Finite Group Databasebeta

← #20254475

Subgroups — #20254475

Order 6016.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689742C211yesmaximal, characteristic, complemented
2#15689691C211yesmaximal, characteristic, complemented
3#15689513C211yesmaximal, characteristic, complemented
4#15689482C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689347C211yesmaximal, characteristic, complemented
7#15689340C211yesmaximal, characteristic, complemented
8#15689321C211yesmaximal, characteristic, complemented
9#15689316C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689267C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic, complemented
14#15689182C211yesmaximal, characteristic, complemented
15C47×#495C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625336C2211yescharacteristic, complemented
20C2×#10625334C2211yescharacteristic
21C2×#10625334C2211yescharacteristic, complemented
22#13094024C2211yescharacteristic, complemented
23#13094021C2211yescharacteristic
24#13094020C2211yescharacteristic
25#13094017—21no—
26#13094013C2211yescharacteristic
27#13094010—21no—
28#13094008—21no—
29#13094001—21no—
30#13094000C2211yescharacteristic
31#13093997—21no—
32#13093997—21no—
33#13093995C2211yescharacteristic
34#13093994—21no—
35#13093994—21no—
36Q8×Dic47C2211yescharacteristic, complemented
37D4×Dic47C2211yescharacteristic, complemented
38#13093981C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic
57#124×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69#10625354—41no—
70#10625354—41no—
71D4×D47—41no—
72D4×D47—41no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×Dic94—21no—
81Q16×C47—41no—
82SD16×C47—41no—
83SD16×C47—41no—
84D8×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C42×C47C2311yescharacteristic
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94#10625336—41no—
95#10625336—41no—
96#10625334—41no—
97#10625334—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4D411yescharacteristic
102(C2×D47)⋊C4D411yescharacteristic
103C4⋊Dic47—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4D411yescharacteristic
109Dic47⋊C4D411yescharacteristic
110C4×Dic47—21no—
111C4×Dic47C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—42no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47C2×D411yescharacteristic
122Q8×C47—21no—
123Q8×C47—21no—
124Q8×C47—21no—
125Q8×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—42no—
136C22⋊D47—81no—
137C22⋊D47—81no—
138C22⋊D47—81no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—81no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—42no—
150D188—81no—
151D188—81no—
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—42no—
155Dic94—81no—
156C8×C47—21no—
157C8×C47—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47C22×D411yescharacteristic
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—84no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47H(5,𝔽2)11yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—21no—
186Dic47—41no—
187Dic47—41no—
188#3224—471nomaximal, Sylow
189C2×C47—81no—
190C2×C47—81no—
191C2×C47#53511yescharacteristic
192C2×C47#57611yescharacteristic
193C2×C47#57711yescharacteristic
194D47—41no—
195D47—81no—
196D47—81no—
197#542—471no—
198#535—471no—
199#496—471no—
200#495D4711yescharacteristic, complemented
201#489—471no—
202#486—471no—
203#464—471no—
204#463—471no—
205#460—471no—
206#459—471no—
207#452—471no—
208#450—471no—
209#449—471no—
210#447—471no—
211#433—471no—
212C47#322411yescharacteristic, complemented, Sylow
213C2×#41—471no—
214C22×D4—471no—
215C2×Q16C2×D4711yescharacteristic, complemented
216C2×SD16—471no—
217C2×SD16—471no—
218C2×SD16C2×D4711yescharacteristic
219C2×SD16C2×D4711yescharacteristic, complemented
220C2×D8—471no—
221C2×D8—471no—
222C2×D8C2×D4711yescharacteristic
223C4⋊Q8—471no—
224#127—471no—
225#127—471no—
226#126—941no—
227#124—471no—
228#124—941no—
229#124C2×D4711yescharacteristic
230#124C2×D4711yescharacteristic, complemented
231#123—941no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234#121—471no—
235#121—941no—
236#121—941no—
237#120—941no—
238#120—941no—
239C4×Q8—471no—
240C4×D4—471no—
241#117—471no—
242C4⋊C8—471no—
243C4⋊C8—471no—
244#103—471no—
245#103—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252C22⋊C8—471no—
253C22⋊C8—471no—
254#97—471no—
255C4×C8C2×D4711yescharacteristic, complemented
256C24—941no—
257#41—1881no—
258#41—1881no—
259C2×Q8—941no—
260C2×Q8C22×D4711yescharacteristic
261C2×Q8C22×D4711yescharacteristic
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—1881no—
272C2×D4—1881no—
273C2×D4C22×D4711yescharacteristic
274C2×D4C22×D4711yescharacteristic
275C22×C4—471no—
276C22×C4—941no—
277C22×C4—941no—
278Q16—41no—
279SD16—41no—
280SD16—41no—
281SD16—1881no—
282SD16—1881no—
283D8—41no—
284D8—1881no—
285D8—1881no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8C22×D4711yescharacteristic
289C2×C8C22×D4711yescharacteristic
290C4⋊C4—471no—
291C4⋊C4—471no—
292C4⋊C4—471no—
293C4⋊C4—471no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—471no—
302C22⋊C4—471no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C42—471no—
309C42—941no—
310C42C22×D4711yescharacteristic
311C23—21no—
312C23—21no—
313C23—471no—
314C23—941no—
315C23—941no—
316C23—3761no—
317C23—3761no—
318C23—1882no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—3761no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—941no—
329D4—941no—
330D4—941no—
331D4—941no—
332D4—3761no—
333D4—3761no—
334D4—3761no—
335D4—3761no—
336D4—3761no—
337D4—1882no—
338D4—1882no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—471no—
342C2×C4—471no—
343C2×C4—471no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—3761no—
349C2×C4—1882no—
350C2×C4D4×D4711yescharacteristic
351C2×C4D4×D4711yescharacteristic
352C2×C4C23×D4711yescharacteristic
353C8—21no—
354C8—21no—
355C8—941no—
356C8—941no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—941no—
364C22—941no—
365C22—941no—
366C22—3764no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22C2×D4×D4711yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—941no—
379C4—941no—
380C4—941no—
381C4—1881no—
382C4—1881no—
383C4#1309406911yescharacteristic
384C4#1309406911yescharacteristic
385C2—81no—
386C2—81no—
387C2—3761no—
388C2—3761no—
389C2—1881no—
390C2#1568968611yescharacteristic
391C2#1568992511yescharacteristic
392C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #15689742C2semidirect
2. #15689691C2semidirect
3. #15689513C2semidirect
4. #15689482C2semidirect
5. #15689470C2semidirect
6. #15689347C2semidirect
7. #15689340C2semidirect
8. #15689321C2semidirect
9. #15689316C2semidirect
10. #15689284C2semidirect
11. #15689272C2semidirect
12. #15689267C2semidirect
13. #15689255C2semidirect
14. #15689182C2semidirect
15. C47×#495C2semidirect
19. C2×#10625336C22semidirect
21. C2×#10625334C22semidirect
22. #13094024C22semidirect
36. Q8×Dic47C22semidirect
37. D4×Dic47C22semidirect
39. Dic47⋊C8C22semidirect
40. Dic47⋊C8C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
45. #13093946C22semidirect
46. #13093946C22semidirect
51. #13093935C22semidirect
52. C2×Q16×C47C22semidirect
54. C2×SD16×C47C22semidirect
57. #124×C47C22semidirect
58. C4×C8×C47C22semidirect
200. #495D47semidirect
212. C47#3224semidirect
215. C2×Q16C2×D47semidirect
219. C2×SD16C2×D47semidirect
230. #124C2×D47semidirect
255. C4×C8C2×D47semidirect