Finite Group Databasebeta

← #20254482

Subgroups — #20254482

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#15689744C211yesmaximal, characteristic, complemented
2#15689510C211yesmaximal, characteristic, complemented
3#15689505C211yesmaximal, characteristic, complemented
4#15689482C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689320C211yesmaximal, characteristic, complemented
9#15689315C211yesmaximal, characteristic, complemented
10#15689285C211yesmaximal, characteristic, complemented
11#15689274C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689257C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#535C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic, complemented
17C2×#10625335C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625336C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625334C2211yescharacteristic, complemented
24#13094024C2211yescharacteristic, complemented
25#13094019—21no—
26#13094012C2211yescharacteristic, complemented
27#13094010—21no—
28#13094006—21no—
29#13094003C2211yescharacteristic
30#13094002—21no—
31#13093998C2211yescharacteristic
32C4×Dic94C2211yescharacteristic, complemented
33C4×D188C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35C4⋊(C47⋊C8)C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic, complemented
47C4×C47⋊C8C2211yescharacteristic, complemented
48C2×#41×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50#127×C47C2211yescharacteristic
51#127×C47C2211yescharacteristic
52#124×C47C2211yescharacteristic
53#124×C47C2211yescharacteristic
54#121×C47—21no—
55#121×C47—21no—
56#120×C47—21no—
57#120×C47—21no—
58#117×C47C2211yescharacteristic
59C24×C47—21no—
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47C2311yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C22×C4×C47—21no—
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—21no—
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×Dic94—21no—
80C2×Dic94C2311yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47D411yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47C2311yescharacteristic
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92#10625337—41no—
93#10625336—41no—
94#10625335—41no—
95#10625335—41no—
96#10625335—41no—
97#10625334—41no—
98#10625334—41no—
99#10625334—41no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109C4×Dic47—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—42no—
118C23×C47—81no—
119C23×C47—81no—
120C23×C47C2×D411yescharacteristic
121C22×D47—21no—
122Q8×C47—21no—
123Q8×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—42no—
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—42no—
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2411yescharacteristic
146C22⋊D47—81no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150D188—21no—
151D188—21no—
152C4×D47—81no—
153Dic94—21no—
154Dic94—21no—
155Dic94—81no—
156C47⋊C8—21no—
157C47⋊C8—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×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—84no—
173C22×C47C22×D411yescharacteristic
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—41no—
183C4×C47H(5,𝔽2)11yescharacteristic
184C4×C47H(5,𝔽2)11yescharacteristic
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188#3224—471nomaximal, Sylow
189C2×C47—41no—
190C2×C47—81no—
191C2×C47—81no—
192C2×C47—81no—
193C2×C47#53511yescharacteristic
194C2×C47#57611yescharacteristic
195C2×C47#57711yescharacteristic
196D47—81no—
197#542—471no—
198#535D4711yescharacteristic, complemented
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#449—471no—
210#447—471no—
211#433—471no—
212C47#322411yescharacteristic, complemented, Sylow
213C2×#41C2×D4711yescharacteristic
214C22×D4C2×D4711yescharacteristic
215C2×Q16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×SD16—471no—
219C2×SD16—471no—
220C2×D8—471no—
221C2×D8—471no—
222C2×D8—471no—
223C4⋊Q8—471no—
224#127C2×D4711yescharacteristic
225#127C2×D4711yescharacteristic
226#126—941no—
227#124—471no—
228#124—941no—
229#124C2×D4711yescharacteristic
230#124C2×D4711yescharacteristic
231#123—941no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234#121—21no—
235#121—21no—
236#121—471no—
237#120—21no—
238#120—21no—
239C4×Q8—471no—
240C4×D4—471no—
241#117C2×D4711yescharacteristic
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×C8—471no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—471no—
260C2×Q8—941no—
261C2×Q8C22×D4711yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—471no—
271C2×D4—941no—
272C2×D4C22×D4711yescharacteristic
273C2×D4C22×D4711yescharacteristic
274C2×D4C22×D4711yescharacteristic
275C22×C4—21no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278Q16—1881no—
279SD16—1881no—
280SD16—1881no—
281SD16—1881no—
282SD16—1881no—
283D8—1881no—
284D8—1881no—
285D8—1881no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—471no—
289C2×C8—471no—
290C4⋊C4—471no—
291C4⋊C4—471no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
295C4⋊C4C22⋊D4711yescharacteristic
296C4⋊C4C22⋊D4711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4C22⋊D4711yescharacteristic
307C22⋊C4C22⋊D4711yescharacteristic
308C42—941no—
309C42C22×D4711yescharacteristic
310C42C22×D4711yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—941no—
318C23C2×C22⋊D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—941no—
322Q8—941no—
323Q8—3761no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—941no—
337D4—941no—
338D4—3761no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—3761no—
347C2×C4C2×C22⋊D4711yescharacteristic
348C2×C4C2×C22⋊D4711yescharacteristic
349C2×C4C2×C22⋊D4711yescharacteristic
350C2×C4C2×C22⋊D4711yescharacteristic
351C2×C4C2×C22⋊D4711yescharacteristic
352C2×C4C23×D4711yescharacteristic
353C8—941no—
354C8—941no—
355C8—941no—
356C8—941no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22C22×C22⋊D4711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—1881no—
381C4—1881no—
382C4—1881no—
383C4#1309406911yescharacteristic
384C4#1309406911yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—3761no—
390C2#1568969011yescharacteristic
391C2#1568992611yescharacteristic
392C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#535C2
socleC22×C47C22×D4
hypercenter#535D47
hypocenterC47#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689510C2semidirect
3. #15689505C2semidirect
4. #15689482C2semidirect
5. #15689469C2semidirect
6. #15689342C2semidirect
7. #15689335C2semidirect
8. #15689320C2semidirect
9. #15689315C2semidirect
10. #15689285C2semidirect
11. #15689274C2semidirect
12. #15689268C2semidirect
13. #15689257C2semidirect
14. #15689184C2semidirect
15. C47×#535C2semidirect
16. C2×#10625337C22semidirect
19. C2×#10625335C22semidirect
20. C2×#10625336C22semidirect
23. C2×#10625334C22semidirect
24. #13094024C22semidirect
26. #13094012C22semidirect
32. C4×Dic94C22semidirect
33. C4×D188C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. C4⋊(C47⋊C8)C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
42. #13093945C22semidirect
43. #13093945C22semidirect
46. #13093935C22semidirect
47. C4×C47⋊C8C22semidirect
198. #535D47semidirect
212. C47#3224semidirect