Finite Group Databasebeta

← #20252694

Subgroups — #20252694

Order 6016.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094070C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic, complemented
3C2×#13094044C211yesmaximal, characteristic, complemented
4#15689704C211yesmaximal, characteristic, complemented
5#15689288C212yesmaximal, complemented
6#15689275C212yesmaximal, complemented
7#15689271C212yesmaximal, complemented
8#15689258C212yesmaximal, complemented
9C2×#13093944C211yesmaximal, characteristic, complemented
10#15689091C211yesmaximal, characteristic, complemented
11C47×#417C211yesmaximal, characteristic, complemented
12#13094070—24no—
13#13094070—24no—
14C2×#10625354C2212yes—
15C2×#10625350—21no—
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic, complemented
18C22×D188—21no—
19C22×D188C2211yescharacteristic
20C2×D4×D47—22no—
21C2×D4×D47C2212yes—
22#13094052—24no—
23#13094044—24no—
24C2×#10625337C2211yescharacteristic, complemented
25C2×#10625325C2212yescomplemented
26C2×#10625335C2211yescharacteristic, complemented
27C2×#10625336C2211yescharacteristic, complemented
28C2×D376C2212yescomplemented
29C2×#10625334C2211yescharacteristic, complemented
30C22×C47⋊C8C2211yescharacteristic, complemented
31#13094004—21no—
32#13094004C2212yescomplemented
33#13093999—21no—
34#13093999C2212yescomplemented
35#13093998—22no—
36#13093944C2212yescomplemented
37#13093944C2212yescomplemented
38(C2×D47)⋊C8C2212yescomplemented
39(C2×D47)⋊C8C2212yescomplemented
40C2×#41×C47C2211yescharacteristic
41C2×M16×C47C2211yescharacteristic, complemented
42C2×C4⋊C4×C47C2211yescharacteristic, complemented
43#103×C47C2212yescomplemented
44#102×C47C2212yescomplemented
45C23×D47—21no—
46C23×D47—22no—
47#41×C47—22no—
48#41×C47D414yescomplemented
49C2×Q8×C47C2311yescharacteristic
50C2×D4×C47—21no—
51C2×D4×C47C2311yescharacteristic
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—21no—
56C2×C22⋊D47—22no—
57C2×C22⋊D47D412yes—
58#10625354—24no—
59#10625354—24no—
60D4×D47—216no—
61D4×D47—24no—
62D4×D47—24no—
63#10625350—28no—
64#10625350—22no—
65#10625350—22no—
66#10625350—22no—
67#10625350—22no—
68C2×D188—28no—
69C2×D188—22no—
70C2×D188—21no—
71C2×D188—22no—
72C2×D188—22no—
73C2×D188D411yescharacteristic
74C2×D188D414yescomplemented
75C2×D188C2311yescharacteristic
76C2×D188C2312yes—
77C2×C4×D47—22no—
78C2×C4×D47—21no—
79C2×C4×D47C2312yes—
80C2×Dic94D411yescharacteristic
81C2×Dic94C2311yescharacteristic
82M16×C47—22no—
83C2×C8×C47C2312yes—
84C4⋊C4×C47—21no—
85C4⋊C4×C47C2312yes—
86#10625337—22no—
87#10625336—22no—
88#10625335—22no—
89#10625334—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92C4⋊Dic47—22no—
93C2×C47⋊C8—22no—
94C2×C47⋊C8C2311yescharacteristic
95C2×C47⋊C8C2311yescharacteristic
96D376—24no—
97#10625325—24no—
98C23×C47—21no—
99C23×C47C2×D411yescharacteristic
100C22×D47—22no—
101C22×D47—28no—
102C22×D47—24no—
103C22×D47—21no—
104C22×D47—82no—
105C22×D47—82no—
106C22×D47—81no—
107C22×D47—81no—
108C22×D47C2×D412yes—
109Q8×C47—21no—
110Q8×C47C2×D412yes—
111D4×C47—24no—
112D4×C47—21no—
113D4×C47C2×D412yes—
114C2×C4×C47—21no—
115C2×C4×C47—24no—
116C2×C4×C47—22no—
117C2×C4×C47—81no—
118C2×C4×C47C2×D412yes—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D412yes—
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—28no—
123C22⋊D47—24no—
124C22⋊D47—42no—
125C2×Dic47—21no—
126C2×Dic47C2×D412yes—
127D188—28no—
128D188—22no—
129D188—24no—
130D188—22no—
131D188—21no—
132D188—21no—
133D188—82no—
134D188C2×D414yes—
135C4×D47—28no—
136C4×D47—22no—
137C4×D47—22no—
138C4×D47—42no—
139Dic94—22no—
140Dic94—21no—
141Dic94—21no—
142C8×C47—22no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—22no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47#12012yes—
151C22×C47C22×D411yescharacteristic
152C2×D47—22no—
153C2×D47—24no—
154C2×D47—22no—
155C2×D47—22no—
156C2×D47—42no—
157C2×D47—42no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—84no—
162C2×D47—88no—
163C4×C47—22no—
164C4×C47—42no—
165C4×C47#12012yes—
166C4×C47C22×D411yescharacteristic
167C4×C47C22×D411yescharacteristic
168Dic47—22no—
169Dic47—41no—
170#3012—471nomaximal, Sylow
171C2×C47—22no—
172C2×C47—42no—
173C2×C47C2×#12011yescharacteristic
174C2×C47#57611yescharacteristic
175C2×C47#57711yescharacteristic
176D47—42no—
177D47—44no—
178D47—81no—
179C2×H(5,𝔽2)—471no—
180C2×AGL(1,ℤ/8)—471no—
181C2×#135—471no—
182#537—471no—
183#452—472no—
184#450—472no—
185#449—472no—
186#447—472no—
187#417D4711yescharacteristic, complemented
188C2×#102—471no—
189#408—471no—
190C47#301211yescharacteristic, complemented, Sylow
191H(5,𝔽2)—944no—
192H(5,𝔽2)—944no—
193C2×#41—471no—
194C2×#41—472no—
195C2×#41—471no—
196C2×#41—941no—
197C2×#41C2×D4711yescharacteristic
198C22×D4—472no—
199C22×D4—471no—
200C22×D4—941no—
201C22×D4—942no—
202AGL(1,ℤ/8)—944no—
203#135—944no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×SD16—472no—
208C2×D8—471no—
209C2×D8—472no—
210C2×M16C2×D4711yescharacteristic, complemented
211C22×C8—471no—
212C22⋊Q8—472no—
213C22⋊Q8—941no—
214#121—472no—
215#121—941no—
216#121—942no—
217C2×C4⋊C4C2×D4711yescharacteristic, complemented
218#103C2×D4712yescomplemented
219#102—472no—
220#102—472no—
221#102C2×D4712yescomplemented
222C22⋊C8—472no—
223C22⋊C8—472no—
224C24—942no—
225C24—941no—
226#41—22no—
227#41—948no—
228#41—944no—
229#41—944no—
230#41—942no—
231#41—942no—
232#41—942no—
233#41—942no—
234#41D18814yescomplemented
235C2×Q8—471no—
236C2×Q8—471no—
237C2×Q8C22×D4711yescharacteristic
238C2×D4—21no—
239C2×D4—472no—
240C2×D4—474no—
241C2×D4—471no—
242C2×D4—472no—
243C2×D4—471no—
244C2×D4—942no—
245C2×D4—948no—
246C2×D4—942no—
247C2×D4—942no—
248C2×D4—944no—
249C2×D4—9416no—
250C2×D4—944no—
251C2×D4—941no—
252C2×D4—942no—
253C2×D4—941no—
254C2×D4C22×D4711yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—472no—
258C22×C4—942no—
259C22×C4—941no—
260C22×C4C22×D4711yescharacteristic
261Q16—942no—
262SD16—944no—
263SD16—942no—
264SD16—942no—
265D8—944no—
266D8—942no—
267M16—22no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8—942no—
271C2×C8C22×D4712yes—
272C4⋊C4—21no—
273C4⋊C4—942no—
274C4⋊C4C22×D4712yes—
275C22⋊C4—942no—
276C22⋊C4—942no—
277C23—21no—
278C23—472no—
279C23—948no—
280C23—944no—
281C23—942no—
282C23—941no—
283C23—3761no—
284C23—3761no—
285C23—3762no—
286C23—3762no—
287C23D4×D4711yescharacteristic
288Q8—21no—
289Q8—942no—
290Q8—941no—
291Q8—941no—
292Q8C2×D18812yes—
293D4—24no—
294D4—21no—
295D4—474no—
296D4—948no—
297D4—948no—
298D4—944no—
299D4—944no—
300D4—942no—
301D4—941no—
302D4—942no—
303D4—941no—
304D4—3762no—
305D4—1882no—
306D4C2×D18812yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—81no—
311C2×C4—472no—
312C2×C4—948no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—941no—
316C2×C4—1882no—
317C2×C4C2×D18812yes—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4712yes—
320C2×C4C23×D4711yescharacteristic
321C8—22no—
322C8—941no—
323C8—941no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—944no—
330C22—942no—
331C22—942no—
332C22—942no—
333C22—3764no—
334C22—3768no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22—1882no—
339C22—1882no—
340C22#1309399412yes—
341C22C2×D4×D4711yescharacteristic
342C4—22no—
343C4—42no—
344C4—942no—
345C4—1881no—
346C4#1309399412yes—
347C4C2×D4×D4711yescharacteristic
348C4C22×D18811yescharacteristic
349C2—22no—
350C2—42no—
351C2—3761no—
352C2—1882no—
353C2—1884no—
354C2C2×#1309399411yescharacteristic
355C2#1568992711yescharacteristic
356C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3012
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094052C2semidirect
3. C2×#13094044C2semidirect
4. #15689704C2semidirect
5. #15689288C2semidirect
6. #15689275C2semidirect
7. #15689271C2semidirect
8. #15689258C2semidirect
9. C2×#13093944C2semidirect
10. #15689091C2semidirect
11. C47×#417C2semidirect
17. C2×#10625350C22semidirect
24. C2×#10625337C22semidirect
25. C2×#10625325C22semidirect
26. C2×#10625335C22semidirect
27. C2×#10625336C22semidirect
28. C2×D376C22semidirect
29. C2×#10625334C22semidirect
30. C22×C47⋊C8C22semidirect
32. #13094004C22semidirect
34. #13093999C22semidirect
36. #13093944C22semidirect
37. #13093944C22semidirect
38. (C2×D47)⋊C8C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C2×M16×C47C22semidirect
42. C2×C4⋊C4×C47C22semidirect
43. #103×C47C22semidirect
44. #102×C47C22semidirect
48. #41×C47D4semidirect
74. C2×D188D4semidirect
187. #417D47semidirect
190. C47#3012semidirect
210. C2×M16C2×D47semidirect
217. C2×C4⋊C4C2×D47semidirect
218. #103C2×D47semidirect
221. #102C2×D47semidirect
234. #41D188semidirect