Finite Group Databasebeta

← #20252413

Subgroups — #20252413

Order 6016.

456 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
1C4×D4×D47C211yesmaximal, characteristic
2#15689197C211yesmaximal, characteristic, complemented
3#15689196C211yesmaximal, characteristic, complemented
4#15689195C211yesmaximal, characteristic, complemented
5#15689194C211yesmaximal, characteristic, complemented
6#15689193C211yesmaximal, characteristic, complemented
7#15689192C211yesmaximal, characteristic, complemented
8#15689191C211yesmaximal, characteristic, complemented
9#15689179C211yesmaximal, characteristic, complemented
10#15689178C211yesmaximal, characteristic, complemented
11#15689086C211yesmaximal, characteristic, complemented
12#15689085C211yesmaximal, characteristic, complemented
13C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×D4×D47C411yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×#10625329C2211yescharacteristic, complemented
20C2×#10625324C2211yescharacteristic, complemented
21C2×#10625324C2211yescharacteristic, complemented
22C22×C47⋊C8C2211yescharacteristic, complemented
23C2×C8×D47C2211yescharacteristic, complemented
24C2×C8×D47C2211yescharacteristic, complemented
25C4×D188C2211yescharacteristic
26D4×Dic47C411yescharacteristic
27#13093986C411yescharacteristic
28C4×C22⋊D47C2211yescharacteristic
29C4×C22⋊D47C2211yescharacteristic
30(C22⋊D47)⋊C4C411yescharacteristic
31(C22⋊D47)⋊C4C411yescharacteristic
32C4⋊C4×D47C411yescharacteristic
33C22⋊C4×D47C411yescharacteristic
34C22⋊C4×D47C411yescharacteristic
35C42×D47C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic, complemented
37Dic47⋊C8C2211yescharacteristic, complemented
38Dic47⋊C8C2211yescharacteristic, complemented
39C22⋊(C47⋊C8)C2211yescharacteristic, complemented
40C22⋊(C47⋊C8)C2211yescharacteristic, complemented
41(C2×D47)⋊C8C2211yescharacteristic
42(C2×D47)⋊C8C2211yescharacteristic
43(C2×D47)⋊C8C2211yescharacteristic
44(C2×D47)⋊C8C2211yescharacteristic
45(C2×D47)⋊C8C2211yescharacteristic, complemented
46(C2×D47)⋊C8C2211yescharacteristic, complemented
47(C2×D47)⋊C8C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50#13093934C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C2×M16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic, complemented
56C22⋊C8×C47C2211yescharacteristic, complemented
57C22⋊C8×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47C2×C411yescharacteristic
60C23×D47C2×C411yescharacteristic
61C2×D4×C47C2×C411yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47C2×C411yescharacteristic
65C2×C22⋊D47C2×C411yescharacteristic
66C22×Dic47C2×C411yescharacteristic
67C22×Dic47C2×C411yescharacteristic
68D4×D47—24no—
69C2×D188C2×C411yescharacteristic
70C2×C4×D47—41no—
71C2×C4×D47—41no—
72C2×C4×D47—41no—
73C2×C4×D47—41no—
74C2×C4×D47C2×C411yescharacteristic
75C2×C4×D47C2×C411yescharacteristic
76C2×C4×D47C2×C411yescharacteristic
77C2×C4×D47C2×C411yescharacteristic
78C2×C4×D47C2×C411yescharacteristic
79C2×C4×D47C2×C411yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×C4×D47C2311yescharacteristic
83M16×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C2×C8×C47C2311yescharacteristic
89C4⋊C4×C47C2×C411yescharacteristic
90C22⋊C4×C47C2×C411yescharacteristic
91C22⋊C4×C47C2×C411yescharacteristic
92C42×C47C2311yescharacteristic
93C22⋊Dic47C2×C411yescharacteristic
94C22⋊Dic47C2×C411yescharacteristic
95(C2×D47)⋊C4C2×C411yescharacteristic
96(C2×D47)⋊C4C2×C411yescharacteristic
97(C2×D47)⋊C4C2×C411yescharacteristic
98(C2×D47)⋊C4C2×C411yescharacteristic
99C4⋊Dic47C2×C411yescharacteristic
100Dic47⋊C4C2×C411yescharacteristic
101Dic47⋊C4C2×C411yescharacteristic
102C4×Dic47C2×C411yescharacteristic
103C4×Dic47C2×C411yescharacteristic
104C4×Dic47C2311yescharacteristic
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112#10625324—41no—
113C8×D47—41no—
114C8×D47—41no—
115C23×C47C22×C411yescharacteristic
116C23×C47C22×C411yescharacteristic
117C22×D47—22no—
118C22×D47—41no—
119C22×D47—41no—
120C22×D47—41no—
121C22×D47—41no—
122C22×D47M1614yescomplemented
123C22×D47C22×C411yescharacteristic
124C22×D47C22×C411yescharacteristic
125C22×D47C22×C411yescharacteristic
126D4×C47—22no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47C22×C411yescharacteristic
132C2×C4×C47C22×C411yescharacteristic
133C2×C4×C47C22×C411yescharacteristic
134C2×C4×C47C22×C411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—22no—
137C22⋊D47—22no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47C22×C411yescharacteristic
141C2×Dic47C22×C411yescharacteristic
142C2×Dic47C22×C411yescharacteristic
143C2×Dic47C22×C411yescharacteristic
144C2×Dic47C22×C411yescharacteristic
145D188—22no—
146C4×D47—22no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—41no—
154C4×D47—41no—
155C4×D47—41no—
156C4×D47—41no—
157C4×D47—41no—
158C8×C47—21no—
159C8×C47—21no—
160C8×C47—21no—
161C8×C47—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C47⋊C8—21no—
165C47⋊C8—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47C2×M1612yes—
172C22×C47C23×C411yescharacteristic
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—44no—
181C2×D47—44no—
182C2×D47C2×M1612yes—
183C2×D47C2×M1612yes—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47H(5,𝔽2)11yescharacteristic
189C4×C47H(5,𝔽2)11yescharacteristic
190Dic47—21no—
191Dic47—21no—
192Dic47—21no—
193Dic47—21no—
194Dic47—21no—
195#2973—471nomaximal, Sylow
196C2×C47—22no—
197C2×C47—41no—
198C2×C47#51811yescharacteristic
199C2×C47C22×M1611yescharacteristic
200C2×C47#56811yescharacteristic
201D47—22no—
202D47—22no—
203D47—41no—
204C2×C4×D4—471no—
205#435—471no—
206#435—471no—
207#435—471no—
208#435—471no—
209#435—471no—
210#435—471no—
211#435—471no—
212#435D4711yescharacteristic, complemented
213#432—471no—
214#432—471no—
215#407—471no—
216#407—471no—
217C2×C22⋊C8—471no—
218C2×C22⋊C8—471no—
219C47#297311yescharacteristic, complemented, Sylow
220C22×D4—471no—
221C23×C4—471no—
222C23×C4—471no—
223C2×M16—471no—
224C2×M16—471no—
225C2×M16—471no—
226C2×M16C2×D4711yescharacteristic, complemented
227C22×C8—471no—
228C22×C8—471no—
229C22×C8—471no—
230C22×C8C2×D4711yescharacteristic, complemented
231C4×D4—471no—
232C4×D4—471no—
233C4×D4—471no—
234C4×D4—471no—
235C4×D4—471no—
236C4×D4—471no—
237C4×D4—471no—
238C4×D4C2×D4711yescharacteristic
239C2×C4⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C42—471no—
243C4⋊C8—471no—
244C4⋊C8—471no—
245C4⋊C8—471no—
246C4⋊C8C2×D4711yescharacteristic, complemented
247C22⋊C8—471no—
248C22⋊C8—471no—
249C22⋊C8—471no—
250C22⋊C8—471no—
251C22⋊C8—471no—
252C22⋊C8—471no—
253C22⋊C8—471no—
254C22⋊C8—471no—
255C22⋊C8—471no—
256C22⋊C8—471no—
257C22⋊C8C2×D4711yescharacteristic, complemented
258C22⋊C8C2×D4711yescharacteristic, complemented
259#97—471no—
260#97—471no—
261#97—471no—
262#97C2×D4711yescharacteristic, complemented
263C24—471no—
264C24—471no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—471no—
268C2×D4—944no—
269C2×D4C4×D4711yescharacteristic
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—1881no—
282C22×C4—1881no—
283C22×C4—1881no—
284C22×C4—1881no—
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287M16—41no—
288M16—1881no—
289M16—1881no—
290M16—1881no—
291C2×C8—41no—
292C2×C8—471no—
293C2×C8—471no—
294C2×C8—471no—
295C2×C8—471no—
296C2×C8—1881no—
297C2×C8—1881no—
298C2×C8—1881no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C2×C8C22×D4711yescharacteristic
302C2×C8C22×D4711yescharacteristic
303C4⋊C4—471no—
304C4⋊C4—471no—
305C4⋊C4—471no—
306C4⋊C4C4×D4711yescharacteristic
307C22⋊C4—471no—
308C22⋊C4—471no—
309C22⋊C4—471no—
310C22⋊C4—471no—
311C22⋊C4—471no—
312C22⋊C4—471no—
313C22⋊C4C4×D4711yescharacteristic
314C22⋊C4C4×D4711yescharacteristic
315C42—471no—
316C42—471no—
317C42—471no—
318C42C22×D4711yescharacteristic
319C23—471no—
320C23—471no—
321C23—474no—
322C23—471no—
323C23—942no—
324C23—1881no—
325C23—1881no—
326C23—1881no—
327C23—1881no—
328C23C2×C4×D4711yescharacteristic
329C23C2×C4×D4711yescharacteristic
330D4—22no—
331D4—942no—
332D4—942no—
333D4—942no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—471no—
339C2×C4—471no—
340C2×C4—471no—
341C2×C4—471no—
342C2×C4—471no—
343C2×C4—942no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—1881no—
351C2×C4—1881no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4—1881no—
355C2×C4—1881no—
356C2×C4—1881no—
357C2×C4C2×C4×D4711yescharacteristic
358C2×C4C2×C4×D4711yescharacteristic
359C2×C4C2×C4×D4711yescharacteristic
360C2×C4C2×C4×D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—21no—
366C8—941no—
367C8—941no—
368C8—941no—
369C8—941no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—472no—
376C22—472no—
377C22—941no—
378C22—941no—
379C22—941no—
380C22—941no—
381C22—941no—
382C22—941no—
383C22—941no—
384C22—1884no—
385C22—1884no—
386C22M16×D4712yes—
387C22C22×C4×D4711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—941no—
393C4—941no—
394C4—941no—
395C4—941no—
396C4—941no—
397C4#1309406911yescharacteristic
398C4#1309407011yescharacteristic
399C2—22no—
400C2—41no—
401C2—942no—
402C2—942no—
403C2—1881no—
404C2#1568959511yescharacteristic
405C2C2×M16×D4711yescharacteristic
406C2#1568988811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D47
commutator, socleC22×C47C23×C4
FittingC47×#435C2
hypercenter#435D47
hypocenterC47#2973
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #15689197C2semidirect
3. #15689196C2semidirect
4. #15689195C2semidirect
5. #15689194C2semidirect
6. #15689193C2semidirect
7. #15689192C2semidirect
8. #15689191C2semidirect
9. #15689179C2semidirect
10. #15689178C2semidirect
11. #15689086C2semidirect
12. #15689085C2semidirect
13. C2×(C2×D47)⋊C8C2semidirect
14. C22⋊C8×D47C2semidirect
15. C47×#435C2semidirect
19. C2×#10625329C22semidirect
20. C2×#10625324C22semidirect
21. C2×#10625324C22semidirect
22. C22×C47⋊C8C22semidirect
23. C2×C8×D47C22semidirect
24. C2×C8×D47C22semidirect
36. C4⋊(C47⋊C8)C22semidirect
37. Dic47⋊C8C22semidirect
38. Dic47⋊C8C22semidirect
39. C22⋊(C47⋊C8)C22semidirect
40. C22⋊(C47⋊C8)C22semidirect
45. (C2×D47)⋊C8C22semidirect
46. (C2×D47)⋊C8C22semidirect
47. (C2×D47)⋊C8C22semidirect
48. (C2×D47)⋊C8C22semidirect
49. #13093935C22semidirect
50. #13093934C22semidirect
51. #13093934C22semidirect
52. C2×M16×C47C22semidirect
53. C22×C8×C47C22semidirect
55. C4⋊C8×C47C22semidirect
56. C22⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. #97×C47C22semidirect
122. C22×D47M16semidirect
212. #435D47semidirect
219. C47#2973semidirect
226. C2×M16C2×D47semidirect
230. C22×C8C2×D47semidirect
246. C4⋊C8C2×D47semidirect
257. C22⋊C8C2×D47semidirect
258. C22⋊C8C2×D47semidirect
262. #97C2×D47semidirect