Finite Group Databasebeta

← #20253739

Subgroups — #20253739

Order 6016.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689750C211yesmaximal, characteristic, complemented
2#15689691C211yesmaximal, characteristic
3#15689488C211yesmaximal, characteristic, complemented
4#15689486C211yesmaximal, characteristic, complemented
5#15689484C211yesmaximal, characteristic, complemented
6#15689479C211yesmaximal, characteristic, complemented
7#15689477C211yesmaximal, characteristic, complemented
8#15689471C211yesmaximal, characteristic, complemented
9#15689468C211yesmaximal, characteristic, complemented
10#15689126C211yesmaximal, characteristic, complemented
11#15689123C211yesmaximal, characteristic, complemented
12#15689118C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#489C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023C2211yescharacteristic, complemented
21#13094022—21no—
22#13094021C2211yescharacteristic
23#13094020C2211yescharacteristic
24#13094016C2211yescharacteristic, complemented
25#13094015C2211yescharacteristic, complemented
26#13094014—21no—
27#13094013C2211yescharacteristic
28#13094002—21no—
29#13094000—21no—
30#13093997—21no—
31#13093997—21no—
32#13093994—21no—
33#13093994—21no—
34#13093982C2211yescharacteristic
35#13093981C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093948C2211yescharacteristic, complemented
38#13093948C2211yescharacteristic, complemented
39#13093946C2211yescharacteristic
40#13093946C2211yescharacteristic
41#13093946C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49#13093934C2211yescharacteristic, complemented
50C4×C47⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C4⋊Q8×C47C2211yescharacteristic, complemented
53#124×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic, complemented
55#103×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66#10625354—22no—
67#10625354—22no—
68D4×D47—22no—
69D4×D47—22no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—21no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C42×C47C2311yescharacteristic
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4D411yescharacteristic
91(C2×D47)⋊C4D411yescharacteristic
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—42no—
112C22×D47—81no—
113C22×D47—81no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—81no—
118D4×C47—21no—
119D4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—42no—
127C22⋊D47—81no—
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134D188—21no—
135D188—21no—
136D188—21no—
137D188—21no—
138D188—42no—
139D188—81no—
140D188—81no—
141C4×D47—42no—
142C4×D47—81no—
143C4×D47#4112yes—
144C4×D47#4112yes—
145Dic94—81no—
146C8×C47—21no—
147C8×C47—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47C22×D411yescharacteristic
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—84no—
163C2×D47#12412yes—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47C2×#4111yescharacteristic
171Dic47—21no—
172Dic47—21no—
173Dic47—41no—
174Dic47—41no—
175Dic47#12412yes—
176#3136—471nomaximal, Sylow
177C2×C47—81no—
178C2×C47C2×#12411yescharacteristic
179C2×C47#57611yescharacteristic
180C2×C47#57711yescharacteristic
181D47—22no—
182D47—81no—
183D47—81no—
184#544—471no—
185#535—471no—
186#490—471no—
187#490—471no—
188#489—471no—
189#489D4711yescharacteristic, complemented
190#488—471no—
191#488—471no—
192#486—471no—
193#486—471no—
194#418—471no—
195#417—471no—
196#416—471no—
197C2×#102—471no—
198#405—471no—
199C47#313611yescharacteristic, complemented, Sylow
200C2×#41—471no—
201C22×D4—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8—471no—
205C4⋊Q8—941no—
206C4⋊Q8C2×D4711yescharacteristic, complemented
207#127—471no—
208#127—471no—
209#125—471no—
210#125—471no—
211#125—941no—
212#124—471no—
213#124C2×D4711yescharacteristic
214C22⋊Q8—941no—
215C22⋊Q8—941no—
216#121—941no—
217#121—941no—
218#120—941no—
219#120—941no—
220#117—471no—
221#117—471no—
222C2×C4⋊C4—471no—
223#103—471no—
224#103—471no—
225#103C2×D4711yescharacteristic, complemented
226#103C2×D4711yescharacteristic, complemented
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102C2×D4711yescharacteristic
238#102C2×D4711yescharacteristic
239#97—471no—
240#97C2×D4711yescharacteristic, complemented
241C4×C8—471no—
242C4×C8—471no—
243C24—941no—
244#41—942no—
245#41—942no—
246C2×Q8—21no—
247C2×Q8—941no—
248C2×Q8C22×D4711yescharacteristic
249C2×D4—471no—
250C2×D4—471no—
251C2×D4—941no—
252C2×D4—942no—
253C2×D4—942no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4C22×D4711yescharacteristic
260C22×C4—471no—
261C22×C4—941no—
262C22×C4—941no—
263M16—942no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8—942no—
267C2×C8C22×D4711yescharacteristic
268C2×C8C22×D4711yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4C22×D4711yescharacteristic
281C4⋊C4C22×D4711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—471no—
285C22⋊C4—471no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—471no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—21no—
293C23—471no—
294C23—941no—
295C23—941no—
296C23—3761no—
297C23—3761no—
298C23—1882no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—3761no—
303D4—21no—
304D4—21no—
305D4—941no—
306D4—941no—
307D4—941no—
308D4—941no—
309D4—3761no—
310D4—3761no—
311D4—3761no—
312D4—3761no—
313D4—1882no—
314D4—1882no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—471no—
319C2×C4—472no—
320C2×C4—472no—
321C2×C4—471no—
322C2×C4—471no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—3761no—
326C2×C4—1882no—
327C2×C4D4×D4711yescharacteristic
328C2×C4D4×D4711yescharacteristic
329C2×C4C23×D4711yescharacteristic
330C8—21no—
331C8—21no—
332C8—941no—
333C8—941no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—472no—
338C22—941no—
339C22—941no—
340C22—3764no—
341C22—1881no—
342C22—1881no—
343C22—1881no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22C2×D4×D4711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—472no—
354C4—941no—
355C4—941no—
356C4—1881no—
357C4—1881no—
358C4#41×D4711yescharacteristic
359C4#41×D4711yescharacteristic
360C2—81no—
361C2—942no—
362C2—3761no—
363C2—3761no—
364C2#124×D4711yescharacteristic
365C2#1568992711yescharacteristic
366C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3136
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689488C2semidirect
4. #15689486C2semidirect
5. #15689484C2semidirect
6. #15689479C2semidirect
7. #15689477C2semidirect
8. #15689471C2semidirect
9. #15689468C2semidirect
10. #15689126C2semidirect
11. #15689123C2semidirect
12. #15689118C2semidirect
13. #102×D47C2semidirect
14. #15689080C2semidirect
15. C47×#489C2semidirect
20. #13094023C22semidirect
24. #13094016C22semidirect
25. #13094015C22semidirect
37. #13093948C22semidirect
38. #13093948C22semidirect
41. #13093946C22semidirect
42. #13093946C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. #13093934C22semidirect
50. C4×C47⋊C8C22semidirect
51. C8×Dic47C22semidirect
52. C4⋊Q8×C47C22semidirect
54. #103×C47C22semidirect
55. #103×C47C22semidirect
58. #97×C47C22semidirect
189. #489D47semidirect
199. C47#3136semidirect
206. C4⋊Q8C2×D47semidirect
225. #103C2×D47semidirect
226. #103C2×D47semidirect
240. #97C2×D47semidirect