Finite Group Databasebeta

← #20254178

Subgroups — #20254178

Order 6016.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689633C211yesmaximal, characteristic, complemented
2#15689630C211yesmaximal, characteristic, complemented
3#15689465C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689446C211yesmaximal, characteristic, complemented
6#15689444C211yesmaximal, characteristic, complemented
7#15689363C211yesmaximal, characteristic, complemented
8#15689356C211yesmaximal, characteristic, complemented
9#15689351C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689285C211yesmaximal, characteristic, complemented
12#15689282C211yesmaximal, characteristic, complemented
13#15689265C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625335C2211yescharacteristic, complemented
20C2×C8×D47C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094006—21no—
23#13094005—21no—
24#13094004C2211yescharacteristic
25#13094003C2211yescharacteristic
26#13094000C2211yescharacteristic
27#13094000C2211yescharacteristic
28#13093995C2211yescharacteristic
29#13093995C2211yescharacteristic
30#13093995C2211yescharacteristic
31#13093992—21no—
32#13093992—21no—
33D4×Dic47—21no—
34C4×C22⋊D47—21no—
35C4×C22⋊D47—21no—
36(C22⋊D47)⋊C4—21no—
37#13093983C2211yescharacteristic
38#13093982C2211yescharacteristic
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
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×D47D411yescharacteristic
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—
74C22×Dic47D411yescharacteristic
75#10625352—41no—
76#10625352—41no—
77C2×C4×D47—41no—
78C2×C4×D47—41no—
79C2×C4×D47D411yescharacteristic
80C2×C4×D47D411yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×C4×D47C2311yescharacteristic
83C2×Dic94C2311yescharacteristic
84SD16×C47—41no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95#10625337—41no—
96#10625335—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C4×Dic47—21no—
109C4×Dic47—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C8×D47—41no—
113C8×D47—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47C2×D411yescharacteristic
117C22×D47—22no—
118C22×D47—41no—
119C22×D47—41no—
120C22×D47C2×D411yescharacteristic
121C22×D47C2×D411yescharacteristic
122Q8×C47—21no—
123Q8×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—42no—
129D4×C47—42no—
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—42no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—42no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—41no—
146C2×Dic47—42no—
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149C4×D47—21no—
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—41no—
154C4×D47—41no—
155Dic94—21no—
156Dic94—21no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47C22×D411yescharacteristic
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—44no—
177C2×D47#13512yes—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47H(5,𝔽2)11yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189#3191—471nomaximal, Sylow
190C2×C47—41no—
191C2×C47—81no—
192C2×C47—81no—
193C2×C47#53411yescharacteristic
194C2×C47C2×#13511yescharacteristic
195C2×C47#57511yescharacteristic
196D47—22no—
197D47—41no—
198#525—471no—
199#525—471no—
200#485—471no—
201#485—471no—
202#482—471no—
203#482—471no—
204#467—471no—
205#466—471no—
206#465—471no—
207#465—471no—
208#452—471no—
209#452—471no—
210#449—471no—
211#449D4711yescharacteristic, complemented
212C2×C22⋊C8—471no—
213C47#319111yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C2×#41C2×D4711yescharacteristic
216C23×C4—471no—
217C2×Q16—471no—
218C2×SD16—471no—
219C2×SD16C2×D4711yescharacteristic, complemented
220C2×D8C2×D4711yescharacteristic, complemented
221C22×C8—471no—
222C22×C8—471no—
223#123—941no—
224#123—941no—
225C22⋊Q8—471no—
226C22⋊Q8—471no—
227C22⋊Q8—471no—
228C22⋊Q8—471no—
229#121—471no—
230#121—471no—
231#121—471no—
232#121C2×D4711yescharacteristic
233#120—941no—
234#120—941no—
235C4×D4—941no—
236C4×D4—941no—
237C4×D4—941no—
238C4×D4—941no—
239#117—471no—
240#117—471no—
241#107—471no—
242#107—471no—
243#106—471no—
244#106—471no—
245#103—471no—
246#103—471no—
247#103—471no—
248#103C2×D4711yescharacteristic, complemented
249#102—471no—
250#102—471no—
251#102—471no—
252#102C2×D4711yescharacteristic, complemented
253C22⋊C8—471no—
254C22⋊C8—471no—
255C22⋊C8—471no—
256C22⋊C8C2×D4711yescharacteristic
257C24—471no—
258#41—41no—
259#41—41no—
260#41—1881no—
261#41—1881no—
262C2×Q8—471no—
263C2×Q8C22×D4711yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4C22×D4711yescharacteristic
271C2×D4C22×D4711yescharacteristic
272C22×C4—21no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—941no—
279C22×C4—1881no—
280C22×C4—1881no—
281C22×C4C22×D4711yescharacteristic
282Q16—1881no—
283SD16—41no—
284SD16—1881no—
285D8—41no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—1881no—
289C2×C8—1881no—
290C2×C8C22×D4711yescharacteristic
291C2×C8C22×D4711yescharacteristic
292C4⋊C4—471no—
293C4⋊C4—471no—
294C4⋊C4—471no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4—941no—
299C4⋊C4C22×D4711yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C42—941no—
311C42—941no—
312C23—21no—
313C23—21no—
314C23—471no—
315C23—471no—
316C23—942no—
317C23—1881no—
318C23—1881no—
319C23D4×D4711yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—941no—
323Q8—941no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—1882no—
331D4—1882no—
332D4—1882no—
333D4—1882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—471no—
340C2×C4—471no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—1881no—
350C2×C4—1881no—
351C2×C4—1881no—
352C2×C4—1882no—
353C2×C4D4×D4711yescharacteristic
354C2×C4C23×D4711yescharacteristic
355C8—21no—
356C8—21no—
357C8—941no—
358C8—941no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—472no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22—941no—
374C22—1884no—
375C22C2×D4×D4711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—941no—
380C4—941no—
381C4—1881no—
382C4—1881no—
383C4—1881no—
384C4—1881no—
385C4#1309406911yescharacteristic
386C4#1309406911yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—942no—
391C2—1881no—
392C2#1568968311yescharacteristic
393C2#135×D4711yescharacteristic
394C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3191
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. #15689633C2semidirect
2. #15689630C2semidirect
3. #15689465C2semidirect
4. #15689463C2semidirect
5. #15689446C2semidirect
6. #15689444C2semidirect
7. #15689363C2semidirect
8. #15689356C2semidirect
9. #15689351C2semidirect
10. #15689349C2semidirect
11. #15689285C2semidirect
12. #15689282C2semidirect
13. #15689265C2semidirect
14. C22⋊C8×D47C2semidirect
15. C47×#449C2semidirect
18. C2×#10625337C22semidirect
19. C2×#10625335C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
53. C2×SD16×C47C22semidirect
54. C2×D8×C47C22semidirect
56. #103×C47C22semidirect
57. #102×C47C22semidirect
211. #449D47semidirect
213. C47#3191semidirect
219. C2×SD16C2×D47semidirect
220. C2×D8C2×D47semidirect
248. #103C2×D47semidirect
252. #102C2×D47semidirect