Finite Group Databasebeta

← #20254348

Subgroups — #20254348

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#15689652C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic, complemented
3#15689505C211yesmaximal, characteristic, complemented
4#15689478C211yesmaximal, characteristic, complemented
5#15689477C211yesmaximal, characteristic, complemented
6#15689347C211yesmaximal, characteristic, complemented
7#15689343C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689260C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic
14#15689174C211yesmaximal, characteristic, complemented
15C47×#495C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625336C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22#13094017—21no—
23#13094016C2211yescharacteristic, complemented
24#13094013C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094011C2211yescharacteristic
27#13094010—21no—
28#13094010—21no—
29#13094006—21no—
30#13094000C2211yescharacteristic
31#13093995C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic, complemented
33D4×Dic47C2211yescharacteristic, complemented
34(C22⋊D47)⋊C4—21no—
35#13093980—21no—
36C22⋊C4×D47—21no—
37C22⋊C4×D47—21no—
38C42×D47C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093949C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic
57#124×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67Q8×D47—41no—
68Q8×D47—41no—
69D4×D47—41no—
70D4×D47—41no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78Q16×C47—41no—
79SD16×C47—41no—
80SD16×C47—41no—
81D8×C47—41no—
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93#10625337—41no—
94#10625336—41no—
95#10625335—41no—
96#10625334—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C4×Dic47—21no—
109C4×Dic47D411yescharacteristic
110C4×Dic47D411yescharacteristic
111C4×Dic47C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
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—
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—42no—
135C22⋊D47—42no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—42no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143D188—21no—
144D188—21no—
145C4×D47—22no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—41no—
149C4×D47—42no—
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#495D4711yescharacteristic, complemented
195#488—471no—
196#488—471no—
197#464—471no—
198#464—471no—
199#463—471no—
200#463—471no—
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×Q16C2×D4711yescharacteristic, complemented
211C2×SD16—471no—
212C2×SD16—471no—
213C2×SD16C2×D4711yescharacteristic
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—941no—
223#124—941no—
224#124C2×D4711yescharacteristic
225#124C2×D4711yescharacteristic, complemented
226#123—941no—
227C22⋊Q8—471no—
228#121—471no—
229C4×Q8—471no—
230C4×D4—471no—
231C4×D4—941no—
232#117—941no—
233C2×C22⋊C4—941no—
234C2×C22⋊C4—941no—
235C2×C42—471no—
236C4⋊C8—471no—
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#103—471no—
241#103—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246C22⋊C8—471no—
247C22⋊C8—471no—
248C4×C8—471no—
249C4×C8C2×D4711yescharacteristic, complemented
250C24—941no—
251C2×Q8—471no—
252C2×Q8—941no—
253C2×Q8—1881no—
254C2×Q8—1881no—
255C2×Q8C22×D4711yescharacteristic
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—471no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—941no—
268C22×C4—941no—
269Q16—41no—
270Q16—1881no—
271SD16—41no—
272SD16—41no—
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—471no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
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—21no—
315Q8—21no—
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—471no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—942no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—1881no—
339C2×C4—1882no—
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#1309406911yescharacteristic
374C2—81no—
375C2—81no—
376C2—942no—
377C2—3761no—
378C2#1568968611yescharacteristic
379C2#135×D4711yescharacteristic
380C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3211
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #15689652C2semidirect
2. #124×D47C2semidirect
3. #15689505C2semidirect
4. #15689478C2semidirect
5. #15689477C2semidirect
6. #15689347C2semidirect
7. #15689343C2semidirect
8. #15689340C2semidirect
9. #15689336C2semidirect
10. #15689277C2semidirect
11. #15689272C2semidirect
12. #15689260C2semidirect
14. #15689174C2semidirect
15. C47×#495C2semidirect
18. C2×#10625337C22semidirect
19. C2×#10625335C22semidirect
23. #13094016C22semidirect
32. Q8×Dic47C22semidirect
33. D4×Dic47C22semidirect
39. Dic47⋊C8C22semidirect
40. Dic47⋊C8C22semidirect
41. #13093949C22semidirect
42. #13093949C22semidirect
43. #13093948C22semidirect
44. #13093948C22semidirect
51. C4×C47⋊C8C22semidirect
52. C2×Q16×C47C22semidirect
54. C2×SD16×C47C22semidirect
57. #124×C47C22semidirect
58. C4×C8×C47C22semidirect
194. #495D47semidirect
206. C47#3211semidirect
210. C2×Q16C2×D47semidirect
214. C2×SD16C2×D47semidirect
225. #124C2×D47semidirect
249. C4×C8C2×D47semidirect