Finite Group Databasebeta

← #20254457

Subgroups — #20254457

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689731C211yesmaximal, characteristic, complemented
2#15689691C211yesmaximal, characteristic
3#15689516C211yesmaximal, characteristic, complemented
4#15689494C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689479C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689324C211yesmaximal, characteristic, complemented
9#15689323C211yesmaximal, characteristic, complemented
10#15689288C211yesmaximal, characteristic, complemented
11#15689284C211yesmaximal, characteristic, complemented
12#15689275C211yesmaximal, characteristic, complemented
13#15689272C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625336C2211yescharacteristic, complemented
24#13094022C2211yescharacteristic, complemented
25#13094021C2211yescharacteristic
26#13094020C2211yescharacteristic
27#13094019—21no—
28#13094018—21no—
29#13094016—21no—
30#13094015C2211yescharacteristic, complemented
31#13094014—21no—
32#13094013C2211yescharacteristic
33#13094004C2211yescharacteristic
34#13094000C2211yescharacteristic
35#13093997—21no—
36#13093997—21no—
37#13093994—21no—
38#13093994—21no—
39C4×Dic94C2211yescharacteristic, complemented
40#13093981C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66#10625354—41no—
67#10625354—41no—
68D4×D47—41no—
69D4×D47—41no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78Q16×C47—41no—
79SD16×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88#10625337—41no—
89#10625336—41no—
90#10625336—41no—
91#10625335—41no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4D411yescharacteristic
97(C2×D47)⋊C4D411yescharacteristic
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4D411yescharacteristic
107Dic47⋊C4D411yescharacteristic
108C4×Dic47—21no—
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112#10625325—41no—
113#10625325—41no—
114C23×C47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47—81no—
120C22×D47C2×D411yescharacteristic
121Q8×C47—21no—
122Q8×C47—21no—
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C22⋊D47—42no—
134C22⋊D47—81no—
135C22⋊D47—81no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141D188—21no—
142D188—21no—
143D188—21no—
144D188—21no—
145D188—42no—
146D188—81no—
147D188—81no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—42no—
151Dic94—21no—
152Dic94—21no—
153C8×C47—21no—
154C8×C47—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—84no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47H(5,𝔽2)11yescharacteristic
177C4×C47H(5,𝔽2)11yescharacteristic
178Dic47—21no—
179Dic47—21no—
180Dic47—21no—
181Dic47—41no—
182Dic47—41no—
183#3222—471nomaximal, Sylow
184C2×C47—81no—
185C2×C47#53511yescharacteristic
186C2×C47#57711yescharacteristic
187C2×C47#57711yescharacteristic
188D47—41no—
189D47—81no—
190D47—81no—
191#541—471no—
192#535—471no—
193#497—471no—
194#492—471no—
195#490—471no—
196#488—471no—
197#464—471no—
198#464D4711yescharacteristic, complemented
199#460—471no—
200#460—471no—
201#452—471no—
202#452—471no—
203#450—471no—
204#450—471no—
205#433—471no—
206C47#322211yescharacteristic, complemented, Sylow
207C2×#41—471no—
208C22×D4—471no—
209C2×Q16—471no—
210C2×Q16C2×D4711yescharacteristic, complemented
211C2×SD16—471no—
212C2×SD16—471no—
213C2×SD16—471no—
214C2×SD16—471no—
215C2×SD16—471no—
216C2×SD16C2×D4711yescharacteristic
217C4⋊Q8—471no—
218#127—471no—
219#127—471no—
220#126—941no—
221#126—941no—
222#125—471no—
223#125—941no—
224#125—941no—
225#124—471no—
226#124C2×D4711yescharacteristic
227C22⋊Q8—471no—
228C22⋊Q8—471no—
229#121—941no—
230#121—941no—
231#120—941no—
232#120—941no—
233C4×Q8—471no—
234C4×Q8C2×D4711yescharacteristic, complemented
235#117—471no—
236C4⋊C8—471no—
237C4⋊C8C2×D4711yescharacteristic, complemented
238#103—471no—
239#103C2×D4711yescharacteristic, complemented
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102C2×D4711yescharacteristic
246C22⋊C8—471no—
247C22⋊C8—471no—
248#97—471no—
249C4×C8—471no—
250C24—941no—
251#41—1881no—
252#41—1881no—
253C2×Q8—471no—
254C2×Q8C22×D4711yescharacteristic
255C2×Q8C22×D4711yescharacteristic
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—1881no—
265C2×D4—1881no—
266C2×D4C22×D4711yescharacteristic
267C22×C4—471no—
268C22×C4—941no—
269Q16—41no—
270Q16—1881no—
271SD16—41no—
272SD16—1881no—
273SD16—1881no—
274SD16—1881no—
275SD16—1881no—
276SD16—1881no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4C22×D4711yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—471no—
296C22⋊C4—471no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C42—21no—
302C42—471no—
303C42—941no—
304C42C22×D4711yescharacteristic
305C23—21no—
306C23—471no—
307C23—941no—
308C23—941no—
309C23—3761no—
310C23—3761no—
311C23—1882no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—941no—
317Q8—941no—
318D4—21no—
319D4—21no—
320D4—941no—
321D4—941no—
322D4—941no—
323D4—941no—
324D4—3761no—
325D4—3761no—
326D4—3761no—
327D4—3761no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—1882no—
341C2×C4D4×D4711yescharacteristic
342C2×C4D4×D4711yescharacteristic
343C2×C4C23×D4711yescharacteristic
344C8—21no—
345C8—21no—
346C8—941no—
347C8—941no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—941no—
352C22—941no—
353C22—941no—
354C22—3764no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22C2×D4×D4711yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—941no—
368C4—941no—
369C4—941no—
370C4—1881no—
371C4—1881no—
372C4#1309406911yescharacteristic
373C4#1309407011yescharacteristic
374C2—81no—
375C2—3761no—
376C2—3761no—
377C2—1881no—
378C2#1568968911yescharacteristic
379C2#1568993011yescharacteristic
380C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3222
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #15689731C2semidirect
3. #15689516C2semidirect
4. #15689494C2semidirect
5. #15689486C2semidirect
6. #15689479C2semidirect
7. #15689342C2semidirect
8. #15689324C2semidirect
9. #15689323C2semidirect
10. #15689288C2semidirect
11. #15689284C2semidirect
12. #15689275C2semidirect
13. #15689272C2semidirect
14. #15689183C2semidirect
15. C47×#464C2semidirect
18. C2×#10625337C22semidirect
20. C2×#10625325C22semidirect
23. C2×#10625336C22semidirect
24. #13094022C22semidirect
30. #13094015C22semidirect
39. C4×Dic94C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093948C22semidirect
44. #13093946C22semidirect
47. #13093944C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
52. C2×Q16×C47C22semidirect
55. C4×Q8×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
198. #464D47semidirect
206. C47#3222semidirect
210. C2×Q16C2×D47semidirect
234. C4×Q8C2×D47semidirect
237. C4⋊C8C2×D47semidirect
239. #103C2×D47semidirect