Finite Group Databasebeta

← #20254351

Subgroups — #20254351

Order 6016.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689655C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic, complemented
3#15689506C211yesmaximal, characteristic, complemented
4#15689504C211yesmaximal, characteristic, complemented
5#15689479C211yesmaximal, characteristic, complemented
6#15689476C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689338C211yesmaximal, characteristic, complemented
10#15689280C211yesmaximal, characteristic, complemented
11#15689275C211yesmaximal, characteristic, complemented
12#15689260C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic
14#15689175C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625337C2211yescharacteristic, complemented
20C2×#10625325C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625335C2211yescharacteristic, complemented
23C2×#10625334C2211yescharacteristic
24#13094017—21no—
25#13094015C2211yescharacteristic, complemented
26#13094013C2211yescharacteristic
27#13094012C2211yescharacteristic
28#13094011C2211yescharacteristic
29#13094011C2211yescharacteristic, complemented
30#13094010—21no—
31#13094010—21no—
32#13094006—21no—
33#13094004C2211yescharacteristic
34#13093995C2211yescharacteristic
35C4×Dic94C2211yescharacteristic, complemented
36C4×C22⋊D47—21no—
37#13093983—21no—
38C22⋊C4×D47—21no—
39C22⋊C4×D47—21no—
40C42×D47C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic, complemented
53C2×D8×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66Q8×D47—41no—
67Q8×D47—41no—
68D4×D47—41no—
69D4×D47—41no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47D411yescharacteristic
73C2×C4×D47D411yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78SD16×C47—41no—
79D8×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92#10625337—41no—
93#10625335—41no—
94#10625335—41no—
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—
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C4×Dic47D411yescharacteristic
108C4×Dic47D411yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112Dic188—41no—
113#10625325—41no—
114C23×C47—21no—
115C23×C47—21no—
116C22×D47—21no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47C2×D411yescharacteristic
121Q8×C47—21no—
122Q8×C47—21no—
123D4×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—42no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C22⋊D47—42no—
134C22⋊D47—42no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141D188—21no—
142D188—21no—
143C4×D47—22no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—41no—
147C4×D47—42no—
148Dic94—21no—
149Dic94—21no—
150Dic94—21no—
151Dic94—21no—
152Dic94—42no—
153C8×C47—21no—
154C8×C47—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47C22×D411yescharacteristic
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—84no—
170C2×D47#13512yes—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47H(5,𝔽2)11yescharacteristic
176C4×C47H(5,𝔽2)11yescharacteristic
177Dic47—21no—
178Dic47—21no—
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3211—471nomaximal, Sylow
184C2×C47—81no—
185C2×C47—81no—
186C2×C47#53511yescharacteristic
187C2×C47C2×#13511yescharacteristic
188C2×C47#57511yescharacteristic
189D47—22no—
190D47—81no—
191#529—471no—
192C2×#124—471no—
193#495—471no—
194#495—471no—
195#488—471no—
196#488—471no—
197#464—471no—
198#464—471no—
199#463—471no—
200#463D4711yescharacteristic, complemented
201#451—471no—
202#450—471no—
203#448—471no—
204#447—471no—
205#431—471no—
206C47#321111yescharacteristic, complemented, Sylow
207C22×Q8—471no—
208C22×D4—471no—
209C2×Q16—471no—
210C2×Q16—471no—
211C2×SD16—471no—
212C2×SD16—471no—
213C2×SD16—471no—
214C2×SD16C2×D4711yescharacteristic, complemented
215C2×D8—471no—
216C2×D8C2×D4711yescharacteristic
217#126—941no—
218#125—471no—
219#124—471no—
220#124—471no—
221#124—471no—
222#124—471no—
223#124—941no—
224#124—941no—
225#124C2×D4711yescharacteristic
226#123—941no—
227C22⋊Q8—471no—
228#121—471no—
229C4×Q8—471no—
230C4×D4—941no—
231C4×D4C2×D4711yescharacteristic, complemented
232#117—941no—
233C2×C22⋊C4—941no—
234C2×C22⋊C4—941no—
235C2×C42—471no—
236C4⋊C8—471no—
237C4⋊C8C2×D4711yescharacteristic, complemented
238#103—471no—
239#103—471no—
240#103—471no—
241#103C2×D4711yescharacteristic, complemented
242#102—471no—
243#102—471no—
244#102—471no—
245#102C2×D4711yescharacteristic
246C22⋊C8—471no—
247C22⋊C8—471no—
248C4×C8—471no—
249C4×C8—471no—
250C24—941no—
251C2×Q8—471no—
252C2×Q8—471no—
253C2×Q8—941no—
254C2×Q8—1881no—
255C2×Q8—1881no—
256C2×Q8C22×D4711yescharacteristic
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—1881no—
261C2×D4—1881no—
262C2×D4C22×D4711yescharacteristic
263C2×D4C22×D4711yescharacteristic
264C22×C4—21no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—941no—
269Q16—1881no—
270Q16—1881no—
271SD16—41no—
272SD16—1881no—
273SD16—1881no—
274SD16—1881no—
275D8—41no—
276D8—1881no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—471no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22×D4711yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C42—471no—
301C42—471no—
302C42—471no—
303C42—941no—
304C42C22×D4711yescharacteristic
305C23—21no—
306C23—21no—
307C23—471no—
308C23—941no—
309C23—1882no—
310C23—1882no—
311C23—1882no—
312Q8—21no—
313Q8—21no—
314Q8—941no—
315Q8—941no—
316Q8—941no—
317Q8—941no—
318Q8—1882no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—941no—
324D4—941no—
325D4—1882no—
326D4—1882no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—471no—
333C2×C4—942no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—1881no—
340C2×C4—1882no—
341C2×C4D4×D4711yescharacteristic
342C2×C4D4×D4711yescharacteristic
343C2×C4C23×D4711yescharacteristic
344C8—21no—
345C8—21no—
346C8—941no—
347C8—941no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—472no—
355C22—941no—
356C22—941no—
357C22—3764no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22C2×D4×D4711yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—941no—
367C4—941no—
368C4—941no—
369C4—1881no—
370C4—1881no—
371C4—1881no—
372C4#1309406911yescharacteristic
373C4#1309407011yescharacteristic
374C2—81no—
375C2—81no—
376C2—942no—
377C2—3761no—
378C2#1568968911yescharacteristic
379C2#135×D4711yescharacteristic
380C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3211
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #15689655C2semidirect
2. #124×D47C2semidirect
3. #15689506C2semidirect
4. #15689504C2semidirect
5. #15689479C2semidirect
6. #15689476C2semidirect
7. #15689346C2semidirect
8. #15689342C2semidirect
9. #15689338C2semidirect
10. #15689280C2semidirect
11. #15689275C2semidirect
12. #15689260C2semidirect
14. #15689175C2semidirect
15. C47×#463C2semidirect
18. C2×Dic188C22semidirect
19. C2×#10625337C22semidirect
22. C2×#10625335C22semidirect
25. #13094015C22semidirect
29. #13094011C22semidirect
35. C4×Dic94C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093948C22semidirect
44. #13093947C22semidirect
50. C8×Dic47C22semidirect
51. C8×Dic47C22semidirect
52. C2×SD16×C47C22semidirect
55. C4×D4×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
200. #463D47semidirect
206. C47#3211semidirect
214. C2×SD16C2×D47semidirect
231. C4×D4C2×D47semidirect
237. C4⋊C8C2×D47semidirect
241. #103C2×D47semidirect