Finite Group Databasebeta

← #20254456

Subgroups — #20254456

Order 6016.

396 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#15689733C211yesmaximal, characteristic, complemented
2#15689690C211yesmaximal, characteristic
3#15689514C211yesmaximal, characteristic, complemented
4#15689494C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689476C211yesmaximal, characteristic, complemented
7#15689344C211yesmaximal, characteristic, complemented
8#15689343C211yesmaximal, characteristic, complemented
9#15689322C211yesmaximal, characteristic, complemented
10#15689321C211yesmaximal, characteristic, complemented
11#15689287C211yesmaximal, characteristic, complemented
12#15689283C211yesmaximal, characteristic, complemented
13#15689274C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Dic188C2211yescharacteristic, complemented
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic, complemented
20C2×#10625335C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625336C2211yescharacteristic, complemented
23#13094022C2211yescharacteristic, complemented
24#13094020C2211yescharacteristic
25#13094020C2211yescharacteristic
26#13094017—21no—
27#13094017—21no—
28#13094015—21no—
29#13094015C2211yescharacteristic, complemented
30#13094014—21no—
31#13094011C2211yescharacteristic
32#13094011C2211yescharacteristic
33#13094003C2211yescharacteristic
34#13093995—21no—
35#13093995—21no—
36#13093993—21no—
37#13093993—21no—
38Q8×Dic47C2211yescharacteristic, complemented
39#13093989C2211yescharacteristic, complemented
40#13093983C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72#10625350—41no—
73#10625350—41no—
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78SD16×C47—41no—
79SD16×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91C22⋊Dic47D411yescharacteristic
92#10625337—41no—
93#10625336—41no—
94#10625335—41no—
95#10625335—41no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47D411yescharacteristic
99C4⋊Dic47D411yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108C4×Dic47C2311yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112Dic188—41no—
113#10625325—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—42no—
117C23×C47—81no—
118C23×C47—81no—
119C23×C47C2×D411yescharacteristic
120C22×D47—21no—
121Q8×C47—21no—
122Q8×C47—21no—
123D4×C47—21no—
124D4×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×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—42no—
135C22⋊D47—81no—
136C22⋊D47—81no—
137C22⋊D47—81no—
138C22⋊D47—81no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145C2×Dic47C2×D411yescharacteristic
146D188—21no—
147D188—21no—
148C4×D47—42no—
149Dic94—21no—
150Dic94—21no—
151Dic94—21no—
152Dic94—21no—
153C8×C47—21no—
154C8×C47—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—84no—
167C22×C47C22×D411yescharacteristic
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C4×C47—21no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47H(5,𝔽2)11yescharacteristic
175C4×C47H(5,𝔽2)11yescharacteristic
176Dic47—21no—
177Dic47—21no—
178Dic47—21no—
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3222—471nomaximal, Sylow
184C2×C47—41no—
185C2×C47—81no—
186C2×C47—81no—
187C2×C47#53511yescharacteristic
188C2×C47#57711yescharacteristic
189C2×C47#57711yescharacteristic
190D47—81no—
191#541—471no—
192#535—471no—
193#497—471no—
194#492—471no—
195#490—471no—
196#488—471no—
197#464—471no—
198#464—471no—
199#460—471no—
200#460—471no—
201#452—471no—
202#452—471no—
203#450—471no—
204#450D4711yescharacteristic, complemented
205#433—471no—
206C47#322211yescharacteristic, complemented, Sylow
207C2×#41—471no—
208C22×D4C2×D4711yescharacteristic
209C2×Q16—471no—
210C2×Q16—471no—
211C2×SD16—471no—
212C2×SD16—471no—
213C2×SD16—471no—
214C2×SD16—471no—
215C2×SD16C2×D4711yescharacteristic
216C2×SD16C2×D4711yescharacteristic
217C4⋊Q8—471no—
218#127—471no—
219#127—471no—
220#126—941no—
221#126—941no—
222#125—471no—
223#125—941no—
224#125—941no—
225#124—471no—
226#124—471no—
227C22⋊Q8—471no—
228C22⋊Q8C2×D4711yescharacteristic
229#121—941no—
230#121—941no—
231#120—941no—
232#120—941no—
233C4×Q8—471no—
234C4×Q8—471no—
235#117—471no—
236C4⋊C8—471no—
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102C2×D4711yescharacteristic
245#102C2×D4711yescharacteristic
246C22⋊C8—471no—
247C22⋊C8C2×D4711yescharacteristic
248#97—471no—
249C4×C8—471no—
250C24—21no—
251#41—1881no—
252#41—1881no—
253C2×Q8—471no—
254C2×Q8—471no—
255C2×Q8C22×D4711yescharacteristic
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—471no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4C22×D4711yescharacteristic
266C2×D4C22×D4711yescharacteristic
267C22×C4—941no—
268C22×C4C22×D4711yescharacteristic
269Q16—1881no—
270Q16—1881no—
271SD16—41no—
272SD16—41no—
273SD16—1881no—
274SD16—1881no—
275SD16—1881no—
276SD16—1881no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4C22×D4711yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—471no—
295C22⋊C4—471no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C42—471no—
302C42—471no—
303C42—941no—
304C42—941no—
305C23—21no—
306C23—21no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—941no—
311C23D4×D4711yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—941no—
315Q8—941no—
316Q8—941no—
317Q8—941no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—941no—
324D4—941no—
325D4—3761no—
326D4—3761no—
327D4—3761no—
328D4—3761no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—471no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—1882no—
342C2×C4D4×D4711yescharacteristic
343C2×C4C23×D4711yescharacteristic
344C8—21no—
345C8—21no—
346C8—941no—
347C8—941no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—84no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22C2×D4×D4711yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—941no—
366C4—941no—
367C4—941no—
368C4—941no—
369C4—1881no—
370C4—1881no—
371C4—1881no—
372C4#1309406911yescharacteristic
373C4#1309406911yescharacteristic
374C2—41no—
375C2—81no—
376C2—81no—
377C2—3761no—
378C2#1568968811yescharacteristic
379C2#1568992911yescharacteristic
380C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3222
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689733C2semidirect
3. #15689514C2semidirect
4. #15689494C2semidirect
5. #15689486C2semidirect
6. #15689476C2semidirect
7. #15689344C2semidirect
8. #15689343C2semidirect
9. #15689322C2semidirect
10. #15689321C2semidirect
11. #15689287C2semidirect
12. #15689283C2semidirect
13. #15689274C2semidirect
14. #15689181C2semidirect
15. C47×#450C2semidirect
17. C2×Dic188C22semidirect
18. C2×#10625337C22semidirect
19. C2×#10625325C22semidirect
22. C2×#10625336C22semidirect
23. #13094022C22semidirect
29. #13094015C22semidirect
38. Q8×Dic47C22semidirect
39. #13093989C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
45. #13093946C22semidirect
48. #13093944C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
204. #450D47semidirect
206. C47#3222semidirect