Finite Group Databasebeta

← #20253314

Subgroups — #20253314

Order 6016.

458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689635C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689460C212yesmaximal, complemented
4#15689455C212yesmaximal, complemented
5#15689443C212yesmaximal, complemented
6#15689438C212yesmaximal, complemented
7#15689166C211yesmaximal, characteristic, complemented
8#15689125C211yesmaximal, characteristic, complemented
9#15689122C211yesmaximal, characteristic, complemented
10#15689086C211yesmaximal, characteristic, complemented
11C47×#428C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×C4×D47—21no—
14C22×C4×D47C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13094008—21no—
17#13094004C2211yescharacteristic
18#13094004C2211yescharacteristic
19#13093999C2211yescharacteristic
20#13093999C2211yescharacteristic
21#13093994—21no—
22C4×D188—21no—
23C4×D188—21no—
24C2×C4⋊Dic47C2211yescharacteristic
25C2×Dic47⋊C4—21no—
26C4⋊C4×D47—21no—
27C4⋊C4×D47—21no—
28C4⋊C4×D47C2212yes—
29C4⋊C4×D47C2212yes—
30#13093957C2212yescomplemented
31#13093955C2212yescomplemented
32#13093949C2212yescomplemented
33#13093947C2212yescomplemented
34#13093946C2212yescomplemented
35#13093944C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37(C2×D47)⋊C8C2212yes—
38C2×M16×C47C2211yescharacteristic
39#117×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2211yescharacteristic
41#107×C47C2212yescomplemented
42#106×C47C2212yescomplemented
43C23×D47D411yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C22×Dic47D411yescharacteristic
49#10625350—22no—
50#10625350—22no—
51C2×D188—21no—
52C2×D188—21no—
53C2×D188C2311yescharacteristic
54C2×C4×D47—22no—
55C2×C4×D47—22no—
56C2×C4×D47—22no—
57C2×C4×D47—22no—
58C2×C4×D47—21no—
59C2×C4×D47—44no—
60C2×C4×D47D411yescharacteristic
61C2×C4×D47D411yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×C4×D47C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65M16×C47—22no—
66C2×C8×C47C2312yes—
67C4⋊C4×C47—21no—
68C4⋊C4×C47C2311yescharacteristic
69C4⋊C4×C47C2312yes—
70C4⋊C4×C47C2311yescharacteristic
71C22⋊C4×C47—21no—
72C42×C47—21no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77C4⋊Dic47—21no—
78C4⋊Dic47—21no—
79C4⋊Dic47—21no—
80C4⋊Dic47C2312yes—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83#10625329—22no—
84C2×C47⋊C8C2312yes—
85C23×C47C2×D411yescharacteristic
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—21no—
90C22×D47C2×D411yescharacteristic
91C22×D47C2×D411yescharacteristic
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—42no—
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47#4112yes—
98C2×C4×C47#4112yes—
99C2×C4×C47C2411yescharacteristic
100C22⋊D47—42no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—21no—
104C2×Dic47—42no—
105C2×Dic47C2×D411yescharacteristic
106C2×Dic47C2×D411yescharacteristic
107D188—21no—
108D188—21no—
109D188—42no—
110D188—42no—
111C4×D47—22no—
112C4×D47—22no—
113C4×D47—21no—
114C4×D47—21no—
115C4×D47—21no—
116C4×D47—21no—
117C4×D47—44no—
118C4×D47—44no—
119C4×D47—42no—
120Dic94—21no—
121Dic94—21no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47#12312yes—
127C22×C47C22×D411yescharacteristic
128C2×D47—28no—
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—21no—
132C2×D47—21no—
133C2×D47—41no—
134C2×D47—41no—
135C2×D47—41no—
136C2×D47AGL(1,ℤ/8)12yes—
137C2×D47#13712yes—
138C4×C47—42no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C47#12312yes—
142C4×C47C2×#4111yescharacteristic
143C4×C47C2×#4111yescharacteristic
144Dic47—21no—
145Dic47—21no—
146Dic47—41no—
147Dic47—42no—
148#3092—471nomaximal, Sylow
149C2×C47—22no—
150C2×C47C2×#12311yescharacteristic
151C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C47C2×#13711yescharacteristic
153D47—22no—
154D47—22no—
155D47—81no—
156#525—471no—
157C22×C4⋊C4—471no—
158#484—472no—
159#483—472no—
160#481—472no—
161#480—472no—
162#428—471no—
163#428D4711yescharacteristic, complemented
164#417—471no—
165#417—471no—
166#407—471no—
167C47#309211yescharacteristic, complemented, Sylow
168C2×#41—471no—
169C23×C4—471no—
170C23×C4—941no—
171C2×M16—471no—
172C2×M16C2×D4711yescharacteristic
173#123—941no—
174C22⋊Q8—471no—
175C22⋊Q8—471no—
176#121—471no—
177#121—471no—
178#120—941no—
179C4×D4—941no—
180C4×D4—941no—
181#117C2×D4711yescharacteristic
182C2×C4⋊C4—471no—
183C2×C4⋊C4—472no—
184C2×C4⋊C4—472no—
185C2×C4⋊C4—941no—
186C2×C4⋊C4—941no—
187C2×C4⋊C4—941no—
188C2×C4⋊C4C2×D4711yescharacteristic
189#107—472no—
190#107C2×D4712yescomplemented
191#106—472no—
192#106C2×D4712yescomplemented
193#103—472no—
194#103—472no—
195#102—472no—
196#102—472no—
197C22⋊C8—472no—
198C22⋊C8—472no—
199C24—471no—
200#41—942no—
201#41—942no—
202C2×Q8—471no—
203C2×D4—471no—
204C2×D4—941no—
205C2×D4—941no—
206C2×D4—941no—
207C22×C4—21no—
208C22×C4—471no—
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—471no—
213C22×C4—942no—
214C22×C4—942no—
215C22×C4—942no—
216C22×C4—942no—
217C22×C4—941no—
218C22×C4—941no—
219C22×C4—1884no—
220C22×C4C22×D4711yescharacteristic
221M16—22no—
222M16—942no—
223C2×C8—472no—
224C2×C8C22×D4712yes—
225C4⋊C4—21no—
226C4⋊C4—472no—
227C4⋊C4—942no—
228C4⋊C4—942no—
229C4⋊C4—941no—
230C4⋊C4—941no—
231C4⋊C4—941no—
232C4⋊C4C22×D4712yes—
233C4⋊C4C22×D4711yescharacteristic
234C4⋊C4C22×D4711yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—941no—
237C22⋊C4—941no—
238C22⋊C4—941no—
239C22⋊C4—941no—
240C42—21no—
241C23—471no—
242C23—471no—
243C23—942no—
244C23—942no—
245C23—942no—
246C23—941no—
247C23D4×D4711yescharacteristic
248Q8—941no—
249Q8—941no—
250D4—941no—
251D4—941no—
252D4—1882no—
253D4—1882no—
254D4—1882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—471no—
260C2×C4—471no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—941no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—941no—
269C2×C4—942no—
270C2×C4—1884no—
271C2×C4—1884no—
272C2×C4—1882no—
273C2×C4—1882no—
274C2×C4#1062535012yes—
275C2×C4D4×D4711yescharacteristic
276C2×C4#1062535412yes—
277C2×C4C23×D4711yescharacteristic
278C8—22no—
279C8—942no—
280C22—21no—
281C22—21no—
282C22—472no—
283C22—472no—
284C22—948no—
285C22—941no—
286C22—941no—
287C22—941no—
288C22—941no—
289C22—1881no—
290C22—1881no—
291C22—1881no—
292C22#1309400912yes—
293C22C2×D4×D4711yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—941no—
298C4—941no—
299C4—1881no—
300C4—1882no—
301C4#1309400912yes—
302C4C2×#1062535011yescharacteristic
303C4C2×#1062535411yescharacteristic
304C2—22no—
305C2—942no—
306C2—942no—
307C2—3761no—
308C2C2×#1309400911yescharacteristic
309C2AGL(1,ℤ/8)×D4711yescharacteristic
310C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3092
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. #15689460C2semidirect
4. #15689455C2semidirect
5. #15689443C2semidirect
6. #15689438C2semidirect
7. #15689166C2semidirect
8. #15689125C2semidirect
9. #15689122C2semidirect
10. #15689086C2semidirect
11. C47×#428C2semidirect
30. #13093957C22semidirect
31. #13093955C22semidirect
32. #13093949C22semidirect
33. #13093947C22semidirect
34. #13093946C22semidirect
35. #13093944C22semidirect
41. #107×C47C22semidirect
42. #106×C47C22semidirect
163. #428D47semidirect
167. C47#3092semidirect
190. #107C2×D47semidirect
192. #106C2×D47semidirect