Finite Group Databasebeta

← #20254634

Subgroups — #20254634

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689750C211yesmaximal, characteristic, complemented
2#15689727C211yesmaximal, characteristic
3#15689529C211yesmaximal, characteristic, complemented
4#15689525C211yesmaximal, characteristic, complemented
5#15689487C211yesmaximal, characteristic, complemented
6#15689446C211yesmaximal, characteristic, complemented
7#15689445C211yesmaximal, characteristic, complemented
8#15689440C211yesmaximal, characteristic, complemented
9#15689435C211yesmaximal, characteristic, complemented
10#15689425C211yesmaximal, characteristic, complemented
11#15689421C211yesmaximal, characteristic, complemented
12#15689411C211yesmaximal, characteristic, complemented
13#15689401C211yesmaximal, characteristic, complemented
14#15689182C211yesmaximal, characteristic, complemented
15C47×#486C211yesmaximal, characteristic, complemented
16#13094023C2211yescharacteristic
17#13094022—21no—
18#13094016C2211yescharacteristic
19#13094016C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094014—21no—
22#13094005—21no—
23#13094005—21no—
24#13094002—21no—
25#13094000—21no—
26#13093996—21no—
27#13093996—21no—
28#13093995C2211yescharacteristic
29#13093995C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#127×C47C2211yescharacteristic
54#102×C47C2211yescharacteristic
55#102×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C42×C47C2311yescharacteristic
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4D411yescharacteristic
83(C2×D47)⋊C4D411yescharacteristic
84C4⋊Dic47—21no—
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47—21no—
103C23×C47—21no—
104C22×D47C2×D411yescharacteristic
105Q8×C47—81no—
106D4×C47—21no—
107D4×C47—21no—
108D4×C47—21no—
109D4×C47—21no—
110D4×C47—81no—
111D4×C47—81no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C22⋊D47—81no—
118C22⋊D47—81no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—81no—
124C2×Dic47—81no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—81no—
131Dic94—81no—
132C8×C47—21no—
133C8×C47—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47C22×D411yescharacteristic
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C472−1+411yescharacteristic
151C4×C472−1+411yescharacteristic
152Dic47—21no—
153Dic47—21no—
154Dic47—21no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#3241—471nomaximal, Sylow
160C2×C47—81no—
161C2×C47—81no—
162C2×C47#53611yescharacteristic
163C2×C47#57611yescharacteristic
164C2×C47#57711yescharacteristic
165D47—41no—
166#544—471no—
167#540—471no—
168#501—471no—
169#499—471no—
170#490—471no—
171#486D4711yescharacteristic, complemented
172#482—471no—
173#482—471no—
174#481—471no—
175#480—471no—
176#478—471no—
177#478—471no—
178#476—471no—
179#474—471no—
180#433—471no—
181C47#324111yescharacteristic, complemented, Sylow
182C4⋊Q8—471no—
183C4⋊Q8—941no—
184C4⋊Q8C2×D4711yescharacteristic
185#127C2×D4711yescharacteristic
186#125—471no—
187#125—471no—
188#125—471no—
189#125—941no—
190#123—941no—
191#123—941no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194#121—471no—
195#121—471no—
196#121—941no—
197#121—941no—
198C4×D4—471no—
199C4×D4—471no—
200#117—471no—
201#117—471no—
202C2×C4⋊C4—471no—
203#107—471no—
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211C4⋊C8—471no—
212C4⋊C8—471no—
213#102—471no—
214#102—471no—
215#102—471no—
216#102—471no—
217#102C2×D4711yescharacteristic
218#102C2×D4711yescharacteristic
219#102C2×D4711yescharacteristic
220#102C2×D4711yescharacteristic
221C22⋊C8—471no—
222C22⋊C8—471no—
223#97—471no—
224C4×C8C2×D4711yescharacteristic
225C2×Q8—21no—
226C2×Q8—941no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—941no—
230C2×D4—941no—
231C2×D4C22×D4711yescharacteristic
232C2×D4C22×D4711yescharacteristic
233C22×C4—471no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C2×C8—471no—
238C2×C8—471no—
239C2×C8C22×D4711yescharacteristic
240C2×C8C22×D4711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—471no—
259C22⋊C4—471no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—471no—
266C42—941no—
267C42C22×D4711yescharacteristic
268C23—21no—
269C23—21no—
270C23—471no—
271Q8—81no—
272Q8—3761no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—3761no—
280D4—3761no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—471no—
284C2×C4—471no—
285C2×C4—471no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4D4×D4711yescharacteristic
296C2×C4D4×D4711yescharacteristic
297C2×C4C23×D4711yescharacteristic
298C8—21no—
299C8—21no—
300C8—941no—
301C8—941no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—941no—
309C22—941no—
310C22—941no—
311C22C2×D4×D4711yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—941no—
317C4—941no—
318C4—941no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4—1881no—
323C4#1309407111yescharacteristic
324C4#1309407111yescharacteristic
325C2—81no—
326C2—81no—
327C2—1881no—
328C2#1568969311yescharacteristic
329C2#1568992411yescharacteristic
330C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689529C2semidirect
4. #15689525C2semidirect
5. #15689487C2semidirect
6. #15689446C2semidirect
7. #15689445C2semidirect
8. #15689440C2semidirect
9. #15689435C2semidirect
10. #15689425C2semidirect
11. #15689421C2semidirect
12. #15689411C2semidirect
13. #15689401C2semidirect
14. #15689182C2semidirect
15. C47×#486C2semidirect
171. #486D47semidirect
181. C47#3241semidirect