yescharacteristic
68Q16×C47—24no—
69SD16×C47—24no—
70M16×C47D414yescomplemented
71C2×C8×C47C2312yes—
72C22⋊Dic47—22no—
73#10625337—24no—
74#10625336—24no—
75#10625336—24no—
76#10625334—24no—
77(C2×D47)⋊C4—24no—
78(C2×D47)⋊C4—24no—
79(C2×D47)⋊C4—22no—
80Dic47⋊C4—22no—
81C4×Dic47D412yes—
82C4×Dic47C2311yescharacteristic
83C4×Dic47C2311yescharacteristic
84#10625329D414yescomplemented
85C2×C47⋊C8C2312yes—
86D376—24no—
87#10625325—24no—
88C23×C47—21no—
89C23×C47C2×D411yescharacteristic
90C22×D47—22no—
91C22×D47—21no—
92C22×D47—44no—
93C22×D47—42no—
94Q8×C47—21no—
95Q8×C47—22no—
96Q8×C47—22no—
97Q8×C47—21no—
98Q8×C47—42no—
99D4×C47—21no—
100D4×C47—21no—
101D4×C47—42no—
102C2×C4×C47—21no—
103C2×C4×C47—22no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2×D412yes—
108C2×C4×C47C2×D412yes—
109C2×C4×C47C2411yescharacteristic
110C22⋊D47—44no—
111C22⋊D47—42no—
112C2×Dic47—21no—
113C2×Dic47—42no—
114C2×Dic47C2×D412yes—
115C2×Dic47C2×D412yes—
116D188—22no—
117D188—21no—
118D188—22no—
119D188—21no—
120D188—42no—
121C4×D47—42no—
122Dic94—21no—
123Dic94—21no—
124C8×C47C2×D414yes—
125C47⋊C8C2×D414yes—
126C22×C47—22no—
127C22×C47—41no—
128C22×C47—42no—
129C22×C47#12712yes—
130C22×C47C22×D411yescharacteristic
131C2×D47—41no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—44no—
135C2×D47—84no—
136C4×C47—41no—
137C4×C47—42no—
138C4×C47#12712yes—
139C4×C47C22×D411yescharacteristic
140C4×C47C22×D411yescharacteristic
141Dic47—22no—
142Dic47—22no—
143Dic47—41no—
144#3153—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—81no—
147C2×C47C2×#12711yescharacteristic
148C2×C47#57512yes—
149D47—81no—
150D47—82no—
151C2×#137—471no—
152C2×#137D4711yescharacteristic, complemented
153C2×AGL(1,ℤ/8)—471no—
154C2×AGL(1,ℤ/8)—471no—
155#532—471no—
156C2×#124—471no—
157#497—472no—
158#496—472no—
159#495—472no—
160#495—472no—
161C4×M16—471no—
162C47#315311yescharacteristic, complemented, Sylow
163C2×#41—471no—
164C2×#41C2×D4711yescharacteristic
165C22×Q8C2×D4711yescharacteristic
166C22×D4—471no—
167#137—24no—
168#137—944no—
169AGL(1,ℤ/8)—944no—
170AGL(1,ℤ/8)—944no—
171C2×Q16—472no—
172C2×Q16C2×D4712yescomplemented
173C2×SD16—472no—
174C2×SD16—472no—
175C2×SD16—472no—
176C2×SD16C2×D4712yescomplemented
177C2×D8—472no—
178C2×D8—472no—
179C2×M16—471no—
180C2×M16C2×D4711yescharacteristic
181C4⋊Q8—471no—
182#127—471no—
183#124—472no—
184#124—472no—
185#124—471no—
186#124—471no—
187#124—942no—
188#121—942no—
189C4×D4—942no—
190C2×C22⋊C4—942no—
191C2×C42—471no—
192#97—472no—
193C4×C8—472no—
194C24—941no—
195#41—22no—
196#41—22no—
197#41—942no—
198#41—942no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—471no—
203C2×Q8C22×D4712yes—
204C2×Q8C22×D4711yescharacteristic
205C2×D4—21no—
206C2×D4—472no—
207C2×D4—471no—
208C2×D4—942no—
209C2×D4—941no—
210C2×D4—942no—
211C2×D4—941no—
212C2×D4—942no—
213C2×D4C22×D4711yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—472no—
217C22×C4—941no—
218C22×C4C22×D4711yescharacteristic
219Q16—24no—
220Q16—944no—
221SD16—24no—
222SD16—944no—
223SD16—944no—
224SD16—944no—
225D8—944no—
226D8—944no—
227M16—474no—
228M16C22⋊D4714yescomplemented
229C2×C8—472no—
230C2×C8C22×D4712yes—
231C4⋊C4—942no—
232C22⋊C4—944no—
233C22⋊C4—944no—
234C22⋊C4—942no—
235C22⋊C4—942no—
236C42—472no—
237C42—471no—
238C42—471no—
239C23—21no—
240C23—942no—
241C23—941no—
242C23—1884no—
243C23—1882no—
244C23D4×D4711yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—941no—
251Q8—941no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—942no—
256D4—941no—
257D4—941no—
258D4—942no—
259D4—1884no—
260D4—1882no—
261D4—1882no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—472no—
267C2×C4—472no—
268C2×C4—941no—
269C2×C4—1882no—
270C2×C4—1882no—
271C2×C4D4×D4711yescharacteristic
272C2×C4D4×D4712yes—
273C2×C4C2×C22⋊D4712yes—
274C2×C4C23×D4711yescharacteristic
275C8—474no—
276C8C2×C22⋊D4714yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—3764no—
281C22—1881no—
282C22—1882no—
283C22—1882no—
284C22—1884no—
285C22#1309402012yes—
286C22C2×D4×D4711yescharacteristic
287C4—41no—
288C4—42no—
289C4—942no—
290C4—942no—
291C4—1881no—
292C4#1309402012yes—
293C4C2×D4×D4711yescharacteristic
294C4C22×C22⋊D4711yescharacteristic
295C2—22no—
296C2—81no—
297C2—3762no—
298C2—3761no—
299C2C2×#1309402011yescharacteristic
300C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3153
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C2×#13094052C2semidirect
3. C2×#13094049C2semidirect
4. #15689669C2semidirect
5. C2×#13094013C2semidirect
6. #15689516C2semidirect
7. #15689509C2semidirect
8. #15689508C2semidirect
9. #15689504C2semidirect
10. M16×Dic47C2semidirect
11. C2×#137×C47C2semidirect
17. C2×#10625337C22semidirect
20. C2×#10625336C22semidirect
24. #13094022C22semidirect
25. #13094020C22semidirect
29. #13094013C22semidirect
30. #13094011C22semidirect
35. #13093934C22semidirect
36. C8×Dic47C22semidirect
40. C2×Q16×C47C22semidirect
41. C2×SD16×C47C22semidirect
70. M16×C47D4semidirect
84. #10625329D4semidirect
152. C2×#137D47semidirect
162. C47#3153semidirect
172. C2×Q16C2×D47semidirect
176. C2×SD16C2×D47semidirect
228. M16C22⋊D47semidirect