Finite Group Databasebeta

← #20255230

Subgroups — #20255230

Order 6016.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689814C211yesmaximal, characteristic, complemented
2#15689766C211yesmaximal, characteristic
3#15689477C211yesmaximal, characteristic, complemented
4#15689452C211yesmaximal, characteristic, complemented
5#15689445C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689361C211yesmaximal, characteristic, complemented
8#15689349C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11C4×#10625336C211yesmaximal, characteristic, complemented
12#15689188C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic, complemented
21#13094018—21no—
22#13094016C2211yescharacteristic, complemented
23#13094014—21no—
24#13094009—21no—
25#13094006—21no—
26#13094000C2211yescharacteristic
27#13094000C2211yescharacteristic
28#13094000C2211yescharacteristic, complemented
29#13093997—21no—
30#13093995C2211yescharacteristic
31#13093994—21no—
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093982C2211yescharacteristic, complemented
35#13093981—21no—
36C4⋊C4×D47C2211yescharacteristic
37C22⋊C4×D47—21no—
38#13093958C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C4×C47⋊C8C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65#10625354—22no—
66#10625354—41no—
67D4×D47—22no—
68D4×D47—41no—
69C2×D188—21no—
70C2×D188D411yescharacteristic
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77Q16×C47—41no—
78SD16×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625336—22no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47D411yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C8×D47—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47—81no—
116C22×D47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—22no—
138D188—21no—
139D188—42no—
140D188#4112yes—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—42no—
146C4×D47—42no—
147C4×D47—81no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—22no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—84no—
165C2×D47#13512yes—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3296—471nomaximal, Sylow
179C2×C47—81no—
180C2×C47#54611yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—22no—
184D47—41no—
185D47—42no—
186#552—471no—
187#546—471no—
188#488—471no—
189#483—471no—
190#482—471no—
191#478—471no—
192#467—471no—
193#465—471no—
194#464D4711yescharacteristic, complemented
195#452—471no—
196#450—471no—
197C4×SD16—471no—
198C8×D4—471no—
199#416—471no—
200C2×#102—471no—
201C47#329611yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4—471no—
204C2×Q16C2×D4711yescharacteristic, complemented
205C2×SD16—471no—
206C2×SD16C2×D4711yescharacteristic
207C22×C8—471no—
208C22×C8—471no—
209#126—941no—
210#125—471no—
211#125—941no—
212#124C2×D4711yescharacteristic
213#123—941no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8C2×D4711yescharacteristic, complemented
222C4×D4—471no—
223C4×D4—471no—
224#117—471no—
225#117—941no—
226C2×C4⋊C4—471no—
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106—471no—
231C4⋊C8C2×D4711yescharacteristic, complemented
232#103—471no—
233#103—471no—
234#103—471no—
235#103C2×D4711yescharacteristic, complemented
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244C4×C8—471no—
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8C22×D4711yescharacteristic
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4—942no—
255C2×D4—941no—
256C2×D4—1881no—
257C2×D4C22×D4711yescharacteristic
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263Q16—41no—
264SD16—41no—
265SD16—942no—
266C2×C8—471no—
267C2×C8—471no—
268C2×C8—1881no—
269C2×C8—1881no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4C22×D4711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—471no—
287C22⋊C4—471no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C42—21no—
295C42—941no—
296C42C22×D4711yescharacteristic
297C23—21no—
298C23—471no—
299C23—471no—
300C23—941no—
301C23—3761no—
302C23—1882no—
303C23—1882no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—472no—
311D4—942no—
312D4—941no—
313D4—3761no—
314D4—1882no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—3761no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—472no—
342C22—941no—
343C22—941no—
344C22—941no—
345C22—942no—
346C22—941no—
347C22—941no—
348C22—3764no—
349C22—1881no—
350C22—1881no—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—941no—
358C4—941no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4#41×D4711yescharacteristic
363C4#1309406911yescharacteristic
364C2—81no—
365C2—942no—
366C2—1881no—
367C2—1882no—
368C2#1568977011yescharacteristic
369C2#135×D4711yescharacteristic
370C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3296
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #15689814C2semidirect
3. #15689477C2semidirect
4. #15689452C2semidirect
5. #15689445C2semidirect
6. #15689424C2semidirect
7. #15689361C2semidirect
8. #15689349C2semidirect
9. #15689284C2semidirect
10. #15689272C2semidirect
11. C4×#10625336C2semidirect
12. #15689188C2semidirect
13. #15689118C2semidirect
14. #102×D47C2semidirect
15. C47×#464C2semidirect
20. C2×C8×D47C22semidirect
22. #13094016C22semidirect
28. #13094000C22semidirect
34. #13093982C22semidirect
38. #13093958C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
43. #13093948C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C4×C47⋊C8C22semidirect
52. C2×Q16×C47C22semidirect
55. C4×Q8×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
194. #464D47semidirect
201. C47#3296semidirect
204. C2×Q16C2×D47semidirect
221. C4×Q8C2×D47semidirect
231. C4⋊C8C2×D47semidirect
235. #103C2×D47semidirect