Finite Group Databasebeta

← #20254635

Subgroups — #20254635

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#15689751C211yesmaximal, characteristic, complemented
2#15689533C211yesmaximal, characteristic, complemented
3#15689522C211yesmaximal, characteristic, complemented
4#15689487C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689444C211yesmaximal, characteristic, complemented
7#15689444C211yesmaximal, characteristic, complemented
8#15689439C211yesmaximal, characteristic, complemented
9#15689434C211yesmaximal, characteristic, complemented
10#15689423C211yesmaximal, characteristic, complemented
11#15689423C211yesmaximal, characteristic, complemented
12#15689413C211yesmaximal, characteristic, complemented
13#15689403C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#540C211yesmaximal, characteristic
16#13094024C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094023—21no—
19#13094016C2211yescharacteristic
20#13094016C2211yescharacteristic
21#13094015—21no—
22#13094001—21no—
23#13094001—21no—
24#13093983C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26#13093957C2211yescharacteristic
27#13093957C2211yescharacteristic
28#13093957C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093955C2211yescharacteristic
31#13093955C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093945C2211yescharacteristic
37#13093945C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48#127×C47C2211yescharacteristic
49#125×C47C2211yescharacteristic
50#123×C47—21no—
51#123×C47—21no—
52#121×C47—21no—
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C22×Dic47—21no—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47D411yescharacteristic
82C22⋊C4×C47D411yescharacteristic
83C42×C47C2311yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C2×C47⋊C8C2311yescharacteristic
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47—21no—
103C23×C47—21no—
104C23×C47C2×D411yescharacteristic
105D4×C47—21no—
106D4×C47—21no—
107D4×C47—21no—
108D4×C47—21no—
109D4×C47—81no—
110D4×C47—81no—
111D4×C47—81no—
112D4×C47—81no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—81no—
118C2×C4×C47—81no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—81no—
130Dic94—81no—
131Dic94—81no—
132C47⋊C8—21no—
133C47⋊C8—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C22×C47—21no—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47C22×D411yescharacteristic
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C472−1+411yescharacteristic
154C4×C472−1+411yescharacteristic
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#3241—471nomaximal, Sylow
160C2×C47—41no—
161C2×C47—81no—
162C2×C47—81no—
163C2×C47#53611yescharacteristic
164C2×C47#57611yescharacteristic
165C2×C47#57711yescharacteristic
166#544—471no—
167#540D4711yescharacteristic
168#501—471no—
169#499—471no—
170#490—471no—
171#486—471no—
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—471no—
184C4⋊Q8—941no—
185#127C2×D4711yescharacteristic
186#125—471no—
187#125—471no—
188#125—941no—
189#125C2×D4711yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194#121—21no—
195#121—21no—
196#121C2×D4711yescharacteristic
197#121C2×D4711yescharacteristic
198C4×D4C2×D4711yescharacteristic
199C4×D4C2×D4711yescharacteristic
200#117—471no—
201#117C2×D4711yescharacteristic
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#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221C22⋊C8—471no—
222C22⋊C8—471no—
223#97—471no—
224C4×C8—471no—
225C2×Q8—941no—
226C2×Q8—941no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C22×D4711yescharacteristic
232C2×D4C22×D4711yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—941no—
236C22×C4C22×D4711yescharacteristic
237C2×C8—471no—
238C2×C8—471no—
239C2×C8—471no—
240C2×C8—471no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C22⋊D4711yescharacteristic
255C4⋊C4C22⋊D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—941no—
263C22⋊C4C22⋊D4711yescharacteristic
264C22⋊C4C22⋊D4711yescharacteristic
265C42—941no—
266C42C22×D4711yescharacteristic
267C42C22×D4711yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×C22⋊D4711yescharacteristic
271Q8—3761no—
272Q8—3761no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—3761no—
292C2×C4C2×C22⋊D4711yescharacteristic
293C2×C4C2×C22⋊D4711yescharacteristic
294C2×C4C2×C22⋊D4711yescharacteristic
295C2×C4C2×C22⋊D4711yescharacteristic
296C2×C4C2×C22⋊D4711yescharacteristic
297C2×C4C23×D4711yescharacteristic
298C8—941no—
299C8—941no—
300C8—941no—
301C8—941no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×C22⋊D4711yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4—1881no—
323C4#1309407111yescharacteristic
324C4#1309407111yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2#1568969411yescharacteristic
329C2#1568992611yescharacteristic
330C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#540C2
socleC22×C47C22×D4
hypercenter#540D47
hypocenterC47#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #15689751C2semidirect
2. #15689533C2semidirect
3. #15689522C2semidirect
4. #15689487C2semidirect
5. #15689469C2semidirect
6. #15689444C2semidirect
7. #15689444C2semidirect
8. #15689439C2semidirect
9. #15689434C2semidirect
10. #15689423C2semidirect
11. #15689423C2semidirect
12. #15689413C2semidirect
13. #15689403C2semidirect
14. #15689184C2semidirect
181. C47#3241semidirect