Finite Group Databasebeta

← #20254480

Subgroups — #20254480

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#15689740C211yesmaximal, characteristic, complemented
2#15689687C211yesmaximal, characteristic, complemented
3#15689511C211yesmaximal, characteristic, complemented
4#15689504C211yesmaximal, characteristic, complemented
5#15689484C211yesmaximal, characteristic, complemented
6#15689468C211yesmaximal, characteristic, complemented
7#15689348C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689322C211yesmaximal, characteristic, complemented
10#15689316C211yesmaximal, characteristic, complemented
11#15689285C211yesmaximal, characteristic, complemented
12#15689276C211yesmaximal, characteristic, complemented
13#15689256C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×#10625337C2211yescharacteristic, complemented
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23#13094023C2211yescharacteristic, complemented
24#13094020C2211yescharacteristic
25#13094020C2211yescharacteristic
26#13094017—21no—
27#13094013C2211yescharacteristic
28#13094013C2211yescharacteristic
29#13094011—21no—
30#13094011C2211yescharacteristic, complemented
31#13094005—21no—
32#13094003C2211yescharacteristic
33#13094001—21no—
34#13093998—21no—
35#13093998—21no—
36#13093992—21no—
37#13093992—21no—
38#13093989C2211yescharacteristic, complemented
39D4×Dic47C2211yescharacteristic, complemented
40#13093983C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47—21no—
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C22×Dic47—21no—
74C2×D188—21no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×Dic94—21no—
80C2×Dic94C2311yescharacteristic
81SD16×C47—41no—
82D8×C47—41no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47D411yescharacteristic
92C22⋊Dic47D411yescharacteristic
93#10625337—41no—
94#10625335—41no—
95#10625334—41no—
96#10625334—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47D411yescharacteristic
102C4⋊Dic47D411yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108C4×Dic47C2311yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112#10625325—41no—
113#10625325—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47C2×D411yescharacteristic
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122Q8×C47—21no—
123Q8×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—42no—
129D4×C47—81no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—42no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—81no—
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—81no—
144C2×Dic47C2×D411yescharacteristic
145C2×Dic47C2×D411yescharacteristic
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148D188—21no—
149D188—21no—
150D188—21no—
151D188—21no—
152D188—42no—
153Dic94—21no—
154Dic94—21no—
155Dic94—81no—
156C8×C47—21no—
157C8×C47—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47C22×D411yescharacteristic
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—41no—
179C4×C47—41no—
180C4×C47H(5,𝔽2)11yescharacteristic
181C4×C47H(5,𝔽2)11yescharacteristic
182Dic47—21no—
183Dic47—21no—
184Dic47—21no—
185Dic47—21no—
186Dic47—41no—
187Dic47—41no—
188#3224—471nomaximal, Sylow
189C2×C47—41no—
190C2×C47—81no—
191C2×C47—81no—
192C2×C47#53511yescharacteristic
193C2×C47#57611yescharacteristic
194C2×C47#57711yescharacteristic
195D47—81no—
196D47—81no—
197#542—471no—
198#535—471no—
199#496—471no—
200#495—471no—
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#449D4711yescharacteristic, complemented
210#447—471no—
211#433—471no—
212C47#322411yescharacteristic, complemented, Sylow
213C2×#41C2×D4711yescharacteristic
214C22×D4—471no—
215C2×Q16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×SD16—471no—
219C2×SD16C2×D4711yescharacteristic, complemented
220C2×D8—471no—
221C2×D8—471no—
222C2×D8C2×D4711yescharacteristic, complemented
223C4⋊Q8—471no—
224#127—471no—
225#127—471no—
226#126—941no—
227#124—471no—
228#124—471no—
229#124—471no—
230#124—941no—
231#123—941no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234#121—941no—
235#121—941no—
236#121C2×D4711yescharacteristic
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#103C2×D4711yescharacteristic, complemented
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102C2×D4711yescharacteristic, complemented
252C22⋊C8—471no—
253C22⋊C8C2×D4711yescharacteristic
254#97—471no—
255C4×C8—471no—
256C24—941no—
257#41—41no—
258#41—41no—
259C2×Q8—471no—
260C2×Q8—941no—
261C2×Q8C22×D4711yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—471no—
265C2×D4—471no—
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—21no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278Q16—1881no—
279SD16—41no—
280SD16—1881no—
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—941no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4C22×D4711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—471no—
299C22⋊C4—471no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C42—471no—
309C42—471no—
310C42—941no—
311C23—21no—
312C23—21no—
313C23—941no—
314C23—941no—
315C23—3761no—
316C23—3761no—
317C23—1882no—
318C23D4×D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—941no—
322Q8—941no—
323Q8—3761no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—81no—
330D4—941no—
331D4—941no—
332D4—941no—
333D4—941no—
334D4—3761no—
335D4—3761no—
336D4—3761no—
337D4—3761no—
338D4—1882no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—471no—
345C2×C4—471no—
346C2×C4—471no—
347C2×C4—471no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—3761no—
351C2×C4D4×D4711yescharacteristic
352C2×C4C23×D4711yescharacteristic
353C8—21no—
354C8—21no—
355C8—941no—
356C8—941no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—3764no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22C2×D4×D4711yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—941no—
378C4—941no—
379C4—941no—
380C4—941no—
381C4—1881no—
382C4—1881no—
383C4#1309406911yescharacteristic
384C4#1309406911yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—3761no—
389C2—3761no—
390C2#1568968811yescharacteristic
391C2#1568992711yescharacteristic
392C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689740C2semidirect
2. #15689687C2semidirect
3. #15689511C2semidirect
4. #15689504C2semidirect
5. #15689484C2semidirect
6. #15689468C2semidirect
7. #15689348C2semidirect
8. #15689340C2semidirect
9. #15689322C2semidirect
10. #15689316C2semidirect
11. #15689285C2semidirect
12. #15689276C2semidirect
13. #15689256C2semidirect
14. #15689181C2semidirect
15. C47×#449C2semidirect
17. C2×#10625337C22semidirect
20. C2×#10625335C22semidirect
23. #13094023C22semidirect
30. #13094011C22semidirect
38. #13093989C22semidirect
39. D4×Dic47C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093948C22semidirect
46. #13093945C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
53. C2×SD16×C47C22semidirect
54. C2×D8×C47C22semidirect
56. #103×C47C22semidirect
57. #102×C47C22semidirect
209. #449D47semidirect
212. C47#3224semidirect
219. C2×SD16C2×D47semidirect
222. C2×D8C2×D47semidirect
245. #103C2×D47semidirect
251. #102C2×D47semidirect