Finite Group Databasebeta

← #20255194

Subgroups — #20255194

Order 6016.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689773C211yesmaximal, characteristic, complemented
2D4×C22⋊D47C211yesmaximal, characteristic, complemented
3#15689468C211yesmaximal, characteristic, complemented
4#15689437C211yesmaximal, characteristic, complemented
5#15689435C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689356C211yesmaximal, characteristic, complemented
9#15689316C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic, complemented
11D8×Dic47C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13C2×#13093945C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C22×C22⋊D47—21no—
18C2×D4×D47C2211yescharacteristic
19C2×#10625334C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic, complemented
21C2×C8×D47C2211yescharacteristic, complemented
22#13094023C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic
24#13094006—21no—
25#13094005—21no—
26#13094001—21no—
27#13093998C2211yescharacteristic
28#13093996—21no—
29#13093995C2211yescharacteristic
30#13093995C2211yescharacteristic, complemented
31#13093993—21no—
32#13093992—21no—
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic, complemented
35C4×C22⋊D47C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic, complemented
37C4⋊C4×D47C2211yescharacteristic, complemented
38#13093958C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C24×C47—21no—
60C23×D47—21no—
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47—41no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—44no—
76C2×C22⋊D47D411yescharacteristic
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80#10625352—44no—
81D4×D47—22no—
82D4×D47—41no—
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×Dic94—21no—
87D8×C47—22no—
88D8×C47—41no—
89C2×C8×C47C2311yescharacteristic
90C2×C8×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47D411yescharacteristic
98#10625334—41no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4D411yescharacteristic
101C4⋊Dic47—21no—
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4D411yescharacteristic
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8—41no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C8×D47—41no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—42no—
117C23×C47—42no—
118C23×C47—81no—
119C23×C47C2×D411yescharacteristic
120C22×D47—21no—
121C22×D47—42no—
122C22×D47—42no—
123C22×D47—81no—
124C22×D47C2×D411yescharacteristic
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—42no—
131D4×C47—42no—
132D4×C47#4112yescomplemented
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—42no—
141C22⋊D47—42no—
142C22⋊D47—42no—
143C22⋊D47—81no—
144C22⋊D47D814yescomplemented
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150C2×Dic47—42no—
151C2×Dic47C2×D411yescharacteristic
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154D188—21no—
155D188—21no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—42no—
159Dic94—42no—
160C8×C47—21no—
161C8×C47—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—22no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—84no—
176C22×C47C2×D812yes—
177C22×C47C22×D411yescharacteristic
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C2×D47C2×D812yes—
185C4×C47—21no—
186C4×C47—41no—
187C4×C47C2×#4111yescharacteristic
188C4×C47H(5,𝔽2)11yescharacteristic
189Dic47—21no—
190Dic47—21no—
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194Dic47C2×D812yes—
195#3294—471nomaximal, Sylow
196C2×C47—22no—
197C2×C47—42no—
198C2×C47—81no—
199C2×C47—81no—
200C2×C47#54611yescharacteristic
201C2×C47C22×D811yescharacteristic
202C2×C47#57711yescharacteristic
203D47—22no—
204D47—81no—
205#547—471no—
206D42—471no—
207#486—471no—
208#480—471no—
209#480—471no—
210#474—471no—
211#466—471no—
212#466—471no—
213#459—471no—
214#447—471no—
215#447D4711yescharacteristic, complemented
216C4×D8—471no—
217C8×D4—471no—
218C2×#102—471no—
219C2×#102—471no—
220C47#329411yescharacteristic, complemented, Sylow
221C2×#41—941no—
222C22×D4—471no—
223C22×D4—941no—
224C22×D4C2×D4711yescharacteristic
225C2×D8—471no—
226C2×D8C2×D4711yescharacteristic
227C2×D8C2×D4711yescharacteristic, complemented
228C22×C8—471no—
229C22×C8—471no—
230C4⋊Q8—471no—
231#127—471no—
232#123—941no—
233#123—941no—
234C22⋊Q8—941no—
235#121—471no—
236#121—471no—
237#121—471no—
238#121—941no—
239#121C2×D4711yescharacteristic, complemented
240#120—941no—
241#120—941no—
242C4×D4—471no—
243C4×D4—471no—
244C4×D4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247#107—471no—
248#107—471no—
249#107—471no—
250C4⋊C8—471no—
251#102—471no—
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258#102—471no—
259#102C2×D4711yescharacteristic
260#102C2×D4711yescharacteristic, complemented
261C22⋊C8—471no—
262C22⋊C8C2×D4711yescharacteristic, complemented
263C4×C8—471no—
264C24—21no—
265C24—941no—
266#41—1884no—
267C2×Q8—941no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—471no—
273C2×D4—471no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—942no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4—1881no—
282C2×D4—1884no—
283C2×D4C22×D4711yescharacteristic
284C2×D4C22×D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—471no—
287C22×C4—941no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4C22×D4711yescharacteristic
292D8—22no—
293D8—41no—
294D8—1881no—
295C2×C8—471no—
296C2×C8—471no—
297C2×C8—1881no—
298C2×C8—1881no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—471no—
302C4⋊C4—471no—
303C4⋊C4—471no—
304C4⋊C4—471no—
305C4⋊C4—941no—
306C4⋊C4—941no—
307C4⋊C4—941no—
308C4⋊C4C22×D4711yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—471no—
311C22⋊C4—471no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C42—471no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—471no—
325C23—941no—
326C23—3761no—
327C23—1882no—
328C23—1882no—
329C23D4×D4711yescharacteristic
330Q8—1882no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—474no—
339D4—941no—
340D4—941no—
341D4—3761no—
342D4—1882no—
343D4—1882no—
344D4—1882no—
345D4—1882no—
346D4—1882no—
347D4#1062535212yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—471no—
352C2×C4—471no—
353C2×C4—471no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—1882no—
360C2×C4—1882no—
361C2×C4—1882no—
362C2×C4—1882no—
363C2×C4D4×D4711yescharacteristic
364C2×C4C23×D4711yescharacteristic
365C8—21no—
366C8—21no—
367C8—941no—
368C8—941no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—472no—
382C22—941no—
383C22—941no—
384C22—3764no—
385C22—1881no—
386C22—1881no—
387C22—1881no—
388C22D8×D4712yes—
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—41no—
392C4—472no—
393C4—941no—
394C4—941no—
395C4—1881no—
396C4—1881no—
397C4—1881no—
398C4C2×#1062535211yescharacteristic
399C4#1309406911yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—942no—
405C2—3761no—
406C2#1568976011yescharacteristic
407C2C2×D8×D4711yescharacteristic
408C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3294
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #15689773C2semidirect
2. D4×C22⋊D47C2semidirect
3. #15689468C2semidirect
4. #15689437C2semidirect
5. #15689435C2semidirect
6. #15689401C2semidirect
7. #15689357C2semidirect
8. #15689356C2semidirect
9. #15689316C2semidirect
10. #15689255C2semidirect
11. D8×Dic47C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. C2×#13093945C2semidirect
14. #102×D47C2semidirect
15. C47×#447C2semidirect
19. C2×#10625334C22semidirect
20. C22×C47⋊C8C22semidirect
21. C2×C8×D47C22semidirect
22. #13094023C22semidirect
30. #13093995C22semidirect
34. D4×Dic47C22semidirect
36. C2×C4⋊Dic47C22semidirect
37. C4⋊C4×D47C22semidirect
38. #13093958C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093946C22semidirect
43. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
54. C2×D8×C47C22semidirect
55. #121×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
132. D4×C47#41semidirect
144. C22⋊D47D8semidirect
215. #447D47semidirect
220. C47#3294semidirect
227. C2×D8C2×D47semidirect
239. #121C2×D47semidirect
260. #102C2×D47semidirect
262. C22⋊C8C2×D47semidirect
347. D4#10625352semidirect