Finite Group Databasebeta

← #20252664

Subgroups — #20252664

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
2C22×#10625336C211yesmaximal, characteristic, complemented
3#15689697C211yesmaximal, characteristic, complemented
4#15689284C214yesmaximal, complemented
5#15689272C214yesmaximal, complemented
6#15689129C211yesmaximal, characteristic, complemented
7#15689119C211yesmaximal, characteristic, complemented
8#15689091C211yesmaximal, characteristic, complemented
9C2×#137×C47C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354C2212yes—
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C22×D188—21no—
16C22×D188C2211yescharacteristic
17C2×D4×D47—22no—
18C2×D4×D47C2212yes—
19C2×#10625336—24no—
20C2×#10625336C2214yescomplemented
21C22×C47⋊C8C2211yescharacteristic, complemented
22#13094022—21no—
23#13094013—21no—
24#13094007—22no—
25#13094000C2214yescomplemented
26#13093983C2211yescharacteristic, complemented
27#13093948C2212yescomplemented
28#13093946C2214yescomplemented
29#13093945C2212yescomplemented
30(C2×D47)⋊C8C2214yescomplemented
31C2×#41×C47C2211yescharacteristic
32C22×Q8×C47C2211yescharacteristic, complemented
33#137×C47—24no—
34C2×Q16×C47C2212yescomplemented
35C2×SD16×C47C2212yescomplemented
36C2×M16×C47C2211yescharacteristic, complemented
37C23×D47—21no—
38C23×D47—22no—
39#41×C47—22no—
40#41×C47D414yes—
41C2×Q8×C47—21no—
42C2×Q8×C47—22no—
43C2×Q8×C47—22no—
44C2×Q8×C47C2312yes—
45C2×Q8×C47C2311yescharacteristic
46C2×D4×C47—21no—
47C2×D4×C47C2311yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—22no—
52C2×C22⋊D47D412yes—
53#10625354—24no—
54#10625354—24no—
55D4×D47—216no—
56D4×D47—24no—
57D4×D47—24no—
58#10625350—28no—
59#10625350—22no—
60#10625350—22no—
61C2×D188—28no—
62C2×D188—22no—
63C2×D188—21no—
64C2×D188—22no—
65C2×D188D411yescharacteristic
66C2×D188D414yes—
67C2×D188C2312yes—
68C2×C4×D47—22no—
69C2×C4×D47C2312yes—
70C2×Dic94D411yescharacteristic
71Q16×C47—24no—
72SD16×C47—24no—
73M16×C47—22no—
74C2×C8×C47C2312yes—
75C22⋊Dic47—21no—
76#10625336—28no—
77(C2×D47)⋊C4—24no—
78C4⋊Dic47C2312yes—
79Dic47⋊C4—24no—
80C4×Dic47—21no—
81C2×C47⋊C8—22no—
82C2×C47⋊C8C2312yes—
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×C47—22no—
93Q8×C47—22no—
94Q8×C47—42no—
95Q8×C47C2×D412yes—
96D4×C47—24no—
97D4×C47—21no—
98D4×C47C2×D412yes—
99C2×C4×C47—21no—
100C2×C4×C47—24no—
101C2×C4×C47—22no—
102C2×C4×C47—42no—
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2×D412yes—
106C2×C4×C47C2411yescharacteristic
107C22⋊D47—28no—
108C22⋊D47—24no—
109C2×Dic47—22no—
110C2×Dic47C2×D412yes—
111D188—28no—
112D188—22no—
113D188—24no—
114D188—22no—
115D188C2×D414yes—
116C4×D47—28no—
117C4×D47—22no—
118C4×D47—22no—
119Dic94—22no—
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×#137D4711yescharacteristic, complemented
149C22×SD16—471no—
150#536—471no—
151#452—474no—
152#450—474no—
153#418—471no—
154#416—471no—
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×Q8C2×D4711yescharacteristic, complemented
164C22×D4—472no—
165C22×D4—471no—
166C22×D4—941no—
167C22×D4—942no—
168#137—24no—
169C2×Q16C2×D4712yescomplemented
170C2×SD16—474no—
171C2×SD16—944no—
172C2×SD16C2×D4712yescomplemented
173C2×M16C2×D4711yescharacteristic, complemented
174C22×C8—471no—
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⋊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#41C22⋊D4714yes—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—471no—
197C2×Q8C22×D4712yes—
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—941no—
211C2×D4—942no—
212C2×D4C22×D4711yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—472no—
216C22×C4—942no—
217C22×C4C22×D4711yescharacteristic
218Q16—24no—
219SD16—24no—
220SD16—948no—
221M16—22no—
222C2×C8—472no—
223C2×C8—942no—
224C2×C8C22×D4712yes—
225C4⋊C4—472no—
226C4⋊C4—944no—
227C22⋊C4—944no—
228C22⋊C4—941no—
229C42—941no—
230C23—21no—
231C23—472no—
232C23—948no—
233C23—944no—
234C23—942no—
235C23—3762no—
236C23—3764no—
237C23D4×D4711yescharacteristic
238Q8—21no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—942no—
243Q8C2×C22⋊D4712yes—
244D4—24no—
245D4—21no—
246D4—474no—
247D4—948no—
248D4—948no—
249D4—944no—
250D4—944no—
251D4—942no—
252D4—942no—
253D4C2×C22⋊D4712yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—472no—
259C2×C4—948no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4D4×D4711yescharacteristic
264C2×C4D4×D4712yes—
265C2×C4C2×C22⋊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#1309399212yes—
279C22C2×D4×D4711yescharacteristic
280C4—22no—
281C4—42no—
282C4—942no—
283C4—1882no—
284C4#1309399212yes—
285C4C2×D4×D4711yescharacteristic
286C4C22×C22⋊D4711yescharacteristic
287C2—22no—
288C2—42no—
289C2—1882no—
290C2—1884no—
291C2C2×#1309399211yescharacteristic
292C2#1568993212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3009
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
2. C22×#10625336C2semidirect
3. #15689697C2semidirect
4. #15689284C2semidirect
5. #15689272C2semidirect
6. #15689129C2semidirect
7. #15689119C2semidirect
8. #15689091C2semidirect
9. C2×#137×C47C2semidirect
20. C2×#10625336C22semidirect
21. C22×C47⋊C8C22semidirect
25. #13094000C22semidirect
26. #13093983C22semidirect
27. #13093948C22semidirect
28. #13093946C22semidirect
29. #13093945C22semidirect
30. (C2×D47)⋊C8C22semidirect
32. C22×Q8×C47C22semidirect
34. C2×Q16×C47C22semidirect
35. C2×SD16×C47C22semidirect
36. C2×M16×C47C22semidirect
148. C2×#137D47semidirect
156. C47#3009semidirect
163. C22×Q8C2×D47semidirect
169. C2×Q16C2×D47semidirect
172. C2×SD16C2×D47semidirect
173. C2×M16C2×D47semidirect