Finite Group Databasebeta

← #20253865

Subgroups — #20253865

Order 6016.

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

normal subgroups only

This group has 564 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×#13094054C211yesmaximal, characteristic, complemented
2C2×#13094049C211yesmaximal, characteristic, complemented
3C22×#10625325C211yesmaximal, characteristic, complemented
4#15689694C211yesmaximal, characteristic, complemented
5#15689687C211yesmaximal, characteristic, complemented
6#15689516C212yesmaximal, complemented
7#15689511C212yesmaximal, complemented
8#15689504C212yesmaximal, complemented
9#15689494C212yesmaximal, complemented
10#15689078C211yesmaximal, characteristic, complemented
11C2×#135×C47C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14#13094054—24no—
15#13094049—24no—
16C2×#10625337C2212yescomplemented
17C2×#10625325—24no—
18C2×#10625325C2212yes—
19C2×#10625325C2212yes—
20C2×#10625335C2212yescomplemented
21C2×#10625336C2212yes—
22C2×#10625334C2212yes—
23C2×#10625329C2211yescharacteristic
24#13094022C2212yescomplemented
25#13094020C2212yes—
26#13094013C2212yes—
27#13094011C2212yescomplemented
28#13094005—22no—
29#13094003—22no—
30#13093998—22no—
31#13093992—22no—
32#13093983C2211yescharacteristic
33#13093934C2212yescomplemented
34C8×Dic47C2212yescomplemented
35C2×#41×C47C2211yescharacteristic
36C2×#41×C47C2211yescharacteristic
37#135×C47—24no—
38C2×Q16×C47C2211yescharacteristic, complemented
39C2×SD16×C47C2211yescharacteristic, complemented
40C2×SD16×C47C2211yescharacteristic, complemented
41C2×D8×C47C2211yescharacteristic, complemented
42C22×C8×C47C2211yescharacteristic
43C23×D47—21no—
44#41×C47—22no—
45#41×C47—22no—
46#41×C47—22no—
47#41×C47—22no—
48C2×Q8×C47C2311yescharacteristic
49C2×Q8×C47C2311yescharacteristic
50C2×D4×C47—21no—
51C2×D4×C47—21no—
52C2×D4×C47C2311yescharacteristic
53C2×D4×C47C2311yescharacteristic
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47C2311yescharacteristic
57C2×C22⋊D47—24no—
58C22×Dic47—21no—
59C2×D188—22no—
60C2×D188—22no—
61C2×D188—21no—
62C2×D188C2312yes—
63C2×Dic94—22no—
64C2×Dic94—22no—
65C2×Dic94—21no—
66C2×Dic94C2312yes—
67Q16×C47—22no—
68SD16×C47—22no—
69SD16×C47—22no—
70D8×C47—22no—
71C2×C8×C47D414yescomplemented
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C22⋊Dic47—24no—
75C22⋊Dic47D412yes—
76#10625337—24no—
77#10625336—24no—
78#10625335—24no—
79#10625334—24no—
80(C2×D47)⋊C4—24no—
81C4⋊Dic47D412yes—
82Dic47⋊C4—24no—
83C4×Dic47C2312yes—
84#10625329D414yescomplemented
85C2×C47⋊C8C2312yes—
86#10625325—24no—
87#10625325—24no—
88C23×C47—21no—
89C23×C47—21no—
90C23×C47C2×D411yescharacteristic
91C22×D47—22no—
92C22×D47—42no—
93C22×D47—82no—
94Q8×C47—21no—
95Q8×C47—21no—
96Q8×C47—21no—
97Q8×C47—21no—
98D4×C47—21no—
99D4×C47—21no—
100D4×C47—21no—
101D4×C47—21no—
102D4×C47—42no—
103D4×C47—42no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—42no—
107C2×C4×C47—42no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D412yes—
110C2×C4×C47C2×D412yes—
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—84no—
113C2×Dic47—22no—
114C2×Dic47—42no—
115C2×Dic47C2×D414yes—
116D188—22no—
117D188—22no—
118D188—42no—
119Dic94—22no—
120Dic94—22no—
121Dic94—42no—
122C8×C47C2×D412yes—
123C8×C47C2×D412yes—
124C47⋊C8C2×D414yes—
125C22×C47—22no—
126C22×C47—41no—
127C22×C47—41no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47#12712yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—42no—
133C2×D47—44no—
134C2×D47—84no—
135C4×C47—41no—
136C4×C47—41no—
137C4×C47#12712yes—
138C4×C47C22×D411yescharacteristic
139C4×C47C22×D411yescharacteristic
140Dic47—24no—
141Dic47—42no—
142#3154—471nomaximal, Sylow
143C2×C47—22no—
144C2×C47—81no—
145C2×C47—81no—
146C2×C47C2×#12711yescharacteristic
147C2×C47#57712yes—
148D47—82no—
149C2×#137—471no—
150C2×AGL(1,ℤ/8)—471no—
151C2×#135D4711yescharacteristic, complemented
152C22×SD16—471no—
153#536—471no—
154#535—471no—
155#497—472no—
156#496—472no—
157#495—472no—
158#492—472no—
159#405—471no—
160C47#315411yescharacteristic, complemented, Sylow
161C2×#41C2×D4711yescharacteristic
162C2×#41C2×D4711yescharacteristic
163C22×Q8—471no—
164C22×D4—471no—
165#137—944no—
166AGL(1,ℤ/8)—944no—
167#135—24no—
168C2×Q16—472no—
169C2×Q16C2×D4711yescharacteristic, complemented
170C2×SD16—472no—
171C2×SD16—472no—
172C2×SD16—472no—
173C2×SD16—472no—
174C2×SD16—944no—
175C2×SD16C2×D4711yescharacteristic, complemented
176C2×SD16C2×D4711yescharacteristic, complemented
177C2×D8—472no—
178C2×D8C2×D4711yescharacteristic, complemented
179C2×M16—471no—
180C22×C8C2×D4711yescharacteristic
181C4⋊Q8—472no—
182#127—472no—
183#124—472no—
184#124—472no—
185#123—942no—
186C22⋊Q8—942no—
187#121—942no—
188#120—942no—
189#117—471no—
190#97—472no—
191C4×C8—472no—
192C24—941no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—472no—
198C2×Q8—941no—
199C2×Q8—942no—
200C2×Q8—942no—
201C2×Q8C22×D4711yescharacteristic
202C2×Q8C22×D4711yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—472no—
206C2×D4—944no—
207C2×D4—942no—
208C2×D4—941no—
209C2×D4—942no—
210C2×D4C22×D4711yescharacteristic
211C2×D4C22×D4711yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—941no—
215C22×C4C22×D4711yescharacteristic
216Q16—22no—
217Q16—944no—
218SD16—22no—
219SD16—22no—
220SD16—944no—
221SD16—944no—
222SD16—944no—
223SD16—944no—
224D8—22no—
225D8—944no—
226M16—474no—
227C2×C8—472no—
228C2×C8C22⋊D4714yescomplemented
229C2×C8C22×D4711yescharacteristic
230C2×C8C22×D4711yescharacteristic
231C4⋊C4—472no—
232C4⋊C4—944no—
233C22⋊C4—472no—
234C22⋊C4—944no—
235C22⋊C4—944no—
236C42—472no—
237C23—21no—
238C23—21no—
239C23—942no—
240C23—3762no—
241C23—1882no—
242C23D4×D4711yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—942no—
248Q8—942no—
249Q8—1882no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—942no—
257D4—942no—
258D4—3764no—
259D4—1882no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—474no—
265C2×C4—942no—
266C2×C4—1882no—
267C2×C4D4×D4711yescharacteristic
268C2×C4D4×D4712yes—
269C2×C4C2×C22⋊D4712yes—
270C2×C4C23×D4711yescharacteristic
271C8—474no—
272C8C2×C22⋊D4712yes—
273C8C2×C22⋊D4712yes—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—3764no—
280C22—1882no—
281C22—1884no—
282C22#1309402012yes—
283C22C2×D4×D4711yescharacteristic
284C4—41no—
285C4—41no—
286C4—944no—
287C4—1882no—
288C4#1309402012yes—
289C4C2×D4×D4711yescharacteristic
290C4C22×C22⋊D4711yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—3762no—
295C2C2×#1309402011yescharacteristic
296C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3154
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C2×#13094049C2semidirect
3. C22×#10625325C2semidirect
4. #15689694C2semidirect
5. #15689687C2semidirect
6. #15689516C2semidirect
7. #15689511C2semidirect
8. #15689504C2semidirect
9. #15689494C2semidirect
10. #15689078C2semidirect
11. C2×#135×C47C2semidirect
16. C2×#10625337C22semidirect
20. C2×#10625335C22semidirect
24. #13094022C22semidirect
27. #13094011C22semidirect
33. #13093934C22semidirect
34. C8×Dic47C22semidirect
38. C2×Q16×C47C22semidirect
39. C2×SD16×C47C22semidirect
40. C2×SD16×C47C22semidirect
41. C2×D8×C47C22semidirect
71. C2×C8×C47D4semidirect
84. #10625329D4semidirect
151. C2×#135D47semidirect
160. C47#3154semidirect
169. C2×Q16C2×D47semidirect
175. C2×SD16C2×D47semidirect
176. C2×SD16C2×D47semidirect
178. C2×D8C2×D47semidirect
228. C2×C8C22⋊D47semidirect