Finite Group Databasebeta

← #20249199

Subgroups — #20249199

Order 6016.

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

normal subgroups only

This group has 668 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×#13094001C211yesmaximal, characteristic, complemented
2C22×(C2×D47)⋊C4C211yesmaximal, characteristic
3#15689058C212yesmaximal, complemented
4#15689047C212yesmaximal, complemented
5#15689045C212yesmaximal, complemented
6#15689036C212yesmaximal, complemented
7#15688996C211yesmaximal, characteristic, complemented
8#15688981C211yesmaximal, characteristic, complemented
9#15688978C211yesmaximal, characteristic
10#15688978C211yesmaximal, characteristic
11C47×#385C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×Dic94C2211yescharacteristic, complemented
14C23×Dic47C2211yescharacteristic
15#13094001—24no—
16C2×C4⋊Dic47C2211yescharacteristic, complemented
17C2×Dic47⋊C4C2211yescharacteristic, complemented
18C2×Dic47⋊C4C2211yescharacteristic, complemented
19C2×Dic47⋊C4C2212yescomplemented
20C2×Dic47⋊C4C2212yescomplemented
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×(C2×D47)⋊C4—24no—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×(C2×D47)⋊C4C2212yes—
30C47⋊#95C2212yescomplemented
31C47⋊#95C2212yescomplemented
32C23×C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yescomplemented
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36#95×C47C2212yescomplemented
37C24×C47C2311yescharacteristic
38C23×D47—22no—
39C23×D47—22no—
40C23×D47—42no—
41C23×D47—42no—
42C23×D47Q814yescomplemented
43C23×D47C2312yes—
44C22×C4×C47—22no—
45C22×C4×C47—42no—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2312yes—
50C22×Dic47—42no—
51C22×Dic47D414yes—
52C22×Dic47C2312yes—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2311yescharacteristic
57C2×Dic94—22no—
58C2×Dic94—42no—
59C4⋊C4×C47—42no—
60C22⋊C4×C47—22no—
61C22⋊C4×C47—22no—
62C22⋊Dic47—22no—
63C22⋊Dic47—22no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—42no—
67(C2×D47)⋊C4—42no—
68(C2×D47)⋊C4—42no—
69(C2×D47)⋊C4—42no—
70C4⋊Dic47—22no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—42no—
74Dic47⋊C4—42no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47C2×D412yes—
78C23×C47C2×Q812yes—
79C23×C47#4112yes—
80C23×C47C2411yescharacteristic
81C22×D47—28no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—48no—
89C22×D47—44no—
90C22×D47—44no—
91C22×D47—48no—
92C22×D47C2×Q814yes—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—44no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—44no—
114C2×Dic47C2×D412yes—
115C2×Dic47C2×D412yes—
116Dic94—44no—
117C22×C47—22no—
118C22×C47—22no—
119C22×C47—24no—
120C22×C47—24no—
121C22×C47C22⋊Q814yes—
122C22×C47C22×D411yescharacteristic
123C22×C47C22×Q811yescharacteristic
124C22×C47C2×#4111yescharacteristic
125C22×C47H(5,𝔽2)12yes—
126C22×C47H(5,𝔽2)12yes—
127C2×D47—24no—
128C2×D47—24no—
129C2×D47—24no—
130C2×D47—416no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—42no—
135C4×C47—41no—
136C4×C47—41no—
137C4×C47—42no—
138C4×C47—42no—
139Dic47—22no—
140Dic47—22no—
141Dic47—41no—
142Dic47—41no—
143Dic47—42no—
144#2626—471nomaximal, Sylow
145C2×C47—24no—
146C2×C47C2×C22⋊Q811yescharacteristic
147C2×C47#53411yescharacteristic
148C2×C47#53511yescharacteristic
149C2×C47#53812yes—
150C2×C47#54312yes—
151D47—44no—
152C2×C22⋊Q8—471no—
153C22×C22⋊C4—471no—
154#399—472no—
155#396—472no—
156#396—472no—
157#393—472no—
158#385—471no—
159#385D4711yescharacteristic, complemented
160#380—471no—
161#379—471no—
162#379—471no—
163C47#262611yescharacteristic, complemented, Sylow
164C25—471no—
165C22×Q8—471no—
166C23×C4—471no—
167C23×C4C2×D4711yescharacteristic
168C22⋊Q8—944no—
169C2×C4⋊C4—471no—
170C2×C4⋊C4—471no—
171C2×C4⋊C4—471no—
172C2×C4⋊C4—472no—
173C2×C4⋊C4—472no—
174C2×C4⋊C4C2×D4712yescomplemented
175C2×C22⋊C4—471no—
176C2×C22⋊C4—471no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—472no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4—472no—
183C2×C22⋊C4—944no—
184C2×C22⋊C4C2×D4711yescharacteristic
185C2×C22⋊C4C2×D4711yescharacteristic
186#95—472no—
187#95—472no—
188#95C2×D4712yescomplemented
189C24—472no—
190C24—474no—
191C24—942no—
192C24—942no—
193C24—1882no—
194C24—1882no—
195C24C22×D4711yescharacteristic
196C2×Q8—942no—
197C2×Q8—1882no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—471no—
201C22×C4—471no—
202C22×C4—474no—
203C22×C4—472no—
204C22×C4—471no—
205C22×C4—471no—
206C22×C4—1882no—
207C22×C4C22×D4712yes—
208C22×C4C22×D4712yes—
209C22×C4C22×D4711yescharacteristic
210C22×C4C22×D4711yescharacteristic
211C4⋊C4—42no—
212C4⋊C4—942no—
213C4⋊C4—942no—
214C4⋊C4—942no—
215C4⋊C4—1882no—
216C4⋊C4—1882no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—944no—
220C22⋊C4—944no—
221C22⋊C4—942no—
222C22⋊C4—942no—
223C22⋊C4—1882no—
224C22⋊C4—1882no—
225C22⋊C4—1882no—
226C22⋊C4—1882no—
227C23—22no—
228C23—22no—
229C23—474no—
230C23—948no—
231C23—942no—
232C23—942no—
233C23—942no—
234C23—942no—
235C23—942no—
236C23—942no—
237C23—1888no—
238C23—1884no—
239C23—1884no—
240C23—1888no—
241C23#1062535012yes—
242C23D4×D4712yes—
243C23Q8×D4712yes—
244C23C23×D4711yescharacteristic
245Q8—1884no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—44no—
257C2×C4—472no—
258C2×C4—472no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—942no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—1884no—
269C22—24no—
270C22—22no—
271C22—22no—
272C22—24no—
273C22—944no—
274C22—944no—
275C22—944no—
276C22—18816no—
277C22—1882no—
278C22—1882no—
279C22—1882no—
280C22—1882no—
281C22#1309400214yes—
282C22C2×D4×D4711yescharacteristic
283C22C2×Q8×D4711yescharacteristic
284C22C2×#1062535011yescharacteristic
285C22#1309406912yes—
286C22#1309407012yes—
287C4—41no—
288C4—42no—
289C4—41no—
290C4—42no—
291C4—942no—
292C4—942no—
293C4—1881no—
294C4—1881no—
295C4—1882no—
296C2—24no—
297C2—1884no—
298C2C2×#1309400211yescharacteristic
299C2#1568968411yescharacteristic
300C2#1568968811yescharacteristic
301C2#1568970612yes—
302C2#1568974812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13094001C2semidirect
3. #15689058C2semidirect
4. #15689047C2semidirect
5. #15689045C2semidirect
6. #15689036C2semidirect
7. #15688996C2semidirect
8. #15688981C2semidirect
11. C47×#385C2semidirect
13. C22×Dic94C22semidirect
16. C2×C4⋊Dic47C22semidirect
17. C2×Dic47⋊C4C22semidirect
18. C2×Dic47⋊C4C22semidirect
19. C2×Dic47⋊C4C22semidirect
20. C2×Dic47⋊C4C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
33. C2×C4⋊C4×C47C22semidirect
36. #95×C47C22semidirect
42. C23×D47Q8semidirect
159. #385D47semidirect
163. C47#2626semidirect
174. C2×C4⋊C4C2×D47semidirect
188. #95C2×D47semidirect