Finite Group Databasebeta

← #20255199

Subgroups — #20255199

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#15689774C211yesmaximal, characteristic, complemented
2#15689757C211yesmaximal, characteristic, complemented
3#15689468C211yesmaximal, characteristic, complemented
4#15689438C211yesmaximal, characteristic, complemented
5#15689402C211yesmaximal, characteristic, complemented
6#15689360C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689317C211yesmaximal, characteristic, complemented
9#15689259C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689205C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13C2×#13093944C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#480C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19C2×D4×D47C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C2×D376C2211yescharacteristic, complemented
22C2×#10625334C2211yescharacteristic, complemented
23C22×C47⋊C8C2211yescharacteristic, complemented
24C2×C8×D47C2211yescharacteristic, complemented
25#13094023C2211yescharacteristic, complemented
26#13094020C2211yescharacteristic
27#13094009—21no—
28#13094007—21no—
29#13094002—21no—
30#13093999C2211yescharacteristic
31#13093999C2211yescharacteristic, complemented
32#13093998C2211yescharacteristic, complemented
33#13093997—21no—
34#13093994—21no—
35#13093992—21no—
36#13093986C2211yescharacteristic
37#13093986C2211yescharacteristic, complemented
38C4×C22⋊D47C2211yescharacteristic
39C4⋊C4×D47C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic, complemented
54#107×C47C2211yescharacteristic, complemented
55#107×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47D411yescharacteristic
70D4×D47—22no—
71D4×D47—41no—
72D4×D47—44no—
73#10625350—44no—
74C2×D188—22no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—41no—
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×Dic94—21no—
87C2×C8×C47C2311yescharacteristic
88C2×C8×C47C2311yescharacteristic
89C4⋊C4×C47—21no—
90C4⋊C4×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C22⋊Dic47D411yescharacteristic
95#10625334—41no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4D411yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110D376—22no—
111D376—41no—
112C8×D47—41no—
113C23×C47—21no—
114C23×C47C2×D411yescharacteristic
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—42no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47C2×D411yescharacteristic
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—42no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—42no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—42no—
137C22⋊D47—42no—
138C22⋊D47—42no—
139C22⋊D47—81no—
140C22⋊D47D814yescomplemented
141C2×Dic47—21no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—21no—
150D188—42no—
151D188—42no—
152D188—42no—
153D188#4112yescomplemented
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—42no—
157C4×D47—42no—
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—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47C2×D812yes—
170C22×C47C22×D411yescharacteristic
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—22no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—84no—
183C2×D47—84no—
184C2×D47C2×D812yes—
185C4×C47—21no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C2×#4111yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—21no—
192Dic47—21no—
193Dic47—41no—
194Dic47C2×D812yes—
195#3294—471nomaximal, Sylow
196C2×C47—22no—
197C2×C47—81no—
198C2×C47#54611yescharacteristic
199C2×C47C22×D811yescharacteristic
200C2×C47#57711yescharacteristic
201D47—22no—
202D47—42no—
203D47—81no—
204D47—81no—
205#547—471no—
206D42—471no—
207#486—471no—
208#480—471no—
209#480D4711yescharacteristic, complemented
210#474—471no—
211#466—471no—
212#466—471no—
213#459—471no—
214#447—471no—
215#447—471no—
216C4×D8—471no—
217C8×D4—471no—
218C2×#102—471no—
219C2×#102—471no—
220C47#329411yescharacteristic, complemented, Sylow
221C2×#41—941no—
222C22×D4—471no—
223C22×D4—471no—
224C22×D4—941no—
225C2×D8—471no—
226C2×D8—471no—
227C2×D8—471no—
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
240#120—941no—
241#120—941no—
242C4×D4—471no—
243C4×D4—471no—
244C4×D4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4C2×D4711yescharacteristic, complemented
247#107—471no—
248#107C2×D4711yescharacteristic, complemented
249#107C2×D4711yescharacteristic, complemented
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, complemented
260#102C2×D4711yescharacteristic, complemented
261C22⋊C8—471no—
262C22⋊C8C2×D4711yescharacteristic, complemented
263C4×C8—471no—
264C24—941no—
265C24—941no—
266#41—1884no—
267C2×Q8—941no—
268C2×D4—21no—
269C2×D4—471no—
270C2×D4—471no—
271C2×D4—471no—
272C2×D4—471no—
273C2×D4—942no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—942no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—1881no—
283C2×D4—1881no—
284C2×D4—1884no—
285C2×D4C22×D4711yescharacteristic
286C22×C4—21no—
287C22×C4—471no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4C22×D4711yescharacteristic
292D8—942no—
293D8—1881no—
294D8—1881no—
295C2×C8—471no—
296C2×C8—471no—
297C2×C8—1881no—
298C2×C8—1881no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—471no—
303C4⋊C4—471no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4C22×D4711yescharacteristic
307C4⋊C4C22×D4711yescharacteristic
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—471no—
320C23—941no—
321C23—941no—
322C23—941no—
323C23—3761no—
324C23—3761no—
325C23—1882no—
326C23—1882no—
327C23—1882no—
328C23—1882no—
329C23D4×D4711yescharacteristic
330Q8—1882no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—474no—
335D4—472no—
336D4—941no—
337D4—941no—
338D4—941no—
339D4—941no—
340D4—941no—
341D4—3761no—
342D4—1882no—
343D4—1882no—
344D4—1882no—
345D4—1882no—
346D4—1882no—
347D4—1882no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—471no—
355C2×C4—471no—
356C2×C4—471no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
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—41no—
372C22—41no—
373C22—41no—
374C22—472no—
375C22—941no—
376C22—941no—
377C22—942no—
378C22—3764no—
379C22—3764no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22—1881no—
388C22D8×D4712yes—
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—472no—
395C4—941no—
396C4—941no—
397C4—1881no—
398C4#41×D4711yescharacteristic
399C4#1309407011yescharacteristic
400C2—22no—
401C2—81no—
402C2—942no—
403C2—3761no—
404C2—3761no—
405C2—1882no—
406C2#1568976511yescharacteristic
407C2C2×D8×D4711yescharacteristic
408C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3294
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #15689774C2semidirect
2. #15689757C2semidirect
3. #15689468C2semidirect
4. #15689438C2semidirect
5. #15689402C2semidirect
6. #15689360C2semidirect
7. #15689357C2semidirect
8. #15689317C2semidirect
9. #15689259C2semidirect
10. #15689258C2semidirect
11. #15689205C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. C2×#13093944C2semidirect
14. #102×D47C2semidirect
15. C47×#480C2semidirect
21. C2×D376C22semidirect
22. C2×#10625334C22semidirect
23. C22×C47⋊C8C22semidirect
24. C2×C8×D47C22semidirect
25. #13094023C22semidirect
31. #13093999C22semidirect
32. #13093998C22semidirect
37. #13093986C22semidirect
39. C4⋊C4×D47C22semidirect
40. #13093957C22semidirect
41. Dic47⋊C8C22semidirect
43. #13093946C22semidirect
44. #13093945C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
53. C2×C4⋊C4×C47C22semidirect
54. #107×C47C22semidirect
55. #107×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
140. C22⋊D47D8semidirect
153. D188#41semidirect
209. #480D47semidirect
220. C47#3294semidirect
246. C2×C4⋊C4C2×D47semidirect
248. #107C2×D47semidirect
249. #107C2×D47semidirect
259. #102C2×D47semidirect
260. #102C2×D47semidirect
262. C22⋊C8C2×D47semidirect