Finite Group Databasebeta

← #20253660

Subgroups — #20253660

Order 6016.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689746C211yesmaximal, characteristic, complemented
2#15689604C211yesmaximal, characteristic, complemented
3#15689441C211yesmaximal, characteristic, complemented
4#15689412C211yesmaximal, characteristic, complemented
5#15689407C211yesmaximal, characteristic, complemented
6#15689348C211yesmaximal, characteristic, complemented
7#15689341C211yesmaximal, characteristic, complemented
8#15689283C211yesmaximal, characteristic, complemented
9#15689270C211yesmaximal, characteristic
10#15689234C211yesmaximal, characteristic, complemented
11#15689227C211yesmaximal, characteristic, complemented
12#15689210C211yesmaximal, characteristic, complemented
13#15689208C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#483C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094019—21no—
23#13094013C2211yescharacteristic
24#13094010—21no—
25#13094006—21no—
26#13094004—21no—
27#13093998C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29#13093989C2211yescharacteristic
30#13093989C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34C4×C22⋊D47—21no—
35C4×C22⋊D47—21no—
36#13093983C2211yescharacteristic
37#13093982—21no—
38C4⋊C4×D47—21no—
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64#10625350—22no—
65#10625350—22no—
66C2×D188C2311yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×Dic94—21no—
73C2×Dic94C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊Dic47D411yescharacteristic
83C22⋊Dic47D411yescharacteristic
84#10625337—22no—
85#10625336—22no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47D411yescharacteristic
94C4⋊Dic47D411yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106D376—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C22×D47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—81no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—24no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188—21no—
132D188—21no—
133D188#4112yes—
134C4×D47—24no—
135C4×D47—81no—
136C4×D47—81no—
137C4×D47—81no—
138Dic94—21no—
139Dic94—81no—
140Dic94#4112yes—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47C22×D411yescharacteristic
149C2×D47—22no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47C2×#4111yescharacteristic
161C4×C47C2×#4111yescharacteristic
162Dic47—22no—
163Dic47—21no—
164Dic47—21no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168#3125—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47#52511yescharacteristic
171C2×C47#57711yescharacteristic
172C2×C47#57711yescharacteristic
173D47—42no—
174D47—81no—
175#542—471no—
176#520—471no—
177#483D4711yescharacteristic, complemented
178#481—471no—
179#476—471no—
180#475—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185#442—471no—
186#441—471no—
187C4×SD16—471no—
188C4×SD16—471no—
189#433—471no—
190C47#312511yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196C4⋊Q8—471no—
197#126—941no—
198#124—471no—
199#124—941no—
200#123—941no—
201C22⋊Q8—941no—
202C22⋊Q8C2×D4711yescharacteristic
203#121—471no—
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×D4—471no—
208C4×D4—471no—
209C4×D4—471no—
210C4×D4—941no—
211C4×D4—941no—
212#117—471no—
213#117—941no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4C2×D4711yescharacteristic
216#106—471no—
217#106—471no—
218#106C2×D4711yescharacteristic
219#106C2×D4711yescharacteristic
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103C2×D4711yescharacteristic
225#103C2×D4711yescharacteristic
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8—471no—
231C22⋊C8C2×D4711yescharacteristic
232#97—471no—
233C4×C8—471no—
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8—941no—
238C2×Q8C22×D4711yescharacteristic
239C2×D4—471no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4—941no—
243C22×C4—21no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4C22×D4711yescharacteristic
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—471no—
271C22⋊C4—471no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C42—471no—
279C42—471no—
280C42—941no—
281C42—941no—
282C42—941no—
283C23—941no—
284C23—941no—
285C23D4×D4711yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—472no—
289Q8—941no—
290Q8—3761no—
291D4—472no—
292D4—944no—
293D4—941no—
294D4—941no—
295D4—941no—
296D4—3761no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—471no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—471no—
308C2×C4—944no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—3761no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4D4×D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—941no—
319C8—941no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—942no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22C2×D4×D4711yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—942no—
336C4—941no—
337C4—941no—
338C4—941no—
339C4—941no—
340C4—1881no—
341C4#41×D4711yescharacteristic
342C4#41×D4711yescharacteristic
343C2—41no—
344C2—3761no—
345C2—1882no—
346C2#1568963111yescharacteristic
347C2#1568992911yescharacteristic
348C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3125
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689604C2semidirect
3. #15689441C2semidirect
4. #15689412C2semidirect
5. #15689407C2semidirect
6. #15689348C2semidirect
7. #15689341C2semidirect
8. #15689283C2semidirect
10. #15689234C2semidirect
11. #15689227C2semidirect
12. #15689210C2semidirect
13. #15689208C2semidirect
14. #15689181C2semidirect
15. C47×#483C2semidirect
177. #483D47semidirect
190. C47#3125semidirect