Finite Group Databasebeta

← #20249192

Subgroups — #20249192

Order 6016.

668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13094000C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D47C211yesmaximal, characteristic
3#15689060C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689047C212yesmaximal, complemented
6#15689046C212yesmaximal, complemented
7#15689034C211yesmaximal, characteristic, complemented
8#15688997C212yesmaximal, complemented
9#15688982C211yesmaximal, characteristic, complemented
10#15688978C212yesmaximal
11C47×#393C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15#13094000—24no—
16C2×C4⋊Dic47C2211yescharacteristic, complemented
17C2×C4⋊Dic47C2212yescomplemented
18C2×Dic47⋊C4C2212yescomplemented
19C2×Dic47⋊C4C2212yescomplemented
20C2×Dic47⋊C4C2212yescomplemented
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C22⋊C4×D47—24no—
30C47⋊#95C2211yescharacteristic, complemented
31C47⋊#95C2212yescomplemented
32C22×Q8×C47C2211yescharacteristic, complemented
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic, complemented
36#95×C47C2212yescomplemented
37C24×C47C2311yescharacteristic
38C23×D47—22no—
39C23×D47—22no—
40C23×D47—42no—
41C23×D47—42no—
42C23×D47Q814yescomplemented
43C23×D47C2311yescharacteristic
44C23×D47C2311yescharacteristic
45C2×Q8×C47—22no—
46C2×Q8×C47—42no—
47C22×C4×C47C2312yes—
48C22×C4×C47C2312yes—
49C22×C4×C47C2311yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C2×C4×D47—22no—
56C2×C4×D47—42no—
57C2×C4×D47—42no—
58C2×C4×D47D414yes—
59C22⋊C4×C47—22no—
60C22⋊C4×C47—42no—
61C22⋊Dic47—22no—
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—42no—
68(C2×D47)⋊C4—42no—
69C4⋊Dic47—22no—
70C4⋊Dic47—42no—
71Dic47⋊C4—24no—
72Dic47⋊C4—42no—
73Dic47⋊C4—42no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47C2×Q812yes—
79C23×C47C2411yescharacteristic
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—21no—
83C22×D47—21no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—28no—
87C22×D47—48no—
88C22×D47—44no—
89C22×D47—44no—
90C22×D47—48no—
91C22×D47C2×D412yes—
92C22×D47C2×Q812yes—
93C22×D47C2×Q812yes—
94C22×D47#4112yes—
95Q8×C47—44no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—22no—
105C2×C4×C47C2×D412yes—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47C2×D412yes—
116C4×D47—44no—
117C4×D47—44no—
118C22×C47—22no—
119C22×C47—24no—
120C22×C47—41no—
121C22×C47—41no—
122C22×C47—42no—
123C22×C47C22×D411yescharacteristic
124C22×C47C22×Q811yescharacteristic
125C22×C47C2×#4111yescharacteristic
126C22×C47H(5,𝔽2)12yes—
127C22×C47H(5,𝔽2)12yes—
128C2×D47—22no—
129C2×D47—22no—
130C2×D47—24no—
131C2×D47—24no—
132C2×D47—22no—
133C2×D47—24no—
134C2×D47—416no—
135C2×D47—41no—
136C2×D47—41no—
137C2×D47—42no—
138C2×D47C22⋊Q814yes—
139C4×C47—22no—
140C4×C47—42no—
141C4×C47—41no—
142C4×C47—42no—
143Dic47—22no—
144Dic47—41no—
145Dic47—42no—
146Dic47—42no—
147#2626—471nomaximal, Sylow
148C2×C47—42no—
149C2×C47C2×C22⋊Q811yescharacteristic
150C2×C47#53411yescharacteristic
151C2×C47#53511yescharacteristic
152C2×C47#53812yes—
153C2×C47#54312yes—
154D47—24no—
155D47—42no—
156C2×C22⋊Q8—471no—
157C22×C22⋊C4—471no—
158#399—471no—
159#399—471no—
160#396—472no—
161#396—472no—
162#393—471no—
163#393D4711yescharacteristic, complemented
164#385—472no—
165#380—471no—
166#379—472no—
167C47#262611yescharacteristic, complemented, Sylow
168C25—471no—
169C22×Q8C2×D4711yescharacteristic, complemented
170C23×C4—471no—
171C23×C4—471no—
172C22⋊Q8—944no—
173C2×C4⋊C4—472no—
174C2×C4⋊C4—471no—
175C2×C4⋊C4—472no—
176C2×C4⋊C4—472no—
177C2×C4⋊C4—472no—
178C2×C22⋊C4—471no—
179C2×C22⋊C4—471no—
180C2×C22⋊C4—471no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4—472no—
183C2×C22⋊C4—472no—
184C2×C22⋊C4—472no—
185C2×C22⋊C4—472no—
186C2×C22⋊C4—944no—
187C2×C22⋊C4C2×D4711yescharacteristic
188C2×C22⋊C4C2×D4712yes—
189#95—471no—
190#95—472no—
191#95C2×D4711yescharacteristic, complemented
192#95C2×D4712yescomplemented
193C24—471no—
194C24—471no—
195C24—474no—
196C24—942no—
197C24—942no—
198C24—1882no—
199C24—1882no—
200C24C22×D4711yescharacteristic
201C2×Q8—22no—
202C2×Q8—42no—
203C22×C4—471no—
204C22×C4—474no—
205C22×C4—472no—
206C22×C4—471no—
207C22×C4—472no—
208C22×C4—942no—
209C22×C4—1882no—
210C22×C4—1882no—
211C22×C4C22×D4712yes—
212C22×C4C22×D4712yes—
213C22×C4C22×D4711yescharacteristic
214C22×C4C22×D4711yescharacteristic
215C4⋊C4—944no—
216C4⋊C4—942no—
217C4⋊C4—1882no—
218C4⋊C4—1882no—
219C4⋊C4—1882no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—942no—
223C22⋊C4—944no—
224C22⋊C4—944no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C22⋊C4—1882no—
228C22⋊C4—1882no—
229C22⋊C4—1882no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—472no—
235C23—472no—
236C23—472no—
237C23—472no—
238C23—948no—
239C23—942no—
240C23—942no—
241C23—941no—
242C23—941no—
243C23—942no—
244C23—942no—
245C23—1888no—
246C23—1884no—
247C23—1884no—
248C23—1888no—
249C23Q8×D4712yes—
250C23C23×D4711yescharacteristic
251Q8—44no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—472no—
262C2×C4—942no—
263C2×C4—941no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—1884no—
272C2×C4—1884no—
273C2×C4D4×D4712yes—
274C22—24no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—474no—
280C22—944no—
281C22—942no—
282C22—942no—
283C22—944no—
284C22—944no—
285C22—942no—
286C22—18816no—
287C22—1881no—
288C22—1881no—
289C22—1882no—
290C22C2×D4×D4711yescharacteristic
291C22C2×Q8×D4711yescharacteristic
292C22#41×D4711yescharacteristic
293C22#1309406912yes—
294C22#1309407012yes—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—942no—
300C4—1881no—
301C4—1882no—
302C4—1882no—
303C2—42no—
304C2—944no—
305C2—1882no—
306C2C22⋊Q8×D4711yescharacteristic
307C2#1568968311yescharacteristic
308C2#1568969111yescharacteristic
309C2#1568970712yes—
310C2#1568974812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094000C2semidirect
3. #15689060C2semidirect
4. #15689059C2semidirect
5. #15689047C2semidirect
6. #15689046C2semidirect
7. #15689034C2semidirect
8. #15688997C2semidirect
9. #15688982C2semidirect
11. C47×#393C2semidirect
16. C2×C4⋊Dic47C22semidirect
17. C2×C4⋊Dic47C22semidirect
18. C2×Dic47⋊C4C22semidirect
19. C2×Dic47⋊C4C22semidirect
20. C2×Dic47⋊C4C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
32. C22×Q8×C47C22semidirect
35. #95×C47C22semidirect
36. #95×C47C22semidirect
42. C23×D47Q8semidirect
163. #393D47semidirect
167. C47#2626semidirect
169. C22×Q8C2×D47semidirect
191. #95C2×D47semidirect
192. #95C2×D47semidirect