Finite Group Databasebeta

← #20255207

Subgroups — #20255207

Order 6016.

462 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#15689831C211yesmaximal, characteristic, complemented
2#15689757C211yesmaximal, characteristic
3#15689468C211yesmaximal, characteristic, complemented
4#15689443C211yesmaximal, characteristic, complemented
5#15689439C211yesmaximal, characteristic, complemented
6#15689412C211yesmaximal, characteristic, complemented
7#15689355C211yesmaximal, characteristic, complemented
8#15689321C211yesmaximal, characteristic, complemented
9#15689273C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689208C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic, complemented
13C2×#13093946C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic, complemented
21C2×C8×D47C2211yescharacteristic, complemented
22#13094023C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic
24#13094014—21no—
25#13094004—21no—
26#13094001—21no—
27#13094000C2211yescharacteristic, complemented
28#13093999C2211yescharacteristic
29#13093997—21no—
30#13093994—21no—
31#13093992—21no—
32Q8×Dic47C2211yescharacteristic, complemented
33#13093986C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36C2×C4⋊Dic47C2211yescharacteristic, complemented
37C4⋊C4×D47C2211yescharacteristic, complemented
38#13093955C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093946C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic, complemented
54C22⋊Q8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70D4×D47—22no—
71D4×D47—41no—
72D4×D47—44no—
73C2×D188—22no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—41no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47C2311yescharacteristic
82C2×Dic94—21no—
83SD16×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47—21no—
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊Dic47D411yescharacteristic
93#10625336—22no—
94#10625336—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4D411yescharacteristic
107C4×Dic47—21no—
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C8×D47—41no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
123Q8×C47—21no—
124Q8×C47—21no—
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×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—42no—
136C22⋊D47—42no—
137C22⋊D47—81no—
138C22⋊D47SD1614yescomplemented
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—81no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—42no—
149D188—42no—
150D188#4112yes—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—42no—
154C4×D47—81no—
155Dic94—81no—
156C8×C47—21no—
157C8×C47—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47C2×SD1612yes—
166C22×C47C22×D411yescharacteristic
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—22no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—84no—
176C2×D47—84no—
177C2×D47C2×SD1612yes—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47C2×#4111yescharacteristic
183C4×C47H(5,𝔽2)11yescharacteristic
184Dic47—21no—
185Dic47—21no—
186Dic47—41no—
187Dic47—41no—
188Dic47C2×SD1612yes—
189#3295—471nomaximal, Sylow
190C2×C47—22no—
191C2×C47—81no—
192C2×C47#54611yescharacteristic
193C2×C47C22×SD1611yescharacteristic
194C2×C47#57611yescharacteristic
195D47—22no—
196D47—42no—
197D47—81no—
198#554—471no—
199D42—471no—
200#486—471no—
201#481—471no—
202#481—471no—
203#476—471no—
204#465—471no—
205#465D4711yescharacteristic, complemented
206#460—471no—
207#450—471no—
208#450—471no—
209C4×SD16—471no—
210C8×D4—471no—
211C2×#102—471no—
212C2×#102—471no—
213C47#329511yescharacteristic, complemented, Sylow
214C22×D4—471no—
215C22×D4—471no—
216C22×D4—941no—
217C2×SD16—471no—
218C2×SD16—471no—
219C2×SD16C2×D4711yescharacteristic, complemented
220C22×C8—471no—
221C22×C8C2×D4711yescharacteristic, complemented
222C4⋊Q8—471no—
223#127—471no—
224#125—941no—
225C22⋊Q8—471no—
226C22⋊Q8—941no—
227C22⋊Q8—941no—
228C22⋊Q8C2×D4711yescharacteristic, complemented
229#121—471no—
230#121—941no—
231#121C2×D4711yescharacteristic
232#120—941no—
233#120—941no—
234C4×Q8—471no—
235C4×D4—471no—
236C4×D4—471no—
237C4×D4—941no—
238C2×C4⋊C4—471no—
239C2×C4⋊C4—471no—
240#106—471no—
241#106—471no—
242#106C2×D4711yescharacteristic, complemented
243C4⋊C8—471no—
244#103C2×D4711yescharacteristic, complemented
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252#102—471no—
253#102C2×D4711yescharacteristic, complemented
254C22⋊C8—471no—
255C22⋊C8—471no—
256C4×C8—471no—
257C24—941no—
258C24—941no—
259C2×Q8—941no—
260C2×Q8C22×D4711yescharacteristic
261C2×D4—21no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4—942no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4—942no—
271C2×D4—941no—
272C2×D4—1881no—
273C2×D4—1881no—
274C2×D4—1884no—
275C2×D4C22×D4711yescharacteristic
276C22×C4—471no—
277C22×C4—941no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4C22×D4711yescharacteristic
281SD16—41no—
282SD16—942no—
283SD16—1881no—
284C2×C8—41no—
285C2×C8—471no—
286C2×C8—471no—
287C2×C8—1881no—
288C2×C8C22×D4711yescharacteristic
289C2×C8C22×D4711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—471no—
292C4⋊C4—471no—
293C4⋊C4—471no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4—941no—
299C4⋊C4C22×D4711yescharacteristic
300C4⋊C4C22×D4711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—471no—
304C22⋊C4—471no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C42—471no—
309C42—941no—
310C23—21no—
311C23—471no—
312C23—941no—
313C23—941no—
314C23—3761no—
315C23—3761no—
316C23—1882no—
317C23—1882no—
318C23—1882no—
319C23—1882no—
320C23D4×D4711yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—3761no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—474no—
328D4—472no—
329D4—941no—
330D4—941no—
331D4—941no—
332D4—3761no—
333D4—1882no—
334D4—1882no—
335D4—1882no—
336D4—1882no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—471no—
343C2×C4—471no—
344C2×C4—471no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—3761no—
350C2×C4—3761no—
351C2×C4—1882no—
352C2×C4D4×D4711yescharacteristic
353C2×C4C23×D4711yescharacteristic
354C8—21no—
355C8—21no—
356C8—941no—
357C8—941no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—472no—
364C22—941no—
365C22—941no—
366C22—942no—
367C22—3764no—
368C22—3764no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22SD16×D4712yes—
375C22C2×D4×D4711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—472no—
381C4—941no—
382C4—941no—
383C4—1881no—
384C4—1881no—
385C4#41×D4711yescharacteristic
386C4#1309406911yescharacteristic
387C2—22no—
388C2—81no—
389C2—942no—
390C2—3761no—
391C2—1882no—
392C2#1568976211yescharacteristic
393C2C2×SD16×D4711yescharacteristic
394C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3295
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689831C2semidirect
3. #15689468C2semidirect
4. #15689443C2semidirect
5. #15689439C2semidirect
6. #15689412C2semidirect
7. #15689355C2semidirect
8. #15689321C2semidirect
9. #15689273C2semidirect
10. #15689272C2semidirect
11. #15689208C2semidirect
12. C8×C22⋊D47C2semidirect
13. C2×#13093946C2semidirect
14. #102×D47C2semidirect
15. C47×#465C2semidirect
20. C2×#10625336C22semidirect
21. C2×C8×D47C22semidirect
22. #13094023C22semidirect
27. #13094000C22semidirect
32. Q8×Dic47C22semidirect
36. C2×C4⋊Dic47C22semidirect
37. C4⋊C4×D47C22semidirect
38. #13093955C22semidirect
39. #13093955C22semidirect
40. Dic47⋊C8C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
45. #13093945C22semidirect
46. #13093945C22semidirect
48. #13093944C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
52. C2×SD16×C47C22semidirect
53. C22×C8×C47C22semidirect
54. C22⋊Q8×C47C22semidirect
56. #106×C47C22semidirect
57. #103×C47C22semidirect
58. #102×C47C22semidirect
138. C22⋊D47SD16semidirect
205. #465D47semidirect
213. C47#3295semidirect
219. C2×SD16C2×D47semidirect
221. C22×C8C2×D47semidirect
228. C22⋊Q8C2×D47semidirect
242. #106C2×D47semidirect
244. #103C2×D47semidirect
253. #102C2×D47semidirect