Finite Group Databasebeta

← #20254186

Subgroups — #20254186

Order 6016.

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

normal subgroups only

This group has 514 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×#13093995C211yesmaximal, characteristic, complemented
2#121×D47C211yesmaximal, characteristic, complemented
3#15689442C211yesmaximal, characteristic, complemented
4#15689440C212yesmaximal, complemented
5#15689439C211yesmaximal, characteristic, complemented
6#15689375C212yesmaximal, complemented
7#15689373C212yesmaximal, complemented
8#15689257C211yesmaximal, characteristic, complemented
9#15689255C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#447C211yesmaximal, characteristic, complemented
12C22×C22⋊D47—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2211yescharacteristic, complemented
15C22×C4×D47C2211yescharacteristic
16C2×#10625334C2212yescomplemented
17C2×#10625324C2212yescomplemented
18#13093999C2211yescharacteristic, complemented
19#13093998C2211yescharacteristic
20#13093997—21no—
21#13093996—21no—
22#13093995—21no—
23#13093995—21no—
24#13093995C2212yes—
25#13093995C2211yescharacteristic, complemented
26#13093995C2212yescomplemented
27C2×C4⋊Dic47C2211yescharacteristic, complemented
28C4⋊C4×D47C2211yescharacteristic, complemented
29C2×C22⋊Dic47—21no—
30C22⋊C4×D47—21no—
31#13093956C2212yescomplemented
32#13093955C2212yescomplemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093945C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic, complemented
37(C2×D47)⋊C8C2212yescomplemented
38C22×D4×C47C2211yescharacteristic, complemented
39C2×D8×C47C2212yescomplemented
40#121×C47C2211yescharacteristic
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic, complemented
43C24×C47—21no—
44C23×D47—21no—
45C23×D47D411yescharacteristic
46C2×D4×C47—21no—
47C2×D4×C47—21no—
48C2×D4×C47—42no—
49C2×D4×C47C2311yescharacteristic
50C2×D4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—21no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—21no—
56C2×C22⋊D47—21no—
57C2×C22⋊D47—44no—
58C22×Dic47—21no—
59C22×Dic47D411yescharacteristic
60D4×D47—42no—
61D4×D47—44no—
62C2×D188—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—42no—
66C2×C4×D47D411yescharacteristic
67C2×C4×D47D411yescharacteristic
68C2×C4×D47C2311yescharacteristic
69C2×C4×D47C2311yescharacteristic
70D8×C47—42no—
71C2×C8×C47C2312yes—
72C4⋊C4×C47C2311yescharacteristic
73C22⋊C4×C47—21no—
74C22⋊Dic47—21no—
75C22⋊Dic47—22no—
76C22⋊Dic47—22no—
77#10625334—42no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47C2311yescharacteristic
82C4⋊Dic47C2312yes—
83Dic47⋊C4—21no—
84C2×C47⋊C8C2312yes—
85#10625324—42no—
86C23×C47—22no—
87C23×C47—21no—
88C23×C47—42no—
89C23×C47—42no—
90C23×C47—42no—
91C23×C47C2×D411yescharacteristic
92C22×D47—22no—
93C22×D47—22no—
94C22×D47—21no—
95C22×D47—41no—
96C22×D47—42no—
97C22×D47—42no—
98C22×D47—42no—
99C22×D47C2×D411yescharacteristic
100C22×D47C2×D411yescharacteristic
101D4×C47—22no—
102D4×C47—22no—
103D4×C47—22no—
104D4×C47—42no—
105D4×C47—42no—
106C2×C4×C47—22no—
107C2×C4×C47—21no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2411yescharacteristic
110C22⋊D47—42no—
111C22⋊D47—42no—
112C22⋊D47—44no—
113C22⋊D47—42no—
114C22⋊D47—44no—
115C2×Dic47—21no—
116C2×Dic47—22no—
117C2×Dic47—41no—
118C2×Dic47—42no—
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121D188—22no—
122D188—42no—
123C4×D47—22no—
124C4×D47—22no—
125C4×D47—41no—
126C4×D47—41no—
127C4×D47—42no—
128C8×C47—22no—
129C47⋊C8—22no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—41no—
133C22×C47—42no—
134C22×C47—42no—
135C22×C47—41no—
136C22×C47—41no—
137C22×C47—42no—
138C22×C47—84no—
139C22×C47AGL(1,ℤ/8)12yes—
140C22×C47C22×D411yescharacteristic
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—21no—
146C2×D47—44no—
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—84no—
151C2×D47AGL(1,ℤ/8)12yes—
152C4×C47—21no—
153C4×C47—41no—
154C4×C47H(5,𝔽2)12yes—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—42no—
159#3192—471nomaximal, Sylow
160C2×C47—22no—
161C2×C47—81no—
162C2×C47—82no—
163C2×C47#53411yescharacteristic
164C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
166D47—22no—
167D47—41no—
168D47—81no—
169C2×#121—471no—
170C2×#121—471no—
171#481—471no—
172#481—472no—
173#481—471no—
174#469—472no—
175#469—472no—
176#447—471no—
177#447—472no—
178#447D4711yescharacteristic, complemented
179#407—471no—
180C47#319211yescharacteristic, complemented, Sylow
181C22×D4—471no—
182C22×D4—941no—
183C22×D4—941no—
184C22×D4C2×D4711yescharacteristic, complemented
185C23×C4—471no—
186C2×D8—472no—
187C2×D8C2×D4712yescomplemented
188C2×M16—472no—
189#121—472no—
190#121—471no—
191#121—472no—
192#121—471no—
193#121—471no—
194#121—941no—
195#121—941no—
196#121—941no—
197#121—941no—
198#121C2×D4711yescharacteristic
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C22⋊C4—941no—
202C2×C22⋊C4—941no—
203#106—472no—
204#106—472no—
205#102—472no—
206#102—472no—
207#102—472no—
208#102C2×D4712yescomplemented
209C22⋊C8—471no—
210C22⋊C8—472no—
211C22⋊C8C2×D4711yescharacteristic, complemented
212C24—21no—
213C24—471no—
214C24—941no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—471no—
219C2×D4—941no—
220C2×D4—941no—
221C2×D4—942no—
222C2×D4—941no—
223C2×D4—942no—
224C2×D4—941no—
225C2×D4—1882no—
226C2×D4—1884no—
227C2×D4—1884no—
228C2×D4C22×D4711yescharacteristic
229C2×D4C22×D4712yes—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—1882no—
238C22×C4C22×D4711yescharacteristic
239D8—42no—
240D8—1882no—
241M16—1882no—
242C2×C8—472no—
243C2×C8C22×D4712yes—
244C4⋊C4—471no—
245C4⋊C4—472no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4C22×D4711yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—941no—
251C22⋊C4—941no—
252C22⋊C4—942no—
253C22⋊C4—942no—
254C22⋊C4—941no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—471no—
261C23—471no—
262C23—942no—
263C23—942no—
264C23—941no—
265C23—1881no—
266C23—1882no—
267C23—1882no—
268C23—1882no—
269C23D4×D4711yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—942no—
276D4—1882no—
277D4—1882no—
278D4—1884no—
279D4—1884no—
280D4—1882no—
281D4—1882no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—471no—
285C2×C4—471no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—942no—
289C2×C4—941no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1882no—
293C2×C4—1881no—
294C2×C4—1882no—
295C2×C4D4×D4711yescharacteristic
296C2×C4C23×D4711yescharacteristic
297C8—22no—
298C8—942no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—472no—
309C22—941no—
310C22—941no—
311C22—941no—
312C22—941no—
313C22—941no—
314C22—3764no—
315C22—1884no—
316C22—1881no—
317C22—1881no—
318C22—1881no—
319C22#1309404812yes—
320C22C2×D4×D4711yescharacteristic
321C4—21no—
322C4—41no—
323C4—941no—
324C4—941no—
325C4—1882no—
326C4—1881no—
327C4#1309406912yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—942no—
332C2—3761no—
333C2—1881no—
334C2#1568968311yescharacteristic
335C2AGL(1,ℤ/8)×D4711yescharacteristic
336C2C2×#1309404811yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3192
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#13093995C2semidirect
2. #121×D47C2semidirect
3. #15689442C2semidirect
4. #15689440C2semidirect
5. #15689439C2semidirect
6. #15689375C2semidirect
7. #15689373C2semidirect
8. #15689257C2semidirect
9. #15689255C2semidirect
10. #15689085C2semidirect
11. C47×#447C2semidirect
14. C2×D4×D47C22semidirect
16. C2×#10625334C22semidirect
17. C2×#10625324C22semidirect
18. #13093999C22semidirect
25. #13093995C22semidirect
26. #13093995C22semidirect
27. C2×C4⋊Dic47C22semidirect
28. C4⋊C4×D47C22semidirect
31. #13093956C22semidirect
32. #13093955C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093945C22semidirect
36. C22⋊(C47⋊C8)C22semidirect
37. (C2×D47)⋊C8C22semidirect
38. C22×D4×C47C22semidirect
39. C2×D8×C47C22semidirect
41. #102×C47C22semidirect
42. C22⋊C8×C47C22semidirect
178. #447D47semidirect
180. C47#3192semidirect
184. C22×D4C2×D47semidirect
187. C2×D8C2×D47semidirect
208. #102C2×D47semidirect
211. C22⋊C8C2×D47semidirect