Finite Group Databasebeta

← #20254158

Subgroups — #20254158

Order 6016.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#15689636C211yesmaximal, characteristic, complemented
2C2×#13093999C211yesmaximal, characteristic, complemented
3#15689450C212yesmaximal, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689360C212yesmaximal, complemented
6#15689355C212yesmaximal, complemented
7#15689273C211yesmaximal, characteristic, complemented
8#15689271C212yesmaximal, complemented
9#15689259C211yesmaximal, characteristic, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#484C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic, complemented
13C22×D188—21no—
14C22×D188C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16C2×#10625336C2212yescomplemented
17C2×D376C2212yescomplemented
18C2×C8×D47C2212yescomplemented
19#13094009—21no—
20#13094000C2211yescharacteristic, complemented
21#13093999—21no—
22#13093999—21no—
23#13093999C2212yes—
24#13093999C2212yes—
25#13093999C2211yescharacteristic, complemented
26#13093998C2211yescharacteristic
27#13093994—21no—
28#13093986—21no—
29(C22⋊D47)⋊C4—21no—
30#13093982C2211yescharacteristic, complemented
31C2×(C2×D47)⋊C4—21no—
32#13093955C2212yescomplemented
33#13093946C2212yescomplemented
34#13093944C2212yescomplemented
35#13093944C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yescomplemented
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41#103×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47—21no—
44C23×D47D411yescharacteristic
45C2×Q8×C47C2311yescharacteristic
46C22×C4×C47—21no—
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—21no—
49C22×Dic47D411yescharacteristic
50#10625354—42no—
51C2×D188—21no—
52C2×D188—21no—
53C2×D188—22no—
54C2×D188—22no—
55C2×D188—21no—
56C2×D188—42no—
57C2×D188—44no—
58C2×D188C2311yescharacteristic
59C2×D188C2312yes—
60C2×C4×D47—21no—
61C2×C4×D47—42no—
62C2×C4×D47D411yescharacteristic
63C2×C4×D47D411yescharacteristic
64C2×C4×D47C2311yescharacteristic
65C2×C4×D47C2311yescharacteristic
66C2×C8×C47C2312yes—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47C2312yes—
70C4⋊C4×C47C2311yescharacteristic
71C22⋊C4×C47—21no—
72#10625336—42no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—21no—
79C4⋊Dic47C2311yescharacteristic
80Dic47⋊C4—21no—
81C4×Dic47—21no—
82C2×C47⋊C8C2312yes—
83D376—42no—
84C8×D47—42no—
85C23×C47C2×D411yescharacteristic
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—21no—
89C22×D47—22no—
90C22×D47—41no—
91C22×D47—42no—
92C22×D47—42no—
93C22×D47—42no—
94C22×D47C2×D411yescharacteristic
95C22×D47C2×D411yescharacteristic
96Q8×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—22no—
101C2×C4×C47—42no—
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—42no—
105C2×Dic47—21no—
106C2×Dic47—41no—
107C2×Dic47C2×D411yescharacteristic
108C2×Dic47C2×D411yescharacteristic
109D188—22no—
110D188—22no—
111D188—22no—
112D188—42no—
113D188—44no—
114D188—42no—
115D188—42no—
116D188—44no—
117C4×D47—22no—
118C4×D47—22no—
119C4×D47—41no—
120C4×D47—41no—
121C4×D47—42no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47#13512yes—
127C22×C47C22×D411yescharacteristic
128C2×D47—21no—
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—21no—
132C2×D47—21no—
133C2×D47—44no—
134C2×D47—41no—
135C2×D47—42no—
136C2×D47—41no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—41no—
140C2×D47—84no—
141C2×D47AGL(1,ℤ/8)12yes—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—42no—
145C4×C47—41no—
146C4×C47H(5,𝔽2)12yes—
147Dic47—21no—
148Dic47—21no—
149Dic47—41no—
150#3188—471nomaximal, Sylow
151C2×C47—22no—
152C2×C47#53411yescharacteristic
153C2×C47C2×#13511yescharacteristic
154C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
155D47—22no—
156D47—41no—
157D47—81no—
158D47—82no—
159#525—471no—
160C2×#121—471no—
161#484D4711yescharacteristic, complemented
162#482—472no—
163#481—471no—
164#466—472no—
165#465—472no—
166#450—471no—
167#449—472no—
168#447—471no—
169C2×C22⋊C8—471no—
170C47#318811yescharacteristic, complemented, Sylow
171C2×#41—471no—
172C22×D4—471no—
173C22×D4—941no—
174C23×C4—471no—
175C2×SD16—472no—
176C2×D8—472no—
177C22×C8—472no—
178#123—941no—
179C22⋊Q8—471no—
180C22⋊Q8C2×D4711yescharacteristic
181#121—471no—
182#121—472no—
183#121—472no—
184#121—471no—
185#121—941no—
186#121—941no—
187#120—941no—
188C4×D4—941no—
189C4×D4—941no—
190#117—471no—
191C2×C4⋊C4C2×D4711yescharacteristic
192C2×C22⋊C4—941no—
193#107C2×D4712yescomplemented
194#106—472no—
195#103C2×D4712yescomplemented
196#102—472no—
197#102—472no—
198#102—472no—
199C22⋊C8—471no—
200C22⋊C8—472no—
201C22⋊C8C2×D4711yescharacteristic
202C24—471no—
203C24—941no—
204#41—1882no—
205C2×Q8C22×D4711yescharacteristic
206C2×D4—471no—
207C2×D4—472no—
208C2×D4—941no—
209C2×D4—941no—
210C2×D4—942no—
211C2×D4—942no—
212C2×D4—941no—
213C2×D4—941no—
214C2×D4—1882no—
215C2×D4—1884no—
216C22×C4—21no—
217C22×C4—471no—
218C22×C4—471no—
219C22×C4—471no—
220C22×C4—471no—
221C22×C4—471no—
222C22×C4—941no—
223C22×C4—1882no—
224C22×C4C22×D4711yescharacteristic
225SD16—1882no—
226D8—1882no—
227C2×C8—472no—
228C2×C8—1882no—
229C2×C8C22×D4712yes—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—471no—
233C4⋊C4—941no—
234C4⋊C4C22×D4711yescharacteristic
235C4⋊C4C22×D4712yes—
236C22⋊C4—21no—
237C22⋊C4—942no—
238C22⋊C4—942no—
239C22⋊C4—941no—
240C22⋊C4—941no—
241C22⋊C4—941no—
242C22⋊C4—941no—
243C42—941no—
244C23—471no—
245C23—471no—
246C23—942no—
247C23—942no—
248C23—941no—
249C23—942no—
250C23—1881no—
251C23—1882no—
252C23—1882no—
253C23—1882no—
254C23D4×D4711yescharacteristic
255Q8—22no—
256D4—942no—
257D4—942no—
258D4—942no—
259D4—1882no—
260D4—1882no—
261D4—1884no—
262D4—1884no—
263D4—1882no—
264D4—1882no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—471no—
271C2×C4—471no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—941no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4—1882no—
278C2×C4—1881no—
279C2×C4D4×D4711yescharacteristic
280C2×C4C23×D4711yescharacteristic
281C8—22no—
282C8—942no—
283C22—21no—
284C22—21no—
285C22—472no—
286C22—941no—
287C22—941no—
288C22—941no—
289C22—941no—
290C22—941no—
291C22—3764no—
292C22—1884no—
293C22—1881no—
294C22—1882no—
295C22—1882no—
296C22—1881no—
297C22—1881no—
298C22—1882no—
299C22#1309404712yes—
300C22C2×D4×D4711yescharacteristic
301C4—21no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—941no—
306C4—941no—
307C4—1881no—
308C4#1309407012yes—
309C2—22no—
310C2—942no—
311C2—3762no—
312C2—3761no—
313C2—1881no—
314C2#1568968411yescharacteristic
315C2C2×#1309404711yescharacteristic
316C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3188
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #15689636C2semidirect
2. C2×#13093999C2semidirect
3. #15689450C2semidirect
4. #15689441C2semidirect
5. #15689360C2semidirect
6. #15689355C2semidirect
7. #15689273C2semidirect
8. #15689271C2semidirect
9. #15689259C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#484C2semidirect
12. C2×#10625354C22semidirect
16. C2×#10625336C22semidirect
17. C2×D376C22semidirect
18. C2×C8×D47C22semidirect
20. #13094000C22semidirect
25. #13093999C22semidirect
30. #13093982C22semidirect
32. #13093955C22semidirect
33. #13093946C22semidirect
34. #13093944C22semidirect
35. #13093944C22semidirect
37. (C2×D47)⋊C8C22semidirect
40. #107×C47C22semidirect
41. #103×C47C22semidirect
161. #484D47semidirect
170. C47#3188semidirect
193. #107C2×D47semidirect
195. #103C2×D47semidirect