Finite Group Databasebeta

← #20254409

Subgroups — #20254409

Order 6016.

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

normal subgroups only

This group has 490 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
1C2×#13094020C211yesmaximal, characteristic, complemented
2#15689659C211yesmaximal, characteristic, complemented
3#15689509C212yesmaximal, complemented
4#15689486C212yesmaximal, complemented
5#15689321C212yesmaximal, complemented
6#15689317C212yesmaximal, complemented
7#15689273C211yesmaximal, characteristic, complemented
8#15689259C211yesmaximal, characteristic, complemented
9#15689257C211yesmaximal, characteristic, complemented
10#15689177C211yesmaximal, characteristic, complemented
11C47×#450C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C22⋊D47—21no—
14C22×C22⋊D47—21no—
15C2×#10625336C2212yescomplemented
16C2×D376C2212yescomplemented
17C2×#10625334C2212yescomplemented
18#13094020—21no—
19#13094020—21no—
20#13094020C2212yes—
21#13094020C2212yes—
22#13094019—21no—
23#13094015C2211yescharacteristic, complemented
24#13094013C2211yescharacteristic, complemented
25#13094008—21no—
26#13093998C2211yescharacteristic
27Q8×Dic47C2211yescharacteristic, complemented
28#13093986C2211yescharacteristic, complemented
29(C22⋊D47)⋊C4—21no—
30#13093982—21no—
31C2×C4×Dic47C2211yescharacteristic
32Dic47⋊C8C2212yescomplemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093944C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37#13093934C2212yescomplemented
38C22×D4×C47C2211yescharacteristic
39C2×SD16×C47C2212yescomplemented
40C22⋊Q8×C47C2211yescharacteristic
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C24×C47—21no—
44C23×D47—21no—
45C2×Q8×C47C2311yescharacteristic
46C2×D4×C47—21no—
47C2×D4×C47—42no—
48C2×D4×C47C2312yes—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—22no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—44no—
56C2×C22⋊D47—44no—
57C22×Dic47D411yescharacteristic
58C22×Dic47D411yescharacteristic
59C2×D188—21no—
60C2×D188—42no—
61C2×D188C2312yes—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64SD16×C47—42no—
65C2×C8×C47C2312yes—
66C4⋊C4×C47—21no—
67C4⋊C4×C47C2311yescharacteristic
68C22⋊C4×C47—21no—
69#10625336—42no—
70#10625334—42no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75C4⋊Dic47—21no—
76C4⋊Dic47—21no—
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—21no—
79C4×Dic47—21no—
80C4×Dic47D411yescharacteristic
81C4×Dic47D411yescharacteristic
82C4×Dic47C2311yescharacteristic
83C4×Dic47C2311yescharacteristic
84C2×C47⋊C8C2312yes—
85D376—42no—
86C23×C47—22no—
87C23×C47—42no—
88C23×C47—42no—
89C23×C47—42no—
90C23×C47C2×D411yescharacteristic
91C22×D47—21no—
92C22×D47—22no—
93C22×D47—42no—
94C22×D47—42no—
95C22×D47—42no—
96Q8×C47—22no—
97D4×C47—22no—
98D4×C47—22no—
99D4×C47—42no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2411yescharacteristic
105C22⋊D47—44no—
106C22⋊D47—44no—
107C22⋊D47—44no—
108C22⋊D47—42no—
109C22⋊D47—44no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—21no—
113C2×Dic47C2×D411yescharacteristic
114C2×Dic47C2×D411yescharacteristic
115C2×Dic47C2×D411yescharacteristic
116C2×Dic47C2×D411yescharacteristic
117D188—22no—
118D188—22no—
119D188—22no—
120D188—42no—
121C4×D47—42no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—84no—
130C22×C47AGL(1,ℤ/8)12yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—42no—
133C2×D47—41no—
134C2×D47—41no—
135C2×D47—42no—
136C2×D47—42no—
137C2×D47—41no—
138C2×D47—84no—
139C4×C47—21no—
140C4×C47—41no—
141C4×C47—41no—
142C4×C47H(5,𝔽2)12yes—
143Dic47—21no—
144Dic47—21no—
145Dic47—21no—
146Dic47—41no—
147Dic47AGL(1,ℤ/8)12yes—
148#3217—471nomaximal, Sylow
149C2×C47—22no—
150C2×C47—82no—
151C2×C47#53511yescharacteristic
152C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
154D47—81no—
155D47—82no—
156C2×#127—471no—
157#529—471no—
158#496—472no—
159#490—472no—
160#460—472no—
161#459—472no—
162#450—471no—
163#450D4711yescharacteristic, complemented
164#447—471no—
165#447—471no—
166#432—471no—
167C47#321711yescharacteristic, complemented, Sylow
168C22×D4—471no—
169C22×D4—941no—
170C22×D4—941no—
171C22×D4C2×D4711yescharacteristic
172C2×SD16—472no—
173C2×SD16C2×D4712yescomplemented
174C2×D8—472no—
175C2×D8—472no—
176#127—472no—
177#127—472no—
178#127—941no—
179#127—941no—
180#126—941no—
181#125—471no—
182#124—471no—
183#123—941no—
184C22⋊Q8C2×D4711yescharacteristic
185#121—471no—
186C4×Q8—471no—
187C4×D4—471no—
188C4×D4—941no—
189#117—941no—
190C2×C42—471no—
191C4⋊C8—472no—
192#102—472no—
193#102—472no—
194#102—472no—
195#102C2×D4712yescomplemented
196C22⋊C8—471no—
197C22⋊C8C2×D4711yescharacteristic
198#97—472no—
199C24—21no—
200C24—941no—
201C2×Q8C22×D4711yescharacteristic
202C2×D4—21no—
203C2×D4—42no—
204C2×D4—472no—
205C2×D4—471no—
206C2×D4—942no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—941no—
211C2×D4—941no—
212C2×D4—1882no—
213C2×D4—1884no—
214C2×D4—1884no—
215C2×D4C22×D4712yes—
216C22×C4—471no—
217C22×C4—471no—
218C22×C4—941no—
219C22×C4C22×D4711yescharacteristic
220SD16—42no—
221SD16—1882no—
222D8—1882no—
223D8—1882no—
224C2×C8—472no—
225C2×C8C22×D4712yes—
226C4⋊C4—21no—
227C4⋊C4—471no—
228C4⋊C4—941no—
229C4⋊C4—941no—
230C4⋊C4—941no—
231C4⋊C4C22×D4711yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—941no—
234C22⋊C4—941no—
235C22⋊C4—941no—
236C22⋊C4—941no—
237C42—471no—
238C42—471no—
239C42—471no—
240C42—471no—
241C42—941no—
242C23—22no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—941no—
247C23—942no—
248C23—1882no—
249C23—1882no—
250C23—1882no—
251C23D4×D4711yescharacteristic
252Q8—22no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—942no—
257D4—942no—
258D4—942no—
259D4—1882no—
260D4—1884no—
261D4—1884no—
262D4—1884no—
263D4—1884no—
264D4—1882no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—471no—
269C2×C4—471no—
270C2×C4—471no—
271C2×C4—471no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—941no—
275C2×C4—1882no—
276C2×C4D4×D4711yescharacteristic
277C2×C4C23×D4711yescharacteristic
278C8—22no—
279C8—942no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—3764no—
287C22—1881no—
288C22—1882no—
289C22—1882no—
290C22—1881no—
291C22—1882no—
292C22—1881no—
293C22#1309405112yes—
294C22C2×D4×D4711yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—472no—
299C4—941no—
300C4—941no—
301C4—941no—
302C4—1881no—
303C4#1309406912yes—
304C2—22no—
305C2—82no—
306C2—3762no—
307C2—3761no—
308C2#1568968811yescharacteristic
309C2AGL(1,ℤ/8)×D4711yescharacteristic
310C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3217
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#13094020C2semidirect
2. #15689659C2semidirect
3. #15689509C2semidirect
4. #15689486C2semidirect
5. #15689321C2semidirect
6. #15689317C2semidirect
7. #15689273C2semidirect
8. #15689259C2semidirect
9. #15689257C2semidirect
10. #15689177C2semidirect
11. C47×#450C2semidirect
15. C2×#10625336C22semidirect
16. C2×D376C22semidirect
17. C2×#10625334C22semidirect
23. #13094015C22semidirect
24. #13094013C22semidirect
27. Q8×Dic47C22semidirect
28. #13093986C22semidirect
32. Dic47⋊C8C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093944C22semidirect
37. #13093934C22semidirect
39. C2×SD16×C47C22semidirect
41. #102×C47C22semidirect
163. #450D47semidirect
167. C47#3217semidirect
173. C2×SD16C2×D47semidirect
195. #102C2×D47semidirect