Finite Group Databasebeta

← #20252635

Subgroups — #20252635

Order 6016.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#10625352C211yesmaximal, characteristic, complemented
2C2×#13094048C212yesmaximal, complemented
3#121×D47C211yesmaximal, characteristic, complemented
4#15689269C212yesmaximal, complemented
5#15689265C212yesmaximal, complemented
6#15689264C211yesmaximal, characteristic, complemented
7#15689261C211yesmaximal, characteristic, complemented
8#15689257C211yesmaximal, characteristic, complemented
9#15689121C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#447C211yesmaximal, characteristic, complemented
12C2×#10625352—28no—
13C2×#10625352—21no—
14C2×#10625352—21no—
15C2×#10625352C2212yes—
16C2×#10625352C2212yescomplemented
17C22×Dic94C2211yescharacteristic, complemented
18C22×C22⋊D47—21no—
19C2×D4×D47—21no—
20C2×D4×D47C2211yescharacteristic, complemented
21C23×Dic47—21no—
22C22×C4×D47C2211yescharacteristic
23#13094048—28no—
24C2×#10625325C2212yescomplemented
25C2×#10625335C2212yescomplemented
26C2×#10625334C2212yescomplemented
27C2×#10625324C2212yescomplemented
28#13093999C2211yescharacteristic, complemented
29#13093998C2211yescharacteristic
30#13093997—21no—
31#13093996—21no—
32#13093995C2211yescharacteristic, complemented
33C4⋊C4×D47C2211yescharacteristic, complemented
34C22⋊C4×D47—21no—
35#13093949C2212yescomplemented
36#13093947C2212yescomplemented
37#13093945C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic, complemented
39(C2×D47)⋊C8C2212yescomplemented
40C22×D4×C47C2211yescharacteristic, complemented
41C2×D8×C47C2212yescomplemented
42#121×C47C2211yescharacteristic
43#102×C47C2212yescomplemented
44C22⋊C8×C47C2211yescharacteristic, complemented
45C24×C47—21no—
46C23×D47—21no—
47C23×D47D411yescharacteristic
48C2×D4×C47—24no—
49C2×D4×C47—21no—
50C2×D4×C47—21no—
51C2×D4×C47C2311yescharacteristic
52C2×D4×C47C2312yes—
53C22×C4×C47C2311yescharacteristic
54C2×C22⋊D47—28no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—22no—
57C2×C22⋊D47—21no—
58C2×C22⋊D47—21no—
59C2×C22⋊D47—21no—
60C22×Dic47—28no—
61C22×Dic47—21no—
62C22×Dic47—22no—
63C22×Dic47—22no—
64C22×Dic47D411yescharacteristic
65#10625352—28no—
66#10625352—28no—
67#10625352—24no—
68#10625352—24no—
69#10625352—24no—
70#10625352D418yescomplemented
71D4×D47—24no—
72D4×D47—44no—
73C2×D188—21no—
74C2×D188C2311yescharacteristic
75C2×C4×D47—24no—
76C2×C4×D47—21no—
77C2×C4×D47D411yescharacteristic
78C2×C4×D47D411yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94—24no—
83C2×Dic94C2312yes—
84D8×C47—24no—
85C2×C8×C47C2312yes—
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊Dic47—21no—
89#10625335—24no—
90#10625334—24no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95C2×C47⋊C8C2312yes—
96#10625325—24no—
97#10625324—24no—
98C23×C47—24no—
99C23×C47—22no—
100C23×C47—21no—
101C23×C47—42no—
102C23×C47—42no—
103C23×C47C2×D411yescharacteristic
104C22×D47—22no—
105C22×D47—22no—
106C22×D47—21no—
107C22×D47—41no—
108C22×D47—42no—
109C22×D47—42no—
110C22×D47—42no—
111C22×D47C2×D411yescharacteristic
112C22×D47C2×D411yescharacteristic
113D4×C47—24no—
114D4×C47—22no—
115D4×C47—22no—
116D4×C47—42no—
117D4×C47C2×D414yescomplemented
118C2×C4×C47—22no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—28no—
123C22⋊D47—28no—
124C22⋊D47—42no—
125C22⋊D47—42no—
126C22⋊D47—42no—
127C2×Dic47—24no—
128C2×Dic47—28no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—28no—
132C2×Dic47—21no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—22no—
136D188—42no—
137C4×D47—22no—
138C4×D47—22no—
139C4×D47—22no—
140C4×D47—42no—
141C4×D47C2×D414yes—
142Dic94—24no—
143Dic94—22no—
144Dic94C2×D414yescomplemented
145C8×C47—22no—
146C47⋊C8—22no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—24no—
150C22×C47—48no—
151C22×C47—42no—
152C22×C47—42no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47AGL(1,ℤ/8)12yescomplemented
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—44no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C2×D47#12012yes—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47C22×D412yes—
172Dic47—24no—
173Dic47—21no—
174Dic47—41no—
175Dic47#12012yes—
176#3006—471nomaximal, Sylow
177C2×C47—22no—
178C2×C47—44no—
179C2×C47—81no—
180C2×C47C2×#12011yescharacteristic
181C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
182C2×C47#57511yescharacteristic
183D47—22no—
184D47—41no—
185D47—81no—
186C22×#41—471no—
187C2×AGL(1,ℤ/8)—472no—
188C2×#121—471no—
189#449—472no—
190#449—472no—
191#448—471no—
192#448—471no—
193#447—471no—
194#447D4711yescharacteristic, complemented
195#417—472no—
196#407—471no—
197C47#300611yescharacteristic, complemented, Sylow
198C2×#41—472no—
199C2×#41—472no—
200C2×#41—941no—
201C2×#41—941no—
202C2×#41—948no—
203C22×Q8—471no—
204C22×D4—471no—
205C22×D4—941no—
206C22×D4—941no—
207C22×D4C2×D4711yescharacteristic, complemented
208C23×C4—471no—
209C23×C4—941no—
210AGL(1,ℤ/8)—948no—
211C2×SD16—472no—
212C2×SD16—472no—
213C2×D8—472no—
214C2×D8C2×D4712yescomplemented
215C2×M16—472no—
216#121—471no—
217#121—471no—
218#121—471no—
219#121—941no—
220#121—941no—
221#121C2×D4711yescharacteristic
222C2×C4⋊C4—471no—
223C2×C22⋊C4—941no—
224#103—472no—
225#103—472no—
226#102—472no—
227#102C2×D4712yescomplemented
228C22⋊C8—471no—
229C22⋊C8—472no—
230C22⋊C8C2×D4711yescharacteristic, complemented
231C24—21no—
232C24—471no—
233C24—941no—
234#41—478no—
235#41—944no—
236#41—944no—
237#41—948no—
238#41—948no—
239#41—944no—
240C2×Q8—472no—
241C2×Q8—944no—
242C2×Q8—941no—
243C2×D4—24no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—471no—
247C2×D4—941no—
248C2×D4—944no—
249C2×D4—941no—
250C2×D4—942no—
251C2×D4—942no—
252C2×D4—948no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4—1884no—
256C2×D4C22×D4711yescharacteristic
257C2×D4C22×D4712yes—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—944no—
264C22×C4—941no—
265C22×C4—942no—
266C22×C4—942no—
267C22×C4—948no—
268C22×C4—941no—
269C22×C4C22×D4711yescharacteristic
270SD16—944no—
271SD16—944no—
272D8—24no—
273D8—944no—
274M16—944no—
275C2×C8—472no—
276C2×C8C22×D4712yes—
277C4⋊C4—471no—
278C4⋊C4—941no—
279C4⋊C4C22×D4711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C23—24no—
285C23—22no—
286C23—21no—
287C23—42no—
288C23—42no—
289C23—471no—
290C23—471no—
291C23—942no—
292C23—942no—
293C23—941no—
294C23—1881no—
295C23—1882no—
296C23—1882no—
297C23—1882no—
298C23D4×D4711yescharacteristic
299Q8—474no—
300Q8—944no—
301Q8—942no—
302D4—24no—
303D4—22no—
304D4—22no—
305D4—42no—
306D4—948no—
307D4—948no—
308D4—942no—
309D4—1882no—
310D4—1882no—
311D4—1882no—
312D4—1882no—
313D4D4×D4714yescomplemented
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—471no—
317C2×C4—474no—
318C2×C4—471no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—948no—
323C2×C4—944no—
324C2×C4—948no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—941no—
328C2×C4—1882no—
329C2×C4D4×D4711yescharacteristic
330C2×C4C23×D4711yescharacteristic
331C8—22no—
332C8—942no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—472no—
343C22—941no—
344C22—941no—
345C22—941no—
346C22—941no—
347C22—941no—
348C22—3764no—
349C22—1884no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22#1309404812yescomplemented
354C22C2×D4×D4711yescharacteristic
355C4—21no—
356C4—41no—
357C4—472no—
358C4—941no—
359C4—944no—
360C4—1881no—
361C4C2×D4×D4712yes—
362C2—22no—
363C2—44no—
364C2—81no—
365C2—942no—
366C2—3761no—
367C2—1881no—
368C2#120×D4711yescharacteristic
369C2C2×#1309404811yescharacteristic
370C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3006
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. C22×#10625352C2semidirect
2. C2×#13094048C2semidirect
3. #121×D47C2semidirect
4. #15689269C2semidirect
5. #15689265C2semidirect
6. #15689264C2semidirect
7. #15689261C2semidirect
8. #15689257C2semidirect
9. #15689121C2semidirect
10. #15689085C2semidirect
11. C47×#447C2semidirect
16. C2×#10625352C22semidirect
17. C22×Dic94C22semidirect
20. C2×D4×D47C22semidirect
24. C2×#10625325C22semidirect
25. C2×#10625335C22semidirect
26. C2×#10625334C22semidirect
27. C2×#10625324C22semidirect
28. #13093999C22semidirect
32. #13093995C22semidirect
33. C4⋊C4×D47C22semidirect
35. #13093949C22semidirect
36. #13093947C22semidirect
37. #13093945C22semidirect
38. C22⋊(C47⋊C8)C22semidirect
39. (C2×D47)⋊C8C22semidirect
40. C22×D4×C47C22semidirect
41. C2×D8×C47C22semidirect
43. #102×C47C22semidirect
44. C22⋊C8×C47C22semidirect
70. #10625352D4semidirect
117. D4×C47C2×D4semidirect
144. Dic94C2×D4semidirect
156. C22×C47AGL(1,ℤ/8)semidirect
194. #447D47semidirect
197. C47#3006semidirect
207. C22×D4C2×D47semidirect
214. C2×D8C2×D47semidirect
227. #102C2×D47semidirect
230. C22⋊C8C2×D47semidirect
313. D4D4×D47semidirect
353. C22#13094048semidirect