Finite Group Databasebeta

← #20254410

Subgroups — #20254410

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
1#127×D47C211yesmaximal, characteristic, complemented
2#15689660C211yesmaximal, characteristic, complemented
3#15689509C212yesmaximal, complemented
4#15689486C212yesmaximal, complemented
5#15689323C211yesmaximal, characteristic, complemented
6#15689319C211yesmaximal, characteristic, complemented
7#15689315C211yesmaximal, characteristic, complemented
8#15689272C212yesmaximal, complemented
9#15689258C212yesmaximal, complemented
10#15689179C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15C2×#10625336C2212yescomplemented
16C2×D376C2212yescomplemented
17C2×#10625334C2212yescomplemented
18#13094021C2211yescharacteristic
19#13094020—21no—
20#13094020—21no—
21#13094020C2212yes—
22#13094019—21no—
23#13094015C2211yescharacteristic, complemented
24#13094013C2211yescharacteristic, complemented
25#13094009—21no—
26#13094000C2211yescharacteristic
27#13093999C2211yescharacteristic
28C4×D188—21no—
29C4×D188C2211yescharacteristic, complemented
30#13093981—21no—
31C42×D47C2211yescharacteristic
32C4⋊(C47⋊C8)C2211yescharacteristic, complemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093944C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37#13093934C2212yescomplemented
38C2×SD16×C47C2212yescomplemented
39#127×C47C2211yescharacteristic
40C4×Q8×C47C2211yescharacteristic, complemented
41C4⋊C8×C47C2211yescharacteristic, complemented
42#102×C47C2212yescomplemented
43C23×D47—22no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47—21no—
47C2×D4×C47C2312yes—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51D4×D47—42no—
52D4×D47—42no—
53D4×D47—44no—
54D4×D47—44no—
55C2×D188—21no—
56C2×D188—21no—
57C2×D188—21no—
58C2×D188C2312yes—
59C2×D188C2311yescharacteristic
60C2×C4×D47—21no—
61C2×C4×D47D411yescharacteristic
62C2×C4×D47D411yescharacteristic
63C2×C4×D47C2311yescharacteristic
64SD16×C47—42no—
65C2×C8×C47C2312yes—
66C4⋊C4×C47—21no—
67C4⋊C4×C47C2311yescharacteristic
68C42×C47—21no—
69C42×C47C2311yescharacteristic
70#10625336—42no—
71#10625334—42no—
72(C2×D47)⋊C4—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⋊Dic47C2311yescharacteristic
79Dic47⋊C4—21no—
80Dic47⋊C4—21no—
81C4×Dic47D411yescharacteristic
82C4×Dic47D411yescharacteristic
83C4×Dic47C2311yescharacteristic
84C2×C47⋊C8C2312yes—
85D376—42no—
86C23×C47—22no—
87C22×D47—21no—
88C22×D47—22no—
89C22×D47—44no—
90C22×D47—44no—
91C22×D47—44no—
92C22×D47C2×D411yescharacteristic
93Q8×C47—21no—
94Q8×C47—21no—
95D4×C47—22no—
96D4×C47—22no—
97D4×C47—42no—
98D4×C47—42no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—44no—
105C22⋊D47—44no—
106C22⋊D47—44no—
107C2×Dic47—21no—
108C2×Dic47C2×D411yescharacteristic
109C2×Dic47C2×D411yescharacteristic
110C2×Dic47C2×D411yescharacteristic
111D188—21no—
112D188—22no—
113D188—21no—
114D188—22no—
115D188—42no—
116D188—42no—
117D188—42no—
118C4×D47—22no—
119C4×D47—22no—
120C4×D47—21no—
121C4×D47—21no—
122C4×D47—42no—
123C8×C47—22no—
124C47⋊C8—22no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47C22×D411yescharacteristic
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—42no—
132C2×D47—41no—
133C2×D47—41no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—41no—
137C2×D47—88no—
138C2×D47AGL(1,ℤ/8)12yes—
139C4×C47—21no—
140C4×C47—41no—
141C4×C47—41no—
142C4×C47AGL(1,ℤ/8)12yes—
143C4×C47H(5,𝔽2)11yescharacteristic
144C4×C47H(5,𝔽2)11yescharacteristic
145Dic47—21no—
146Dic47—21no—
147Dic47—21no—
148Dic47—41no—
149#3217—471nomaximal, Sylow
150C2×C47—82no—
151C2×C47#53511yescharacteristic
152C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
154D47—22no—
155D47—81no—
156D47—82no—
157C2×#127—471no—
158#529—471no—
159#496—472no—
160#490—472no—
161#460—471no—
162#460D4711yescharacteristic, complemented
163#459—471no—
164#459—471no—
165#450—472no—
166#447—472no—
167#432—471no—
168C47#321711yescharacteristic, complemented, Sylow
169C22×D4—472no—
170C22×D4—941no—
171C22×D4—941no—
172C2×SD16—472no—
173C2×SD16C2×D4712yescomplemented
174C2×D8—472no—
175C2×D8—472no—
176#127—472no—
177#127—471no—
178#127—941no—
179#127—941no—
180#127C2×D4711yescharacteristic
181#126—941no—
182#125—471no—
183#124—471no—
184#123—941no—
185C22⋊Q8—471no—
186#121—471no—
187C4×Q8C2×D4711yescharacteristic, complemented
188C4×D4—471no—
189C4×D4—941no—
190#117—941no—
191C2×C42—471no—
192C4⋊C8—471no—
193C4⋊C8C2×D4711yescharacteristic, complemented
194#102—472no—
195#102—472no—
196#102—472no—
197#102C2×D4712yescomplemented
198C22⋊C8—472no—
199#97—472no—
200C24—942no—
201C2×Q8C22×D4711yescharacteristic
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—472no—
205C2×D4—471no—
206C2×D4—941no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—941no—
211C2×D4—941no—
212C2×D4—1882no—
213C2×D4—1882no—
214C2×D4—1884no—
215C2×D4—1884no—
216C2×D4C22×D4712yes—
217C22×C4—471no—
218C22×C4—471no—
219C22×C4—471no—
220C22×C4—941no—
221SD16—42no—
222SD16—1882no—
223D8—1882no—
224D8—1882no—
225C2×C8—472no—
226C2×C8C22×D4712yes—
227C4⋊C4—21no—
228C4⋊C4—471no—
229C4⋊C4—941no—
230C4⋊C4—941no—
231C4⋊C4—941no—
232C4⋊C4C22×D4711yescharacteristic
233C22⋊C4—941no—
234C22⋊C4—941no—
235C22⋊C4—941no—
236C22⋊C4—941no—
237C22⋊C4—941no—
238C42—21no—
239C42—471no—
240C42—471no—
241C42—471no—
242C42C22×D4711yescharacteristic
243C23—22no—
244C23—471no—
245C23—941no—
246C23—942no—
247C23—1884no—
248C23—1884no—
249C23—1884no—
250Q8—21no—
251Q8—21no—
252D4—22no—
253D4—22no—
254D4—42no—
255D4—42no—
256D4—941no—
257D4—942no—
258D4—941no—
259D4—942no—
260D4—1882no—
261D4—1882no—
262D4—1884no—
263D4—1884no—
264D4—1884no—
265D4—1882no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—471no—
269C2×C4—471no—
270C2×C4—471no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—941no—
274C2×C4—941no—
275C2×C4—941no—
276C2×C4—1882no—
277C2×C4D4×D4711yescharacteristic
278C2×C4D4×D4711yescharacteristic
279C2×C4C23×D4711yescharacteristic
280C8—22no—
281C8—942no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—472no—
286C22—941no—
287C22—941no—
288C22—3768no—
289C22—1882no—
290C22—1881no—
291C22—1881no—
292C22—1882no—
293C22—1882no—
294C22—1881no—
295C22C2×D4×D4711yescharacteristic
296C4—21no—
297C4—41no—
298C4—41no—
299C4—941no—
300C4—941no—
301C4—941no—
302C4—1881no—
303C4#1309405112yes—
304C4#1309406911yescharacteristic
305C4#1309407011yescharacteristic
306C2—82no—
307C2—942no—
308C2—3762no—
309C2—3761no—
310C2#1568968911yescharacteristic
311C2AGL(1,ℤ/8)×D4711yescharacteristic
312C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3217
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #127×D47C2semidirect
2. #15689660C2semidirect
3. #15689509C2semidirect
4. #15689486C2semidirect
5. #15689323C2semidirect
6. #15689319C2semidirect
7. #15689315C2semidirect
8. #15689272C2semidirect
9. #15689258C2semidirect
10. #15689179C2semidirect
11. C47×#460C2semidirect
15. C2×#10625336C22semidirect
16. C2×D376C22semidirect
17. C2×#10625334C22semidirect
23. #13094015C22semidirect
24. #13094013C22semidirect
29. C4×D188C22semidirect
32. C4⋊(C47⋊C8)C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093944C22semidirect
37. #13093934C22semidirect
38. C2×SD16×C47C22semidirect
40. C4×Q8×C47C22semidirect
41. C4⋊C8×C47C22semidirect
42. #102×C47C22semidirect
162. #460D47semidirect
168. C47#3217semidirect
173. C2×SD16C2×D47semidirect
187. C4×Q8C2×D47semidirect
193. C4⋊C8C2×D47semidirect
197. #102C2×D47semidirect