Finite Group Databasebeta

← #20252668

Subgroups — #20252668

Order 6016.

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

normal subgroups only

This group has 752 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×#13094070C211yesmaximal, characteristic
2C2×#13094054C211yesmaximal, characteristic, complemented
3C22×#10625325C211yesmaximal, characteristic, complemented
4#15689699C211yesmaximal, characteristic, complemented
5#15689288C214yesmaximal, complemented
6#15689275C214yesmaximal, complemented
7#15689127C211yesmaximal, characteristic, complemented
8#15689089C211yesmaximal, characteristic, complemented
9C47×#416C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354C2212yes—
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C22×Dic94C2211yescharacteristic, complemented
16C22×D188—21no—
17C22×D188C2211yescharacteristic
18C2×D4×D47—22no—
19C2×D4×D47C2212yes—
20#13094054—24no—
21C2×#10625337C2212yescomplemented
22C2×#10625325—24no—
23C2×#10625325C2214yescomplemented
24C2×#10625335C2212yescomplemented
25C2×#10625329C2211yescharacteristic, complemented
26#13094024—21no—
27#13094012—21no—
28#13094008—22no—
29#13094004C2214yescomplemented
30#13093944C2214yescomplemented
31(C2×D47)⋊C8C2214yescomplemented
32C2×#41×C47C2211yescharacteristic
33C22×C8×C47C2211yescharacteristic, complemented
34#117×C47C2211yescharacteristic, complemented
35#103×C47C2212yescomplemented
36#102×C47C2212yescomplemented
37C23×D47—21no—
38C23×D47—22no—
39#41×C47—22no—
40#41×C47D414yes—
41C2×Q8×C47C2311yescharacteristic
42C2×D4×C47—21no—
43C2×D4×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—22no—
47C2×C22⋊D47D412yes—
48C22×Dic47—21no—
49#10625354—24no—
50#10625354—24no—
51D4×D47—216no—
52D4×D47—24no—
53D4×D47—24no—
54#10625350—28no—
55#10625350—22no—
56#10625350—22no—
57C2×D188—28no—
58C2×D188—22no—
59C2×D188—21no—
60C2×D188—22no—
61C2×D188D411yescharacteristic
62C2×D188D414yes—
63C2×D188C2312yes—
64C2×C4×D47—22no—
65C2×C4×D47C2312yes—
66C2×Dic94—22no—
67C2×Dic94—22no—
68C2×Dic94—21no—
69C2×Dic94D411yescharacteristic
70C2×Dic94C2312yes—
71C2×C8×C47—22no—
72C2×C8×C47C2312yes—
73C4⋊C4×C47C2312yes—
74C22⋊C4×C47—21no—
75C42×C47—21no—
76#10625337—24no—
77#10625335—24no—
78(C2×D47)⋊C4—24no—
79C4⋊Dic47—24no—
80#10625329—22no—
81C2×C47⋊C8C2312yes—
82#10625325—28no—
83C23×C47—21no—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—28no—
87C22×D47—24no—
88C22×D47—84no—
89C22×D47—82no—
90C22×D47C2×D412yes—
91Q8×C47—21no—
92Q8×C47C2×D412yes—
93D4×C47—24no—
94D4×C47—21no—
95D4×C47C2×D412yes—
96C2×C4×C47—21no—
97C2×C4×C47—24no—
98C2×C4×C47—22no—
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2411yescharacteristic
103C22⋊D47—28no—
104C22⋊D47—24no—
105C2×Dic47—22no—
106C2×Dic47—42no—
107C2×Dic47C2×D412yes—
108D188—28no—
109D188—22no—
110D188—24no—
111D188—22no—
112D188C2×D414yes—
113C4×D47—28no—
114C4×D47—22no—
115C4×D47—22no—
116Dic94—22no—
117Dic94—22no—
118Dic94—22no—
119Dic94—42no—
120C8×C47—22no—
121C47⋊C8—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—42no—
125C22×C47#12012yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—22no—
128C2×D47—24no—
129C2×D47—24no—
130C2×D47—44no—
131C2×D47—84no—
132C2×D47—88no—
133C4×C47—22no—
134C4×C47—42no—
135C4×C47#12012yes—
136C4×C47C22×D411yescharacteristic
137C4×C47C22×D411yescharacteristic
138Dic47—22no—
139Dic47—42no—
140#3009—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47—42no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#57712yes—
145D47—42no—
146D47—44no—
147C2×H(5,𝔽2)—471no—
148C2×#137—471no—
149C22×SD16—471no—
150#536—471no—
151#452—474no—
152#450—474no—
153#418—471no—
154#416D4711yescharacteristic, complemented
155#408—471no—
156C47#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—944no—
158H(5,𝔽2)—944no—
159C2×#41—471no—
160C2×#41—472no—
161C2×#41—941no—
162C2×#41C2×D4711yescharacteristic
163C22×Q8—471no—
164C22×D4—472no—
165C22×D4—471no—
166C22×D4—941no—
167C22×D4—942no—
168#137—944no—
169C2×Q16—472no—
170C2×SD16—472no—
171C2×SD16—474no—
172C2×SD16—944no—
173C2×M16—471no—
174C22×C8C2×D4711yescharacteristic, complemented
175C4⋊Q8—941no—
176#124—941no—
177#123—942no—
178C22⋊Q8—474no—
179#117C2×D4711yescharacteristic, complemented
180#103C2×D4712yescomplemented
181#102—474no—
182#102C2×D4712yescomplemented
183C22⋊C8—474no—
184C24—942no—
185C24—941no—
186#41—22no—
187#41—948no—
188#41—944no—
189#41—944no—
190#41—942no—
191#41—942no—
192#41D18814yes—
193C2×Q8—471no—
194C2×Q8—472no—
195C2×Q8—941no—
196C2×Q8—942no—
197C2×Q8—942no—
198C2×Q8C22×D4711yescharacteristic
199C2×D4—21no—
200C2×D4—472no—
201C2×D4—474no—
202C2×D4—471no—
203C2×D4—472no—
204C2×D4—942no—
205C2×D4—948no—
206C2×D4—942no—
207C2×D4—944no—
208C2×D4—9416no—
209C2×D4—944no—
210C2×D4—942no—
211C2×D4—941no—
212C2×D4C22×D4711yescharacteristic
213C22×C4—21no—
214C22×C4—472no—
215C22×C4—942no—
216C22×C4—941no—
217C22×C4C22×D4711yescharacteristic
218Q16—944no—
219SD16—948no—
220SD16—944no—
221M16—942no—
222C2×C8—22no—
223C2×C8—472no—
224C2×C8C22×D4712yes—
225C4⋊C4—944no—
226C4⋊C4C22×D4712yes—
227C22⋊C4—21no—
228C22⋊C4—944no—
229C42—21no—
230C23—21no—
231C23—472no—
232C23—948no—
233C23—944no—
234C23—942no—
235C23—3762no—
236C23—3764no—
237C23D4×D4711yescharacteristic
238Q8—21no—
239Q8—942no—
240Q8—942no—
241Q8—942no—
242Q8—1882no—
243Q8C2×D18812yes—
244D4—24no—
245D4—21no—
246D4—474no—
247D4—948no—
248D4—948no—
249D4—944no—
250D4—944no—
251D4—942no—
252D4—942no—
253D4C2×D18812yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—472no—
258C2×C4—948no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—1882no—
263C2×C4C2×D18812yes—
264C2×C4D4×D4711yescharacteristic
265C2×C4D4×D4712yes—
266C2×C4C23×D4711yescharacteristic
267C8—22no—
268C8—942no—
269C22—22no—
270C22—22no—
271C22—42no—
272C22—944no—
273C22—942no—
274C22—944no—
275C22—3764no—
276C22—3768no—
277C22—1884no—
278C22#1309399412yes—
279C22C2×D4×D4711yescharacteristic
280C4—22no—
281C4—42no—
282C4—942no—
283C4—1882no—
284C4#1309399412yes—
285C4C2×D4×D4711yescharacteristic
286C4C22×D18811yescharacteristic
287C2—22no—
288C2—42no—
289C2—1882no—
290C2—1884no—
291C2C2×#1309399411yescharacteristic
292C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#416C2
socleC22×C47C22×D4
hypercenter#416D47
hypocenterC47#3009
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#13094054C2semidirect
3. C22×#10625325C2semidirect
4. #15689699C2semidirect
5. #15689288C2semidirect
6. #15689275C2semidirect
7. #15689127C2semidirect
8. #15689089C2semidirect
9. C47×#416C2semidirect
15. C22×Dic94C22semidirect
21. C2×#10625337C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625335C22semidirect
25. C2×#10625329C22semidirect
29. #13094004C22semidirect
30. #13093944C22semidirect
31. (C2×D47)⋊C8C22semidirect
33. C22×C8×C47C22semidirect
34. #117×C47C22semidirect
35. #103×C47C22semidirect
36. #102×C47C22semidirect
154. #416D47semidirect
156. C47#3009semidirect
174. C22×C8C2×D47semidirect
179. #117C2×D47semidirect
180. #103C2×D47semidirect
182. #102C2×D47semidirect