Finite Group Databasebeta

← #20257178

Subgroups — #20257178

Order 6016.

1540 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094072C211yesmaximal, characteristic, complemented
2C2×#13094069C211yesmaximal, characteristic, complemented
3#15689781C214yesmaximal, complemented
4#15689766C214yesmaximal, complemented
5#15689763C218yesmaximal, complemented
6#15689697C211yesmaximal, characteristic, complemented
7#15689693C212yesmaximal, complemented
8#15689691C212yesmaximal, complemented
9#15689690C211yesmaximal, characteristic, complemented
10#15689673C211yesmaximal, characteristic, complemented
11#15689672C212yesmaximal, complemented
12#124×D47C212yesmaximal, complemented
13C4×#10625350C211yesmaximal, characteristic, complemented
14C2×#124×C47C211yesmaximal, characteristic, complemented
15#13094072—28no—
16#13094069—28no—
17C2×#10625354C2212yescomplemented
18C2×#10625354C2212yescomplemented
19C2×#10625350C2211yescharacteristic
20C2×#10625350C2211yescharacteristic
21C2×#10625350C2214yescomplemented
22C2×#10625350C2211yescharacteristic, complemented
23C2×#10625352C2212yes—
24C2×#10625352C2212yes—
25C2×Q8×D47C2212yescomplemented
26C2×Q8×D47C2212yescomplemented
27C22×C22⋊D47C2214yes—
28C2×D4×D47C2212yes—
29C2×D4×D47C2212yes—
30#13094024C2211yescharacteristic, complemented
31#13094022C2212yescomplemented
32#13094021C2211yescharacteristic, complemented
33#13094020C2212yescomplemented
34#13094013C2212yescomplemented
35#13094012C2211yescharacteristic, complemented
36#13094012C2211yescharacteristic, complemented
37#13094011C2212yescomplemented
38#13094010C2218yescomplemented
39#13094007C2214yescomplemented
40#13094006C2218yescomplemented
41#13094001C2218yescomplemented
42#13094000C2214yescomplemented
43#13093998C2214yescomplemented
44#13093997C2218yescomplemented
45#13093997C2218yescomplemented
46#13093995C2214yescomplemented
47#13093994C2218yescomplemented
48#13093993C2214yescomplemented
49C4×Dic94C2212yescomplemented
50C4×D188C2212yescomplemented
51C4×D188C2214yescomplemented
52C4×C22⋊D47C2214yescomplemented
53(C22⋊D47)⋊C4C2218yescomplemented
54#13093983C2211yescharacteristic, complemented
55#13093981C2212yescomplemented
56C22⋊C4×D47C2218yescomplemented
57C42×D47C2212yescomplemented
58C22×Q8×C47C2211yescharacteristic, complemented
59C22×D4×C47C2211yescharacteristic
60#124×C47C2214yescomplemented
61#124×C47C2212yescomplemented
62#124×C47C2212yescomplemented
63C2×C22⋊C4×C47C2214yescomplemented
64C2×C42×C47C2211yescharacteristic, complemented
65C24×C47C2312yes—
66C23×D47C2314yes—
67C2×Q8×C47—24no—
68C2×Q8×C47C2312yes—
69C2×Q8×C47C2312yes—
70C2×D4×C47—24no—
71C2×D4×C47C2312yes—
72C2×D4×C47C2312yes—
73C22×C4×C47C2312yes—
74C22×C4×C47C2312yes—
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—216no—
77C2×C22⋊D47C2312yes—
78C2×C22⋊D47C2314yes—
79C2×C22⋊D47C2314yes—
80C2×C22⋊D47C2312yes—
81C2×C22⋊D47C2318yes—
82C2×C22⋊D47C2312yes—
83C22×Dic47C2314yes—
84#10625354—28no—
85#10625354—28no—
86Q8×D47—28no—
87Q8×D47—28no—
88#10625352—28no—
89#10625352—28no—
90D4×D47—28no—
91D4×D47—28no—
92#10625350—24no—
93#10625350—24no—
94#10625350—216no—
95#10625350D418yescomplemented
96C2×D188C2314yes—
97C2×D188C2311yescharacteristic
98C2×D188C2311yescharacteristic
99C2×D188C2314yes—
100C2×D188C2311yescharacteristic
101C2×C4×D47C2314yes—
102C2×C4×D47C2314yes—
103C2×C4×D47C2312yes—
104C2×C4×D47C2312yes—
105C2×C4×D47C2314yes—
106C2×C4×D47C2312yes—
107C2×Dic94C2314yes—
108C2×Dic94C2311yescharacteristic
109C2×Dic94C2311yescharacteristic
110C2×Dic94C2311yescharacteristic
111C22⋊C4×C47C2318yes—
112C22⋊C4×C47C2318yes—
113C42×C47C2311yescharacteristic
114C42×C47C2311yescharacteristic
115C42×C47C2312yes—
116C22⋊Dic47C2318yes—
117C22⋊Dic47C2312yes—
118(C2×D47)⋊C4C2314yes—
119(C2×D47)⋊C4C2318yes—
120(C2×D47)⋊C4C2314yes—
121(C2×D47)⋊C4C2314yes—
122C4⋊Dic47C2312yes—
123C4⋊Dic47C2314yes—
124Dic47⋊C4C2314yes—
125Dic47⋊C4C2318yes—
126C4×Dic47C2312yes—
127C4×Dic47C2314yes—
128C23×C47—24no—
129C23×C47—44no—
130C23×C47C2414yes—
131C23×C47C2411yescharacteristic
132C22×D47—28no—
133C22×D47—48no—
134C22×D47C2412yes—
135C22×D47C2412yes—
136C22×D47C2412yes—
137Q8×C47—24no—
138Q8×C47—24no—
139D4×C47—24no—
140D4×C47—24no—
141C2×C4×C47—24no—
142C2×C4×C47—42no—
143C2×C4×C47C2×D414yes—
144C2×C4×C47C2412yes—
145C2×C4×C47C2412yes—
146C2×C4×C47C2414yes—
147C2×C4×C47C2411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C22⋊D47—24no—
150C22⋊D47—24no—
151C22⋊D47—28no—
152C22⋊D47—28no—
153C22⋊D47—48no—
154C22⋊D47C2×D418yes—
155C2×Dic47—28no—
156C2×Dic47C2414yes—
157C2×Dic47C2412yes—
158C2×Dic47C2412yes—
159C2×Dic47C2412yes—
160D188—28no—
161D188—22no—
162D188—22no—
163D188—44no—
164D188C2×D414yes—
165C4×D47—28no—
166C4×D47—24no—
167C4×D47—24no—
168C4×D47—28no—
169C4×D47—44no—
170C4×D47C2×D418yes—
171Dic94—22no—
172Dic94—22no—
173Dic94—28no—
174Dic94C2×D414yes—
175C22×C47—22no—
176C22×C47—24no—
177C22×C47—28no—
178C22×C47—84no—
179C22×C47C22×D412yes—
180C22×C47C2511yescharacteristic
181C2×D47—24no—
182C2×D47—22no—
183C2×D47—22no—
184C2×D47—24no—
185C2×D47—24no—
186C2×D47—88no—
187C2×D47C22×D414yes—
188C4×C47—24no—
189C4×C47—22no—
190C4×C47—22no—
191C4×C47C22×D412yes—
192C4×C47C22×D412yes—
193Dic47—22no—
194Dic47—22no—
195Dic47—24no—
196Dic47C22×D414yes—
197#3500—471nomaximal, Sylow
198C2×C47—22no—
199C2×C47—44no—
200C2×C47C23×D411yescharacteristic
201C2×C47#58512yes—
202D47—24no—
203D47—42no—
204D47—42no—
205C2×2−1+4—471no—
206C2×H(5,𝔽2)—471no—
207#548—474no—
208#546—474no—
209#546—478no—
210#536—471no—
211#536—472no—
212#535—471no—
213#535—472no—
214#532—472no—
215#532—471no—
216C2×#124—472no—
217C2×#124D4711yescharacteristic, complemented
218C4×#41—471no—
219C47#350011yescharacteristic, complemented, Sylow
2202−1+4—948no—
221H(5,𝔽2)—948no—
222C2×#41—472no—
223C2×#41—472no—
224C2×#41—472no—
225C2×#41—472no—
226C2×#41—471no—
227C2×#41—471no—
228C2×#41—471no—
229C2×#41—474no—
230C22×Q8—472no—
231C22×Q8—472no—
232C22×Q8C2×D4711yescharacteristic, complemented
233C22×D4—474no—
234C22×D4—472no—
235C22×D4—472no—
236C22×D4C2×D4711yescharacteristic
237C4⋊Q8—472no—
238C4⋊Q8—471no—
239#127—472no—
240#127—471no—
241#124—472no—
242#124—472no—
243#124—478no—
244#124—471no—
245#124—471no—
246#124C2×D4712yescomplemented
247#124C2×D4712yescomplemented
248#124C2×D4714yescomplemented
249#123—474no—
250#123—478no—
251C22⋊Q8—474no—
252C22⋊Q8—478no—
253#121—474no—
254#121—474no—
255#121—478no—
256#121—478no—
257#120—474no—
258#120—478no—
259C4×Q8—472no—
260C4×D4—474no—
261C4×D4—478no—
262C4×D4—472no—
263C4×D4—474no—
264#117—471no—
265#117—472no—
266C2×C22⋊C4—478no—
267C2×C22⋊C4C2×D4714yescomplemented
268C2×C42—472no—
269C2×C42C2×D4711yescharacteristic, complemented
270C24—474no—
271C24C22×D4712yes—
272#41—478no—
273#41—9416no—
274#41—948no—
275#41—948no—
276#41—948no—
277#41—948no—
278#41—944no—
279#41—944no—
280C2×Q8—24no—
281C2×Q8—471no—
282C2×Q8—474no—
283C2×Q8—471no—
284C2×Q8—471no—
285C2×Q8—948no—
286C2×Q8—948no—
287C2×Q8C22×D4712yes—
288C2×Q8C22×D4712yes—
289C2×D4—24no—
290C2×D4—472no—
291C2×D4—472no—
292C2×D4—474no—
293C2×D4—472no—
294C2×D4—474no—
295C2×D4—478no—
296C2×D4—471no—
297C2×D4—474no—
298C2×D4—471no—
299C2×D4—471no—
300C2×D4—474no—
301C2×D4—948no—
302C2×D4—948no—
303C2×D4—9416no—
304C2×D4C22×D4712yes—
305C2×D4C22×D4712yes—
306C22×C4—472no—
307C22×C4—474no—
308C22×C4—474no—
309C22×C4—474no—
310C22×C4—472no—
311C22×C4—472no—
312C22×C4—474no—
313C22×C4C22×D4712yes—
314C22×C4C22×D4712yes—
315C22×C4C22×D4711yescharacteristic
316C4⋊C4—474no—
317C4⋊C4—478no—
318C4⋊C4—472no—
319C4⋊C4—474no—
320C22⋊C4—478no—
321C22⋊C4—472no—
322C22⋊C4—474no—
323C22⋊C4—478no—
324C22⋊C4—474no—
325C22⋊C4—474no—
326C22⋊C4C22×D4718yes—
327C22⋊C4C22×D4718yes—
328C42—472no—
329C42—474no—
330C42C22×D4711yescharacteristic
331C42C22×D4711yescharacteristic
332C42C22×D4712yes—
333C23—24no—
334C23—44no—
335C23—472no—
336C23—472no—
337C23—472no—
338C23—948no—
339C23—1888no—
340C23C23×D4714yes—
341C23C23×D4711yescharacteristic
342Q8—24no—
343Q8—24no—
344Q8—474no—
345Q8—948no—
346Q8—942no—
347Q8—942no—
348D4—24no—
349D4—24no—
350D4—478no—
351D4—474no—
352D4—948no—
353D4—948no—
354D4—948no—
355D4—944no—
356D4—944no—
357D4—942no—
358D4—942no—
359D4—1884no—
360D4—1888no—
361C2×C4—24no—
362C2×C4—42no—
363C2×C4—472no—
364C2×C4—478no—
365C2×C4—474no—
366C2×C4—472no—
367C2×C4—472no—
368C2×C4—948no—
369C2×C4—948no—
370C2×C4—948no—
371C2×C4—944no—
372C2×C4—944no—
373C2×C4—1884no—
374C2×C4D4×D4714yes—
375C2×C4C23×D4712yes—
376C2×C4C23×D4712yes—
377C2×C4C23×D4714yes—
378C2×C4C23×D4711yescharacteristic
379C2×C4C23×D4711yescharacteristic
380C22—22no—
381C22—24no—
382C22—28no—
383C22—84no—
384C22—474no—
385C22—944no—
386C22—942no—
387C22—942no—
388C22—944no—
389C22—944no—
390C22—3768no—
391C22C2×D4×D4712yes—
392C22C24×D4711yescharacteristic
393C4—24no—
394C4—22no—
395C4—22no—
396C4—474no—
397C4—942no—
398C4—942no—
399C4—944no—
400C4C2×D4×D4712yes—
401C4C2×D4×D4712yes—
402C2—22no—
403C2—44no—
404C2—944no—
405C2—1882no—
406C2—1882no—
407C2C22×D4×D4711yescharacteristic
408C2#1568995912yes—
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC2×#124×C47C2
hypercenterC2×#124D47
hypocenterC47#3500
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. C2×#13094069C2semidirect
3. #15689781C2semidirect
4. #15689766C2semidirect
5. #15689763C2semidirect
6. #15689697C2semidirect
7. #15689693C2semidirect
8. #15689691C2semidirect
9. #15689690C2semidirect
10. #15689673C2semidirect
11. #15689672C2semidirect
12. #124×D47C2semidirect
13. C4×#10625350C2semidirect
14. C2×#124×C47C2semidirect
17. C2×#10625354C22semidirect
18. C2×#10625354C22semidirect
21. C2×#10625350C22semidirect
22. C2×#10625350C22semidirect
25. C2×Q8×D47C22semidirect
26. C2×Q8×D47C22semidirect
30. #13094024C22semidirect
31. #13094022C22semidirect
32. #13094021C22semidirect
33. #13094020C22semidirect
34. #13094013C22semidirect
35. #13094012C22semidirect
36. #13094012C22semidirect
37. #13094011C22semidirect
38. #13094010C22semidirect
39. #13094007C22semidirect
40. #13094006C22semidirect
41. #13094001C22semidirect
42. #13094000C22semidirect
43. #13093998C22semidirect
44. #13093997C22semidirect
45. #13093997C22semidirect
46. #13093995C22semidirect
47. #13093994C22semidirect
48. #13093993C22semidirect
49. C4×Dic94C22semidirect
50. C4×D188C22semidirect
51. C4×D188C22semidirect
52. C4×C22⋊D47C22semidirect
53. (C22⋊D47)⋊C4C22semidirect
54. #13093983C22semidirect
55. #13093981C22semidirect
56. C22⋊C4×D47C22semidirect
57. C42×D47C22semidirect
58. C22×Q8×C47C22semidirect
60. #124×C47C22semidirect
61. #124×C47C22semidirect
62. #124×C47C22semidirect
63. C2×C22⋊C4×C47C22semidirect
64. C2×C42×C47C22semidirect
95. #10625350D4semidirect
217. C2×#124D47semidirect
219. C47#3500semidirect
232. C22×Q8C2×D47semidirect
246. #124C2×D47semidirect
247. #124C2×D47semidirect
248. #124C2×D47semidirect
267. C2×C22⋊C4C2×D47semidirect
269. C2×C42C2×D47semidirect