Finite Group Databasebeta

← #20252647

Subgroups — #20252647

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×#10625354C211yesmaximal, characteristic
2C2×#13094056C212yesmaximal, complemented
3C22⋊Q8×D47C211yesmaximal, characteristic, complemented
4#15689288C212yesmaximal, complemented
5#15689284C212yesmaximal, complemented
6#15689279C211yesmaximal, characteristic, complemented
7#15689276C211yesmaximal, characteristic, complemented
8#15689273C211yesmaximal, characteristic, complemented
9#15689123C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#451C211yesmaximal, characteristic, complemented
12C2×#10625354—28no—
13C2×#10625354—21no—
14C2×#10625354—21no—
15C2×#10625354C2212yes—
16C2×#10625354C2212yes—
17C2×Q8×D47C2211yescharacteristic, complemented
18C22×D188—21no—
19C22×D188C2211yescharacteristic
20C22×C4×D47—21no—
21C22×C4×D47C2211yescharacteristic
22#13094056—28no—
23C2×#10625337C2212yescomplemented
24C2×#10625325C2212yescomplemented
25C2×#10625336C2212yescomplemented
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#13093948C2212yescomplemented
36#13093946C2212yescomplemented
37#13093944C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic
39(C2×D47)⋊C8C2212yescomplemented
40C22×Q8×C47C2211yescharacteristic
41C2×Q16×C47C2212yescomplemented
42C22⋊Q8×C47C2211yescharacteristic
43#103×C47C2212yescomplemented
44C22⋊C8×C47C2211yescharacteristic
45C23×D47—21no—
46C23×D47D411yescharacteristic
47C2×Q8×C47—24no—
48C2×Q8×C47—21no—
49C2×Q8×C47C2311yescharacteristic
50C2×Q8×C47C2312yes—
51C22×C4×C47—21no—
52C22×C4×C47C2311yescharacteristic
53C22×Dic47D411yescharacteristic
54#10625354—28no—
55#10625354—28no—
56#10625354—24no—
57#10625354—24no—
58#10625354—24no—
59#10625354D418yes—
60Q8×D47—24no—
61C2×D188—28no—
62C2×D188—22no—
63C2×D188—22no—
64C2×D188—21no—
65C2×D188—24no—
66C2×D188C2312yes—
67C2×C4×D47—28no—
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—24no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79Q16×C47—24no—
80C2×C8×C47C2312yes—
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85#10625337—24no—
86#10625336—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—
95#10625325—24no—
96#10625324—24no—
97C23×C47C2×D411yescharacteristic
98C22×D47—24no—
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—22no—
102C22×D47—41no—
103C22×D47—42no—
104C22×D47—42no—
105C22×D47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107Q8×C47—24no—
108Q8×C47—22no—
109Q8×C47—22no—
110Q8×C47C2×D414yes—
111C2×C4×C47—24no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C2×Dic47—22no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123D188—28no—
124D188—24no—
125D188—28no—
126D188—22no—
127D188C2×D414yes—
128C4×D47—28no—
129C4×D47—22no—
130C4×D47—22no—
131C4×D47—28no—
132C4×D47—22no—
133C4×D47—42no—
134C4×D47—42no—
135C4×D47C2×D414yes—
136Dic94—22no—
137Dic94—42no—
138C8×C47—22no—
139C47⋊C8—22no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47#13712yescomplemented
143C22×C47C22×D411yescharacteristic
144C2×D47—21no—
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—24no—
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—44no—
151C2×D47—48no—
152C2×D47—42no—
153C2×D47—42no—
154C2×D47#12012yes—
155C4×C47—24no—
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C22×D412yes—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163Dic47#12012yes—
164#3007—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47C2×#12011yescharacteristic
167C2×C47C2×#13711yescharacteristic
168C2×C47#57511yescharacteristic
169D47—22no—
170D47—41no—
171D47—44no—
172C22×#41—471no—
173C2×#137—472no—
174C2×C22⋊Q8—471no—
175#452—472no—
176#452—472no—
177#451—471no—
178#451D4711yescharacteristic, complemented
179#450—471no—
180#450—471no—
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×Q8C2×D4711yescharacteristic
191C22×D4—471no—
192C22×D4—941no—
193C23×C4—471no—
194C23×C4—941no—
195#137—948no—
196C2×Q16—472no—
197C2×Q16C2×D4712yescomplemented
198C2×SD16—472no—
199C2×SD16—472no—
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#103C2×D4712yescomplemented
212#102—472no—
213#102—472no—
214C22⋊C8—471no—
215C22⋊C8—472no—
216C22⋊C8C2×D4711yescharacteristic
217C24—471no—
218C24—941no—
219#41—478no—
220#41—944no—
221#41—944no—
222#41—948no—
223#41—948no—
224#41—944no—
225C2×Q8—24no—
226C2×Q8—21no—
227C2×Q8—471no—
228C2×Q8—941no—
229C2×Q8—944no—
230C2×Q8C22×D4711yescharacteristic
231C2×Q8C22×D4712yes—
232C2×D4—472no—
233C2×D4—944no—
234C2×D4—942no—
235C2×D4—942no—
236C2×D4—948no—
237C2×D4—941no—
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—944no—
245C22×C4—942no—
246C22×C4—942no—
247C22×C4—948no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4C22×D4711yescharacteristic
251Q16—24no—
252Q16—944no—
253SD16—944no—
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—471no—
270C23—471no—
271C23—942no—
272C23—944no—
273C23—942no—
274C23—942no—
275C23—1881no—
276C23—1882no—
277C23—1882no—
278C23D4×D4711yescharacteristic
279Q8—24no—
280Q8—22no—
281Q8—22no—
282Q8—942no—
283Q8—1882no—
284Q8D4×D4714yes—
285D4—474no—
286D4—948no—
287D4—948no—
288D4—944no—
289D4—942no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—471no—
296C2×C4—474no—
297C2×C4—471no—
298C2×C4—942no—
299C2×C4—948no—
300C2×C4—942no—
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—472no—
315C22—941no—
316C22—941no—
317C22—944no—
318C22—941no—
319C22—941no—
320C22—941no—
321C22—1884no—
322C22—1888no—
323C22—1882no—
324C22—1882no—
325C22#1309405612yescomplemented
326C22C2×D4×D4711yescharacteristic
327C4—24no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—472no—
332C4—941no—
333C4—1881no—
334C4—1881no—
335C4C2×D4×D4712yes—
336C2—22no—
337C2—942no—
338C2—1881no—
339C2—1884no—
340C2#120×D4711yescharacteristic
341C2C2×#1309405611yescharacteristic
342C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3007
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#13094056C2semidirect
3. C22⋊Q8×D47C2semidirect
4. #15689288C2semidirect
5. #15689284C2semidirect
6. #15689279C2semidirect
7. #15689276C2semidirect
8. #15689273C2semidirect
9. #15689123C2semidirect
10. #15689085C2semidirect
11. C47×#451C2semidirect
17. C2×Q8×D47C22semidirect
23. C2×#10625337C22semidirect
24. C2×#10625325C22semidirect
25. C2×#10625336C22semidirect
26. C2×#10625324C22semidirect
27. #13094004C22semidirect
31. #13094000C22semidirect
33. C4⋊C4×D47C22semidirect
35. #13093948C22semidirect
36. #13093946C22semidirect
37. #13093944C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C2×Q16×C47C22semidirect
43. #103×C47C22semidirect
142. C22×C47#137semidirect
178. #451D47semidirect
183. C47#3007semidirect
197. C2×Q16C2×D47semidirect
211. #103C2×D47semidirect
325. C22#13094056semidirect