Finite Group Databasebeta

← #20252667

Subgroups — #20252667

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×#13094057C211yesmaximal, characteristic, complemented
3C22×#10625325C211yesmaximal, characteristic, complemented
4#15689694C211yesmaximal, characteristic, complemented
5#15689287C214yesmaximal, complemented
6#15689276C214yesmaximal, complemented
7#15689129C211yesmaximal, characteristic, complemented
8#15689120C211yesmaximal, characteristic, complemented
9C47×#408C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354—21no—
13C2×#10625350C2212yes—
14C2×#10625350C2211yescharacteristic
15C22×Dic94C2211yescharacteristic, complemented
16C22×D188C2212yes—
17C22×D188C2211yescharacteristic
18C2×D4×D47—22no—
19C2×D4×D47—21no—
20#13094057—24no—
21C2×Dic188C2212yescomplemented
22C2×#10625325—24no—
23C2×#10625325C2212yescomplemented
24C2×#10625325C2214yescomplemented
25#13094022—21no—
26#13094011—21no—
27#13094005—22no—
28#13094003C2214yescomplemented
29#13093983C2211yescharacteristic, complemented
30#13093949C2212yescomplemented
31#13093946C2212yescomplemented
32#13093946C2214yescomplemented
33C2×#41×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic, complemented
35C22×C8×C47C2211yescharacteristic, complemented
36C22⋊C8×C47C2214yescomplemented
37C23×D47—22no—
38C23×D47—21no—
39#41×C47—22no—
40#41×C47—22no—
41C2×Q8×C47D411yescharacteristic
42C2×D4×C47D412yes—
43C2×D4×C47D411yescharacteristic
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—22no—
47C2×C22⋊D47—21no—
48C22×Dic47—21no—
49#10625354—28no—
50D4×D47—216no—
51D4×D47—28no—
52#10625350—22no—
53#10625350—24no—
54#10625350—24no—
55#10625350D414yes—
56C2×D188—22no—
57C2×D188—21no—
58C2×D188—22no—
59C2×D188—24no—
60C2×D188—24no—
61C2×D188D414yes—
62C2×D188C2311yescharacteristic
63C2×D188C2312yes—
64C2×C4×D47—22no—
65C2×C4×D47—21no—
66C2×Dic94—22no—
67C2×Dic94—22no—
68C2×Dic94—21no—
69C2×Dic94C2312yes—
70C2×Dic94C2311yescharacteristic
71M16×C47—22no—
72C2×C8×C47—22no—
73C2×C8×C47C2312yes—
74C2×C8×C47C2312yes—
75C22⋊Dic47—21no—
76C22⋊Dic47—24no—
77C4⋊Dic47C2312yes—
78Dic47⋊C4—24no—
79C4×Dic47—21no—
80Dic188—24no—
81#10625325—28no—
82#10625325—24no—
83C23×C47C2×D412yes—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—21no—
87C22×D47—28no—
88C22×D47—24no—
89C22×D47—82no—
90C22×D47—84no—
91Q8×C47—22no—
92D4×C47—24no—
93D4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D412yes—
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—28no—
102C22⋊D47—24no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—42no—
107D188—28no—
108D188—24no—
109D188—21no—
110D188—22no—
111D188C2×D412yes—
112D188C2×D414yes—
113C4×D47—28no—
114C4×D47—24no—
115Dic94—21no—
116Dic94—22no—
117Dic94—22no—
118Dic94—42no—
119Dic94C2×D412yes—
120C8×C47—22no—
121C8×C47—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—24no—
125C22×C47#12012yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—24no—
128C2×D47—22no—
129C2×D47—44no—
130C2×D47—42no—
131C2×D47—84no—
132C2×D47—88no—
133C4×C47—22no—
134C4×C47#12012yes—
135C4×C47C22×D411yescharacteristic
136C4×C47C22×D411yescharacteristic
137Dic47—22no—
138Dic47—42no—
139Dic47—42no—
140#3009—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47—42no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#57712yes—
145D47—44no—
146D47—42no—
147C2×H(5,𝔽2)—471no—
148C2×#137—471no—
149C22×SD16—471no—
150#536—471no—
151#452—474no—
152#450—474no—
153#418—471no—
154#416—471no—
155#408D4711yescharacteristic, complemented
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—471no—
165C22×D4—472no—
166C22×D4—942no—
167C22×D4—941no—
168#137—944no—
169C2×Q16—472no—
170C2×SD16—474no—
171C2×SD16—472no—
172C2×SD16—944no—
173C2×M16C2×D4711yescharacteristic, complemented
174C22×C8C2×D4711yescharacteristic, complemented
175C4⋊Q8—941no—
176#124—941no—
177#123—942no—
178C22⋊Q8—474no—
179#117—471no—
180#103—472no—
181#102—472no—
182#102—474no—
183C22⋊C8C2×D4714yescomplemented
184C24—942no—
185C24—941no—
186#41—22no—
187#41—22no—
188#41—474no—
189#41—944no—
190#41—944no—
191#41—948no—
192#41—942no—
193C2×Q8—471no—
194C2×Q8—472no—
195C2×Q8—941no—
196C2×Q8—942no—
197C2×Q8—942no—
198C2×Q8D18811yescharacteristic
199C2×D4—474no—
200C2×D4—472no—
201C2×D4—471no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—9416no—
205C2×D4—948no—
206C2×D4—942no—
207C2×D4—941no—
208C2×D4—942no—
209C2×D4—941no—
210C2×D4—942no—
211C2×D4D18812yes—
212C2×D4D18811yescharacteristic
213C22×C4—942no—
214C22×C4—941no—
215C22×C4—941no—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218Q16—944no—
219SD16—948no—
220SD16—944no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D4712yes—
224C2×C8C22×D4712yes—
225C4⋊C4—472no—
226C4⋊C4—944no—
227C22⋊C4—941no—
228C22⋊C4—944no—
229C42—941no—
230C23—948no—
231C23—944no—
232C23—942no—
233C23—941no—
234C23—3762no—
235C23—3764no—
236C23C2×D18812yes—
237C23C2×D18811yescharacteristic
238Q8—22no—
239Q8—472no—
240Q8—941no—
241Q8—942no—
242Q8—942no—
243Q8—1882no—
244D4—24no—
245D4—22no—
246D4—474no—
247D4—472no—
248D4—948no—
249D4—948no—
250D4—944no—
251D4—944no—
252D4—941no—
253D4—942no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—948no—
257C2×C4—941no—
258C2×C4—944no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—1882no—
262C2×C4C2×D18812yes—
263C2×C4C2×D18811yescharacteristic
264C2×C4D4×D4712yes—
265C2×C4D4×D4712yes—
266C2×C4C23×D4711yescharacteristic
267C8—22no—
268C8—22no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—944no—
273C22—942no—
274C22—3764no—
275C22—3768no—
276C22—1884no—
277C22—1882no—
278C22#1309399412yes—
279C22C22×D18811yescharacteristic
280C4—22no—
281C4—942no—
282C4—1882no—
283C4—1882no—
284C4#1309399412yes—
285C4C2×D4×D4711yescharacteristic
286C4C2×D4×D4711yescharacteristic
287C2—22no—
288C2—42no—
289C2—1884no—
290C2—1882no—
291C2C2×#1309399411yescharacteristic
292C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3009
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#13094057C2semidirect
3. C22×#10625325C2semidirect
4. #15689694C2semidirect
5. #15689287C2semidirect
6. #15689276C2semidirect
7. #15689129C2semidirect
8. #15689120C2semidirect
9. C47×#408C2semidirect
15. C22×Dic94C22semidirect
21. C2×Dic188C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625325C22semidirect
28. #13094003C22semidirect
29. #13093983C22semidirect
30. #13093949C22semidirect
31. #13093946C22semidirect
32. #13093946C22semidirect
34. C2×M16×C47C22semidirect
35. C22×C8×C47C22semidirect
36. C22⋊C8×C47C22semidirect
155. #408D47semidirect
156. C47#3009semidirect
173. C2×M16C2×D47semidirect
174. C22×C8C2×D47semidirect
183. C22⋊C8C2×D47semidirect