Finite Group Databasebeta

← #20252697

Subgroups — #20252697

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×#13094069C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3C2×#13094046C211yesmaximal, characteristic, complemented
4#15689704C211yesmaximal, characteristic, complemented
5#15689286C212yesmaximal, complemented
6#15689275C212yesmaximal, complemented
7#15689269C212yesmaximal, complemented
8#15689258C212yesmaximal, complemented
9#15689122C211yesmaximal, characteristic, complemented
10#15689089C211yesmaximal, characteristic, complemented
11C2×#102×C47C211yesmaximal, characteristic, complemented
12#13094069—24no—
13#13094069—24no—
14C2×#10625350C2211yescharacteristic
15C2×#10625350C2211yescharacteristic
16C2×#10625350C2211yescharacteristic, complemented
17C2×#10625352—21no—
18C2×#10625352C2212yes—
19C22×C22⋊D47—22no—
20C2×D4×D47—21no—
21C2×D4×D47C2212yes—
22#13094050—24no—
23#13094046—24no—
24C2×Dic188C2211yescharacteristic, complemented
25C2×#10625325C2211yescharacteristic, complemented
26C2×#10625325C2211yescharacteristic, complemented
27C2×#10625335C2212yescomplemented
28C2×D376C2211yescharacteristic, complemented
29C2×#10625334C2212yescomplemented
30C2×#10625329C2211yescharacteristic, complemented
31#13094004—21no—
32#13094004C2212yescomplemented
33#13093999—21no—
34#13093999C2212yescomplemented
35#13093998—22no—
36#13093947C2212yescomplemented
37#13093944C2212yescomplemented
38(C2×D47)⋊C8C2212yescomplemented
39(C2×D47)⋊C8C2212yescomplemented
40C22×D4×C47C2211yescharacteristic
41C22×C8×C47C2211yescharacteristic, complemented
42C2×C4⋊C4×C47C2211yescharacteristic, complemented
43#102×C47C2212yescomplemented
44#102×C47C2212yescomplemented
45C24×C47—21no—
46C23×D47—22no—
47C2×D4×C47—21no—
48C2×D4×C47—22no—
49C2×D4×C47D414yescomplemented
50C2×D4×C47C2312yes—
51C22×C4×C47—21no—
52C22×C4×C47C2311yescharacteristic
53C2×C22⋊D47—216no—
54C2×C22⋊D47—21no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—21no—
57C2×C22⋊D47—22no—
58C2×C22⋊D47D412yes—
59C22×Dic47—22no—
60#10625352—28no—
61#10625352—24no—
62#10625352—24no—
63D4×D47—28no—
64D4×D47—24no—
65D4×D47—24no—
66#10625350—22no—
67#10625350—22no—
68#10625350—22no—
69#10625350—22no—
70#10625350—22no—
71#10625350D414yescomplemented
72C2×D188—22no—
73C2×D188D411yescharacteristic
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47C2312yes—
79C2×Dic94D411yescharacteristic
80C2×Dic94C2311yescharacteristic
81C2×Dic94C2311yescharacteristic
82C2×C8×C47—22no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2312yes—
87#10625335—24no—
88#10625334—24no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91C4⋊Dic47—22no—
92#10625329—22no—
93C2×C47⋊C8C2312yes—
94Dic188—22no—
95D376—22no—
96#10625325—22no—
97#10625325—22no—
98C23×C47—22no—
99C23×C47—24no—
100C23×C47—81no—
101C23×C47—81no—
102C23×C47C2×D411yescharacteristic
103C22×D47—21no—
104C22×D47—28no—
105C22×D47—21no—
106C22×D47—82no—
107C22×D47—82no—
108C22×D47C2×D412yes—
109D4×C47—24no—
110D4×C47—22no—
111D4×C47C2×D414yes—
112C2×C4×C47—22no—
113C2×C4×C47—81no—
114C2×C4×C47C2×D412yes—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D412yes—
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—28no—
119C22⋊D47—28no—
120C22⋊D47—24no—
121C22⋊D47—24no—
122C22⋊D47—42no—
123C2×Dic47—28no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D412yes—
127D188—22no—
128D188—21no—
129D188—21no—
130D188—21no—
131D188—82no—
132D188C2×D412yes—
133C4×D47—24no—
134C4×D47—22no—
135C4×D47—22no—
136C4×D47—42no—
137Dic94—22no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94C2×D412yes—
142C8×C47—21no—
143C8×C47—21no—
144C47⋊C8—22no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—24no—
148C22×C47—42no—
149C22×C47—42no—
150C22×C47—84no—
151C22×C47#12012yes—
152C22×C47C22×D411yescharacteristic
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—22no—
156C2×D47—22no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—88no—
163C4×C47—42no—
164C4×C47#12012yes—
165C4×C47C22×D411yescharacteristic
166C4×C47C22×D411yescharacteristic
167Dic47—22no—
168Dic47—22no—
169Dic47—41no—
170#3012—471nomaximal, Sylow
171C2×C47—22no—
172C2×C47—44no—
173C2×C47C2×#12011yescharacteristic
174C2×C47#57611yescharacteristic
175C2×C47#57711yescharacteristic
176D47—42no—
177D47—42no—
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#417—471no—
188C2×#102D4711yescharacteristic, complemented
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—471no—
197C2×#41—941no—
198C22×D4—472no—
199C22×D4—941no—
200C22×D4—942no—
201C22×D4C2×D4711yescharacteristic
202AGL(1,ℤ/8)—944no—
203#135—944no—
204C2×Q16—471no—
205C2×SD16—472no—
206C2×SD16—471no—
207C2×SD16—471no—
208C2×D8—472no—
209C2×D8—471no—
210C2×M16—471no—
211C22×C8C2×D4711yescharacteristic, complemented
212C22⋊Q8—472no—
213C22⋊Q8—941no—
214#121—472no—
215#121—941no—
216#121—942no—
217C2×C4⋊C4C2×D4711yescharacteristic, complemented
218#103—472no—
219#102—472no—
220#102C2×D4712yescomplemented
221#102C2×D4712yescomplemented
222C22⋊C8—472no—
223C22⋊C8—472no—
224C24—21no—
225C24—942no—
226#41—474no—
227#41—944no—
228#41—948no—
229#41—944no—
230#41—942no—
231#41—942no—
232#41—942no—
233#41—942no—
234#41—942no—
235C2×Q8—471no—
236C2×Q8—471no—
237C2×Q8—471no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—472no—
241C2×D4—471no—
242C2×D4—471no—
243C2×D4—471no—
244C2×D4—942no—
245C2×D4—942no—
246C2×D4—944no—
247C2×D4—948no—
248C2×D4—942no—
249C2×D4—9416no—
250C2×D4—941no—
251C2×D4—944no—
252C2×D4—941no—
253C2×D4D18814yescomplemented
254C2×D4C22×D4712yes—
255C22×C4—21no—
256C22×C4—472no—
257C22×C4—942no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4C22×D4711yescharacteristic
261Q16—942no—
262SD16—942no—
263SD16—942no—
264SD16—944no—
265D8—942no—
266D8—944no—
267M16—942no—
268C2×C8—22no—
269C2×C8—472no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—942no—
274C4⋊C4C22×D4712yes—
275C22⋊C4—942no—
276C22⋊C4—942no—
277C23—22no—
278C23—24no—
279C23—81no—
280C23—81no—
281C23—472no—
282C23—948no—
283C23—941no—
284C23—941no—
285C23—3762no—
286C23—3762no—
287C23D4×D4711yescharacteristic
288Q8—472no—
289Q8—942no—
290Q8—941no—
291Q8—941no—
292Q8—941no—
293D4—24no—
294D4—22no—
295D4—472no—
296D4—948no—
297D4—948no—
298D4—944no—
299D4—944no—
300D4—942no—
301D4—941no—
302D4—941no—
303D4—941no—
304D4—3762no—
305D4—1882no—
306D4C2×D18814yes—
307C2×C4—22no—
308C2×C4—81no—
309C2×C4—472no—
310C2×C4—948no—
311C2×C4—941no—
312C2×C4—944no—
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—21no—
322C8—21no—
323C8—942no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—42no—
328C22—42no—
329C22—84no—
330C22—942no—
331C22—942no—
332C22—942no—
333C22—942no—
334C22—3768no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22#1309399412yes—
341C22C2×D4×D4711yescharacteristic
342C4—42no—
343C4—942no—
344C4—942no—
345C4—1881no—
346C4#1309399412yes—
347C4C2×D4×D4711yescharacteristic
348C4C22×D18811yescharacteristic
349C2—22no—
350C2—44no—
351C2—3761no—
352C2—1882no—
353C2—1882no—
354C2C2×#1309399411yescharacteristic
355C2#1568992411yescharacteristic
356C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#102×C47C2
socleC22×C47C22×D4
hypercenterC2×#102D47
hypocenterC47#3012
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13094069C2semidirect
2. C2×#13094050C2semidirect
3. C2×#13094046C2semidirect
4. #15689704C2semidirect
5. #15689286C2semidirect
6. #15689275C2semidirect
7. #15689269C2semidirect
8. #15689258C2semidirect
9. #15689122C2semidirect
10. #15689089C2semidirect
11. C2×#102×C47C2semidirect
16. C2×#10625350C22semidirect
24. C2×Dic188C22semidirect
25. C2×#10625325C22semidirect
26. C2×#10625325C22semidirect
27. C2×#10625335C22semidirect
28. C2×D376C22semidirect
29. C2×#10625334C22semidirect
30. C2×#10625329C22semidirect
32. #13094004C22semidirect
34. #13093999C22semidirect
36. #13093947C22semidirect
37. #13093944C22semidirect
38. (C2×D47)⋊C8C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C22×C8×C47C22semidirect
42. C2×C4⋊C4×C47C22semidirect
43. #102×C47C22semidirect
44. #102×C47C22semidirect
49. C2×D4×C47D4semidirect
71. #10625350D4semidirect
188. C2×#102D47semidirect
190. C47#3012semidirect
211. C22×C8C2×D47semidirect
217. C2×C4⋊C4C2×D47semidirect
220. #102C2×D47semidirect
221. #102C2×D47semidirect
253. C2×D4D188semidirect