Finite Group Databasebeta

← #20254240

Subgroups — #20254240

Order 6016.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689701C211yesmaximal, characteristic, complemented
2#15689464C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689439C211yesmaximal, characteristic, complemented
5#15689434C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689357C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689274C211yesmaximal, characteristic, complemented
11#15689266C211yesmaximal, characteristic, complemented
12#15689266C211yesmaximal, characteristic, complemented
13#15689257C211yesmaximal, characteristic, complemented
14#15689090C211yesmaximal, characteristic, complemented
15C47×#535C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic, complemented
17C2×#10625335C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×#10625329C2211yescharacteristic, complemented
22C22×C47⋊C8C2211yescharacteristic, complemented
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic, complemented
25#13094000—21no—
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic, complemented
28#13093996—21no—
29#13093996—21no—
30#13093995—21no—
31C2×C4⋊Dic47C2211yescharacteristic, complemented
32#13093957C2211yescharacteristic, complemented
33#13093957C2211yescharacteristic, complemented
34#13093955C2211yescharacteristic, complemented
35#13093955C2211yescharacteristic, complemented
36#13093947C2211yescharacteristic, complemented
37#13093947C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic, complemented
43#13093944C2211yescharacteristic, complemented
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C2×#41×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50#127×C47—21no—
51#124×C47—21no—
52#121×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#120×C47—21no—
57#120×C47—21no—
58#117×C47C2211yescharacteristic
59C24×C47—21no—
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47D411yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47D411yescharacteristic
71C2×D4×C47D411yescharacteristic
72C2×D4×C47D411yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C2×D4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C22×Dic47—21no—
82#10625350—41no—
83#10625350—41no—
84C2×D188C2311yescharacteristic
85C2×C4×D47—21no—
86C2×Dic94C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C42×C47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97#10625335—41no—
98#10625335—41no—
99#10625334—41no—
100#10625334—41no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47—21no—
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108#10625329—41no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—42no—
117C23×C47—81no—
118C23×C47—81no—
119C23×C47C2×D411yescharacteristic
120C23×C47C2×D411yescharacteristic
121C23×C47C2×D411yescharacteristic
122C22×D47—21no—
123Q8×C47—41no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—41no—
129D4×C47—41no—
130D4×C47—41no—
131D4×C47—42no—
132D4×C47—81no—
133D4×C47—81no—
134D4×C47—81no—
135D4×C47—81no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C22⋊D47—42no—
149C22⋊D47—81no—
150C22⋊D47—81no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—81no—
155D188—21no—
156D188—21no—
157C4×D47—42no—
158Dic94—21no—
159Dic94—21no—
160C47⋊C8—21no—
161C47⋊C8—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—84no—
180C22×C47C22×D411yescharacteristic
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47H(5,𝔽2)11yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194#3198—471nomaximal, Sylow
195C2×C47—41no—
196C2×C47—41no—
197C2×C47—41no—
198C2×C47—81no—
199C2×C47—81no—
200C2×C47#53411yescharacteristic
201C2×C47#57611yescharacteristic
202C2×C47#57711yescharacteristic
203D47—81no—
204#537—471no—
205#535D4711yescharacteristic, complemented
206#485—471no—
207#482—471no—
208#481—471no—
209#480—471no—
210#469—471no—
211#468—471no—
212#466—471no—
213#465—471no—
214#450—471no—
215#449—471no—
216#449—471no—
217#447—471no—
218#408—471no—
219C47#319811yescharacteristic, complemented, Sylow
220C2×#41—471no—
221C2×#41C2×D4711yescharacteristic
222C22×D4C2×D4711yescharacteristic
223C2×SD16—471no—
224C2×SD16—471no—
225C2×D8—471no—
226C2×D8—471no—
227C2×M16—471no—
228C22×C8—471no—
229#127—21no—
230#124—21no—
231C22⋊Q8—471no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234#121—471no—
235#121—471no—
236#121—941no—
237#121—941no—
238#121—941no—
239#121C2×D4711yescharacteristic
240#121C2×D4711yescharacteristic
241#121C2×D4711yescharacteristic
242#121C2×D4711yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D4711yescharacteristic
246C2×C4⋊C4—471no—
247#107—471no—
248#107—471no—
249#106—471no—
250#106—471no—
251#103—471no—
252#103—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258#102—471no—
259C22⋊C8—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262C22⋊C8—471no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—1881no—
267#41—1881no—
268C2×Q8—471no—
269C2×Q8C22⋊D4711yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—471no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4C22⋊D4711yescharacteristic
282C2×D4C22⋊D4711yescharacteristic
283C2×D4C22⋊D4711yescharacteristic
284C2×D4C22×D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—941no—
287C22×C4—941no—
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290C22×C4C22×D4711yescharacteristic
291SD16—1881no—
292SD16—1881no—
293D8—1881no—
294D8—1881no—
295M16—1881no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—471no—
299C2×C8—471no—
300C2×C8—1881no—
301C4⋊C4—471no—
302C4⋊C4—471no—
303C4⋊C4—941no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4C22×D4711yescharacteristic
307C4⋊C4C22×D4711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—941no—
324C23C2×C22⋊D4711yescharacteristic
325C23C2×C22⋊D4711yescharacteristic
326C23C2×C22⋊D4711yescharacteristic
327Q8—41no—
328Q8—941no—
329Q8—941no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—941no—
343D4—941no—
344D4—3761no—
345D4—3761no—
346D4—1882no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—3761no—
359C2×C4—1882no—
360C2×C4C2×C22⋊D4711yescharacteristic
361C2×C4C2×C22⋊D4711yescharacteristic
362C2×C4C2×C22⋊D4711yescharacteristic
363C2×C4C23×D4711yescharacteristic
364C8—941no—
365C8—941no—
366C8—941no—
367C8—941no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22C22×C22⋊D4711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—1881no—
394C4—1881no—
395C4—1881no—
396C4#1309406911yescharacteristic
397C4#1309406911yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—3761no—
404C2#1568968211yescharacteristic
405C2#1568992611yescharacteristic
406C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#535C2
socleC22×C47C22×D4
hypercenter#535D47
hypocenterC47#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689701C2semidirect
2. #15689464C2semidirect
3. #15689447C2semidirect
4. #15689439C2semidirect
5. #15689434C2semidirect
6. #15689374C2semidirect
7. #15689367C2semidirect
8. #15689357C2semidirect
9. #15689350C2semidirect
10. #15689274C2semidirect
11. #15689266C2semidirect
12. #15689266C2semidirect
13. #15689257C2semidirect
14. #15689090C2semidirect
15. C47×#535C2semidirect
16. C2×#10625350C22semidirect
21. C2×#10625329C22semidirect
22. C22×C47⋊C8C22semidirect
24. #13094003C22semidirect
27. #13093998C22semidirect
31. C2×C4⋊Dic47C22semidirect
32. #13093957C22semidirect
33. #13093957C22semidirect
34. #13093955C22semidirect
35. #13093955C22semidirect
36. #13093947C22semidirect
37. #13093947C22semidirect
42. #13093944C22semidirect
43. #13093944C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. C22⋊(C47⋊C8)C22semidirect
205. #535D47semidirect
219. C47#3198semidirect