Finite Group Databasebeta

← #20252643

Subgroups — #20252643

Order 6016.

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

normal subgroups only

This group has 754 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
2C2×#13094053C212yesmaximal, complemented
3C22⋊Q8×D47C211yesmaximal, characteristic, complemented
4#15689286C212yesmaximal, complemented
5#15689282C212yesmaximal, complemented
6#15689281C211yesmaximal, characteristic, complemented
7#15689278C211yesmaximal, characteristic, complemented
8#15689274C211yesmaximal, characteristic, complemented
9#15689121C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#450C211yesmaximal, characteristic, complemented
12C2×#10625352—28no—
13C2×#10625352—21no—
14C2×#10625352—21no—
15C2×#10625352C2212yes—
16C2×#10625352C2212yes—
17C22×Dic94C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic, complemented
19C22×C22⋊D47—21no—
20C23×Dic47—21no—
21C22×C4×D47C2211yescharacteristic
22#13094053—28no—
23C2×Dic188C2212yescomplemented
24C2×#10625337C2212yescomplemented
25C2×#10625335C2212yescomplemented
26C2×#10625324C2212yescomplemented
27#13094004C2211yescharacteristic, complemented
28#13094003C2211yescharacteristic
29#13094002—21no—
30#13094001—21no—
31#13094000C2211yescharacteristic, complemented
32C4⋊C4×D47—21no—
33C4⋊C4×D47C2211yescharacteristic, complemented
34C22⋊C4×D47—21no—
35#13093949C2212yescomplemented
36#13093947C2212yescomplemented
37#13093945C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic
39(C2×D47)⋊C8C2212yescomplemented
40C22×D4×C47C2211yescharacteristic
41C2×SD16×C47C2212yescomplemented
42C22⋊Q8×C47C2211yescharacteristic
43#102×C47C2212yescomplemented
44C22⋊C8×C47C2211yescharacteristic
45C24×C47—21no—
46C23×D47D411yescharacteristic
47C2×Q8×C47C2311yescharacteristic
48C2×D4×C47—24no—
49C2×D4×C47—21no—
50C2×D4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—28no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C22×Dic47—28no—
56C22×Dic47—21no—
57C22×Dic47—22no—
58C22×Dic47—22no—
59C22×Dic47D411yescharacteristic
60Q8×D47—24no—
61#10625352—28no—
62#10625352—28no—
63#10625352—24no—
64#10625352—24no—
65#10625352—24no—
66#10625352D418yes—
67C2×C4×D47—24no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47D411yescharacteristic
71C2×C4×D47D411yescharacteristic
72C2×C4×D47C2311yescharacteristic
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94—24no—
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78C2×Dic94C2312yes—
79SD16×C47—24no—
80C2×C8×C47C2312yes—
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85#10625337—24no—
86#10625335—24no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94C2×C47⋊C8C2312yes—
95Dic188—24no—
96#10625324—24no—
97C23×C47—24no—
98C23×C47—22no—
99C23×C47—42no—
100C23×C47—42no—
101C23×C47C2×D411yescharacteristic
102C22×D47—22no—
103C22×D47—22no—
104C22×D47—41no—
105C22×D47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107Q8×C47—22no—
108D4×C47—24no—
109D4×C47—22no—
110D4×C47C2×D414yes—
111C2×C4×C47—22no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2411yescharacteristic
116C22⋊D47—28no—
117C22⋊D47—28no—
118C2×Dic47—24no—
119C2×Dic47—28no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—28no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C4×D47—22no—
128C4×D47—22no—
129C4×D47—22no—
130C4×D47—42no—
131C4×D47—42no—
132C4×D47C2×D414yes—
133Dic94—24no—
134Dic94—22no—
135Dic94—22no—
136Dic94—42no—
137Dic94C2×D414yes—
138C8×C47—22no—
139C47⋊C8—22no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—24no—
143C22×C47—48no—
144C22×C47—42no—
145C22×C47—42no—
146C22×C47#13712yescomplemented
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—44no—
154C2×D47#12012yes—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C22×D412yes—
159Dic47—24no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163Dic47#12012yes—
164#3007—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47—44no—
167C2×C47C2×#12011yescharacteristic
168C2×C47C2×#13711yescharacteristic
169C2×C47#57511yescharacteristic
170D47—22no—
171D47—41no—
172C22×#41—471no—
173C2×#137—472no—
174C2×C22⋊Q8—471no—
175#452—472no—
176#452—472no—
177#451—471no—
178#451—471no—
179#450—471no—
180#450D4711yescharacteristic, complemented
181#417—472no—
182#407—471no—
183C47#300711yescharacteristic, complemented, Sylow
184C2×#41—472no—
185C2×#41—472no—
186C2×#41—941no—
187C2×#41—941no—
188C2×#41—948no—
189C22×Q8—471no—
190C22×Q8—471no—
191C22×D4—941no—
192C22×D4C2×D4711yescharacteristic
193C23×C4—471no—
194C23×C4—941no—
195#137—948no—
196C2×Q16—472no—
197C2×Q16—472no—
198C2×SD16—472no—
199C2×SD16C2×D4712yescomplemented
200C2×M16—472no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—471no—
204C22⋊Q8—941no—
205C22⋊Q8—941no—
206C22⋊Q8C2×D4711yescharacteristic
207C2×C4⋊C4—471no—
208C2×C4⋊C4—941no—
209C2×C22⋊C4—941no—
210#103—472no—
211#103—472no—
212#102—472no—
213#102C2×D4712yescomplemented
214C22⋊C8—471no—
215C22⋊C8—472no—
216C22⋊C8C2×D4711yescharacteristic
217C24—21no—
218C24—471no—
219#41—478no—
220#41—944no—
221#41—944no—
222#41—948no—
223#41—948no—
224#41—944no—
225C2×Q8—472no—
226C2×Q8—471no—
227C2×Q8—941no—
228C2×Q8—944no—
229C2×Q8—944no—
230C2×Q8—941no—
231C2×Q8C22×D4711yescharacteristic
232C2×D4—24no—
233C2×D4—21no—
234C2×D4—942no—
235C2×D4—942no—
236C2×D4—948no—
237C2×D4C22×D4712yes—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—944no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—942no—
247C22×C4—942no—
248C22×C4—948no—
249C22×C4—941no—
250C22×C4C22×D4711yescharacteristic
251Q16—944no—
252Q16—944no—
253SD16—24no—
254SD16—944no—
255M16—944no—
256C2×C8—472no—
257C2×C8C22×D4712yes—
258C4⋊C4—21no—
259C4⋊C4—471no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C23—24no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23—471no—
274C23—471no—
275C23—942no—
276C23—942no—
277C23—1881no—
278C23D4×D4711yescharacteristic
279Q8—22no—
280Q8—474no—
281Q8—944no—
282Q8—942no—
283Q8—942no—
284Q8—1882no—
285D4—24no—
286D4—22no—
287D4—948no—
288D4—948no—
289D4D4×D4714yes—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—471no—
294C2×C4—474no—
295C2×C4—471no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—942no—
299C2×C4—948no—
300C2×C4—944no—
301C2×C4—948no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4C23×D4711yescharacteristic
310C8—22no—
311C8—942no—
312C22—21no—
313C22—21no—
314C22—24no—
315C22—48no—
316C22—42no—
317C22—42no—
318C22—472no—
319C22—941no—
320C22—941no—
321C22—941no—
322C22—941no—
323C22—941no—
324C22—1884no—
325C22#1309405312yescomplemented
326C22C2×D4×D4711yescharacteristic
327C4—21no—
328C4—41no—
329C4—41no—
330C4—472no—
331C4—941no—
332C4—944no—
333C4—1881no—
334C4—1881no—
335C4C2×D4×D4712yes—
336C2—22no—
337C2—44no—
338C2—942no—
339C2—1881no—
340C2#120×D4711yescharacteristic
341C2C2×#1309405311yescharacteristic
342C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3007
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×#13094053C2semidirect
3. C22⋊Q8×D47C2semidirect
4. #15689286C2semidirect
5. #15689282C2semidirect
6. #15689281C2semidirect
7. #15689278C2semidirect
8. #15689274C2semidirect
9. #15689121C2semidirect
10. #15689085C2semidirect
11. C47×#450C2semidirect
18. C2×Q8×D47C22semidirect
23. C2×Dic188C22semidirect
24. C2×#10625337C22semidirect
25. C2×#10625335C22semidirect
26. C2×#10625324C22semidirect
27. #13094004C22semidirect
31. #13094000C22semidirect
33. C4⋊C4×D47C22semidirect
35. #13093949C22semidirect
36. #13093947C22semidirect
37. #13093945C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C2×SD16×C47C22semidirect
43. #102×C47C22semidirect
146. C22×C47#137semidirect
180. #450D47semidirect
183. C47#3007semidirect
199. C2×SD16C2×D47semidirect
213. #102C2×D47semidirect
325. C22#13094053semidirect