Finite Group Databasebeta

← #20246369

Subgroups — #20246369

Order 6016.

928 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13093992C211yesmaximal, characteristic
2C2×(C22⋊D47)⋊C4C212yesmaximal, complemented
3C2×C22⋊C4×D47C212yesmaximal, complemented
4#15689011C212yesmaximal, complemented
5#15689003C211yesmaximal, characteristic, complemented
6#15688999C212yesmaximal, complemented
7#15688994C212yesmaximal, complemented
8C4×(C2×D47)⋊C4C212yesmaximal, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C24×D47C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12C23×Dic47C2211yescharacteristic, complemented
13C22×C4×D47C2212yes—
14C22×C4×D47C2212yes—
15#13093992C418yescomplemented
16(C22⋊D47)⋊C4—28no—
17C2×Dic47⋊C4C2212yescomplemented
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2211yescharacteristic, complemented
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C22⋊C4×D47—28no—
25C2×C4×Dic47C2212yescomplemented
26C47⋊#95C2212yescomplemented
27C47⋊#95C2212yescomplemented
28C47⋊#95C2212yescomplemented
29C22×D4×C47C2211yescharacteristic
30C2×C4⋊C4×C47C2211yescharacteristic, complemented
31C2×C22⋊C4×C47C2212yes—
32C2×C22⋊C4×C47C2212yescomplemented
33C2×C42×C47C2211yescharacteristic, complemented
34C24×C47C2311yescharacteristic
35C24×C47C2311yescharacteristic
36C23×D47—24no—
37C23×D47—24no—
38C23×D47—41no—
39C23×D47—41no—
40C23×D47C2×C414yescomplemented
41C23×D47C2312yes—
42C2×D4×C47—41no—
43C2×D4×C47—41no—
44C2×D4×C47C2×C414yescomplemented
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2312yes—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—24no—
50C2×C22⋊D47C2×C418yescomplemented
51C22×Dic47—24no—
52C22×Dic47—41no—
53C22×Dic47C2312yes—
54C22×Dic47C2312yes—
55C22×Dic47C2312yes—
56C2×C4×D47—24no—
57C2×C4×D47—24no—
58C2×C4×D47—24no—
59C2×C4×D47—24no—
60C2×C4×D47—42no—
61C2×C4×D47—42no—
62C4⋊C4×C47—41no—
63C22⋊C4×C47—24no—
64C22⋊C4×C47—24no—
65C42×C47—41no—
66C22⋊Dic47—24no—
67C22⋊Dic47—41no—
68C22⋊Dic47C2×C414yescomplemented
69(C2×D47)⋊C4—24no—
70(C2×D47)⋊C4C2×C418yescomplemented
71(C2×D47)⋊C4D418yescomplemented
72Dic47⋊C4—24no—
73C4×Dic47—24no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—21no—
81C23×C47—21no—
82C23×C47C22×C412yes—
83C23×C47C22×C412yes—
84C23×C47C2411yescharacteristic
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—216no—
90C22×D47—44no—
91C22×D47—44no—
92C22×D47—48no—
93C22×D47—44no—
94C22×D47C22×C414yes—
95C22×D47C2×D414yes—
96C22×D47#4114yes—
97D4×C47—44no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—22no—
105C2×C4×C47C22×C412yes—
106C2×C4×C47C2×D414yes—
107C22⋊D47—216no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—44no—
116C2×Dic47C22×C414yes—
117C2×Dic47C2×D414yes—
118C4×D47—48no—
119C4×D47—48no—
120C22×C47—24no—
121C22×C47—24no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—41no—
125C22×C47—41no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—41no—
129C22×C47—41no—
130C22×C47C23×C411yescharacteristic
131C22×C47C22×D412yes—
132C22×C47C2×#4112yes—
133C22×C47H(5,𝔽2)11yescharacteristic
134C22×C47H(5,𝔽2)11yescharacteristic
135C2×D47—24no—
136C2×D47—24no—
137C2×D47—24no—
138C2×D47—24no—
139C2×D47—24no—
140C2×D47—24no—
141C2×D47—416no—
142C2×D47C4×D418yescomplemented
143C4×C47—22no—
144C4×C47—24no—
145C4×C47—42no—
146Dic47—24no—
147Dic47—24no—
148Dic47—42no—
149#2358—471nomaximal, Sylow
150C2×C47—42no—
151C2×C47—42no—
152C2×C47C2×C4×D412yes—
153C2×C47#51811yescharacteristic
154C2×C47D4211yescharacteristic
155C2×C47#54612yes—
156C2×C47#55111yescharacteristic
157D47—28no—
158C2×#120—471no—
159C2×C4×D4—472no—
160C22×C22⋊C4—472no—
161#390D4711yescharacteristic, complemented
162#388—472no—
163#386—471no—
164#386—472no—
165#385—472no—
166C4×C22⋊C4—472no—
167C47#235811yescharacteristic, complemented, Sylow
168C25—471no—
169C22×D4—472no—
170C22×D4C2×D4711yescharacteristic
171C23×C4—471no—
172C23×C4—472no—
173C23×C4—472no—
174#120—478no—
175C4×D4—948no—
176C2×C4⋊C4—472no—
177C2×C4⋊C4C2×D4711yescharacteristic, complemented
178C2×C22⋊C4—471no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—472no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4—472no—
183C2×C22⋊C4—471no—
184C2×C22⋊C4—948no—
185C2×C22⋊C4C2×D4712yes—
186C2×C22⋊C4C2×D4712yescomplemented
187C2×C42—472no—
188C2×C42C2×D4711yescharacteristic, complemented
189#95—472no—
190#95—472no—
191#95—472no—
192C24—472no—
193C24—474no—
194C24—944no—
195C24—944no—
196C24—1881no—
197C24—1881no—
198C24C22×D4711yescharacteristic
199C24C22×D4711yescharacteristic
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—478no—
203C2×D4—944no—
204C2×D4—944no—
205C2×D4C4×D4714yescomplemented
206C22×C4—472no—
207C22×C4—472no—
208C22×C4—472no—
209C22×C4—944no—
210C22×C4—944no—
211C22×C4—944no—
212C22×C4—944no—
213C22×C4—944no—
214C22×C4—1882no—
215C22×C4—1882no—
216C22×C4—1881no—
217C22×C4C22×D4712yes—
218C22×C4C22×D4711yescharacteristic
219C22×C4C22×D4712yes—
220C4⋊C4—41no—
221C4⋊C4—944no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—474no—
225C22⋊C4—478no—
226C22⋊C4—478no—
227C22⋊C4—944no—
228C22⋊C4—944no—
229C22⋊C4—1881no—
230C42—41no—
231C42—944no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—474no—
241C23—474no—
242C23—474no—
243C23—9416no—
244C23—942no—
245C23—942no—
246C23—942no—
247C23—942no—
248C23—1884no—
249C23—1884no—
250C23—1888no—
251C23—1884no—
252C23C2×C4×D4712yes—
253C23C2×C4×D4712yes—
254C23C23×D4711yescharacteristic
255D4—44no—
256D4—9416no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—474no—
265C2×C4—474no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—1888no—
274C2×C4—1888no—
275C2×C4—1884no—
276C2×C4C2×C4×D4712yes—
277C2×C4D4×D4714yes—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—41no—
287C22—41no—
288C22—478no—
289C22—944no—
290C22—944no—
291C22—944no—
292C22—944no—
293C22—944no—
294C22—944no—
295C22—18816no—
296C22C22×C4×D4711yescharacteristic
297C22C2×D4×D4712yes—
298C22#41×D4712yes—
299C22#1309406911yescharacteristic
300C22#1309406911yescharacteristic
301C4—24no—
302C4—22no—
303C4—42no—
304C4—944no—
305C4—944no—
306C4—1882no—
307C2—42no—
308C2—42no—
309C2—948no—
310C2C4×D4×D4712yes—
311C2#1568959611yescharacteristic
312C2#1568975811yescharacteristic
313C2#1568976212yes—
314C2#1568980311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#390C2
socleC23×C47C24
hypercenter#390D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D47)⋊C4C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689011C2semidirect
5. #15689003C2semidirect
6. #15688999C2semidirect
7. #15688994C2semidirect
8. C4×(C2×D47)⋊C4C2semidirect
9. C47×#390C2semidirect
12. C23×Dic47C22semidirect
15. #13093992C4semidirect
17. C2×Dic47⋊C4C22semidirect
20. C2×C22⋊Dic47C22semidirect
25. C2×C4×Dic47C22semidirect
26. C47⋊#95C22semidirect
27. C47⋊#95C22semidirect
28. C47⋊#95C22semidirect
30. C2×C4⋊C4×C47C22semidirect
32. C2×C22⋊C4×C47C22semidirect
33. C2×C42×C47C22semidirect
40. C23×D47C2×C4semidirect
44. C2×D4×C47C2×C4semidirect
50. C2×C22⋊D47C2×C4semidirect
68. C22⋊Dic47C2×C4semidirect
70. (C2×D47)⋊C4C2×C4semidirect
71. (C2×D47)⋊C4D4semidirect
142. C2×D47C4×D4semidirect
161. #390D47semidirect
167. C47#2358semidirect
177. C2×C4⋊C4C2×D47semidirect
186. C2×C22⋊C4C2×D47semidirect
188. C2×C42C2×D47semidirect
205. C2×D4C4×D47semidirect