Finite Group Databasebeta

← #20256163

Subgroups — #20256163

Order 6016.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689856C211yesmaximal, characteristic
2#15689848C211yesmaximal, characteristic, complemented
3#15689486C211yesmaximal, characteristic
4#15689485C211yesmaximal, characteristic, complemented
5#15689476C211yesmaximal, characteristic, complemented
6#15689433C211yesmaximal, characteristic, complemented
7#15689422C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689344C211yesmaximal, characteristic, complemented
10#15689322C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689229C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689210C211yesmaximal, characteristic, complemented
15C47×#476C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19#13094022—21no—
20#13094020C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094014—21no—
25#13094012C2211yescharacteristic
26#13094011C2211yescharacteristic
27#13094010—21no—
28#13094007—21no—
29#13094006—21no—
30Q8×Dic47—21no—
31C4×Dic94C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33#13093989C2211yescharacteristic
34#13093989C2211yescharacteristic
35#13093989C2211yescharacteristic
36#13093986C2211yescharacteristic
37C4×C22⋊D47—21no—
38#13093957C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×Dic94D411yescharacteristic
67C2×Dic94C2311yescharacteristic
68C2×Dic94C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C42×C47C2311yescharacteristic
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79#10625335—22no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47D411yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4D411yescharacteristic
94Dic47⋊C4D411yescharacteristic
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103Dic188—22no—
104#10625325—22no—
105C23×C47—21no—
106C22×D47—21no—
107Q8×C47—42no—
108D4×C47—21no—
109D4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—81no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C22⋊D47—42no—
118C22⋊D47—81no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126D188—21no—
127D188—21no—
128C4×D47—81no—
129Dic94—21no—
130Dic94—21no—
131Dic94—21no—
132Dic94—41no—
133Dic94#4112yes—
134C8×C47—21no—
135C8×C47—21no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47C22×D411yescharacteristic
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47C2×#4111yescharacteristic
151C4×C472−1+411yescharacteristic
152Dic47—22no—
153Dic47—21no—
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159#3371—471nomaximal, Sylow
160C2×C47—81no—
161C2×C47#54811yescharacteristic
162C2×C47#57511yescharacteristic
163C2×C47#57711yescharacteristic
164D47—81no—
165#559—471no—
166#557—471no—
167#490—471no—
168#489—471no—
169#488—471no—
170#479—471no—
171#478—471no—
172#476D4711yescharacteristic, complemented
173#464—471no—
174#464—471no—
175#460—471no—
176#446—471no—
177#441—471no—
178#440—471no—
179C4×SD16—471no—
180C47#337111yescharacteristic, complemented, Sylow
181C2×Q16—471no—
182C2×SD16—471no—
183C2×SD16—471no—
184C4⋊Q8—941no—
185C4⋊Q8C2×D4711yescharacteristic
186#127—471no—
187#125—471no—
188#125—471no—
189#125—941no—
190#125—941no—
191#124—471no—
192#124—471no—
193#124—941no—
194#123—941no—
195#123—941no—
196C4×Q8—471no—
197C4×Q8—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—941no—
202C4×D4—471no—
203C4×D4—941no—
204C4×D4C2×D4711yescharacteristic
205#107—471no—
206#106C2×D4711yescharacteristic
207#106C2×D4711yescharacteristic
208C4⋊C8—471no—
209C4⋊C8—471no—
210C4⋊C8C2×D4711yescharacteristic
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102C2×D4711yescharacteristic
220#102C2×D4711yescharacteristic
221#97—471no—
222#97—471no—
223C4×C8—471no—
224C2×Q8—21no—
225C2×Q8—471no—
226C2×Q8—471no—
227C2×Q8—471no—
228C2×D4—471no—
229C2×D4—941no—
230C2×D4—941no—
231C2×D4C22×D4711yescharacteristic
232C22×C4—21no—
233C22×C4—941no—
234Q16—942no—
235SD16—942no—
236SD16—942no—
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—941no—
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
257C22⋊C4—21no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C42—471no—
264C42—471no—
265C42—941no—
266C42—941no—
267C42—941no—
268C42—941no—
269C42C22×D4711yescharacteristic
270C23—21no—
271C23—941no—
272Q8—42no—
273Q8—472no—
274Q8—941no—
275Q8—941no—
276Q8—941no—
277Q8—1881no—
278D4—21no—
279D4—21no—
280D4—941no—
281D4—941no—
282D4—3761no—
283D4—1882no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—471no—
291C2×C4—471no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—3761no—
296C2×C4D4×D4711yescharacteristic
297C2×C4D4×D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—21no—
301C8—941no—
302C8—941no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22C2×D4×D4711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—942no—
316C4—941no—
317C4—941no—
318C4—941no—
319C4—941no—
320C4—1881no—
321C4—1881no—
322C4#41×D4711yescharacteristic
323C4#1309407211yescharacteristic
324C2—81no—
325C2—3761no—
326C2#1568978311yescharacteristic
327C2#1568991911yescharacteristic
328C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3371
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #15689848C2semidirect
4. #15689485C2semidirect
5. #15689476C2semidirect
6. #15689433C2semidirect
7. #15689422C2semidirect
8. #15689346C2semidirect
9. #15689344C2semidirect
11. #15689252C2semidirect
12. #15689229C2semidirect
13. #15689223C2semidirect
14. #15689210C2semidirect
15. C47×#476C2semidirect
172. #476D47semidirect
180. C47#3371semidirect