Finite Group Databasebeta

← #20254564

Subgroups — #20254564

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689676C211yesmaximal, characteristic, complemented
2#15689654C211yesmaximal, characteristic
3#15689524C211yesmaximal, characteristic, complemented
4#15689523C211yesmaximal, characteristic, complemented
5#15689476C211yesmaximal, characteristic, complemented
6#15689476C211yesmaximal, characteristic, complemented
7#15689465C211yesmaximal, characteristic, complemented
8#15689464C211yesmaximal, characteristic, complemented
9#15689444C211yesmaximal, characteristic
10#15689417C211yesmaximal, characteristic, complemented
11#15689411C211yesmaximal, characteristic, complemented
12#15689407C211yesmaximal, characteristic, complemented
13#15689401C211yesmaximal, characteristic, complemented
14#15689173C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic
16#13094023C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094017—21no—
19#13094015C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094011C2211yescharacteristic
23#13094005—21no—
24#13094003C2211yescharacteristic
25#13094001—21no—
26#13094001—21no—
27C4×Dic94—21no—
28C4×Dic94—21no—
29#13093989C2211yescharacteristic
30D4×Dic47—21no—
31D4×Dic47C2211yescharacteristic
32#13093983C2211yescharacteristic
33#13093980—21no—
34C2×C4×Dic47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47—21no—
63C22×Dic47D411yescharacteristic
64C22×Dic47D411yescharacteristic
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47C2311yescharacteristic
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C22⋊C4×C47—21no—
74C22⋊C4×C47—21no—
75C42×C47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47C2311yescharacteristic
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C4×Dic47D411yescharacteristic
97C4×Dic47D411yescharacteristic
98C4×Dic47C2311yescharacteristic
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47—21no—
103C23×C47C2×D411yescharacteristic
104D4×C47—21no—
105D4×C47—21no—
106D4×C47—42no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2411yescharacteristic
114C2×Dic47—22no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—41no—
120C2×Dic47—42no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125Dic94—21no—
126Dic94—21no—
127Dic94—42no—
128Dic94—42no—
129C8×C47—21no—
130C8×C47—21no—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C22×C47—21no—
134C22×C47—21no—
135C22×C47—21no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47—41no—
139C22×C47C22×D411yescharacteristic
140C4×C47—21no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C472−1+411yescharacteristic
145C4×C472−1+411yescharacteristic
146Dic47—21no—
147Dic47—21no—
148Dic47—21no—
149Dic47—41no—
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47#13512yes—
154#3233—471nomaximal, Sylow
155C2×C47—41no—
156C2×C47—81no—
157C2×C47#53611yescharacteristic
158C2×C47C2×#13511yescharacteristic
159C2×C47#57511yescharacteristic
160#533—471no—
161#529—471no—
162#499—471no—
163#499—471no—
164#488—471no—
165#488—471no—
166#485—471no—
167#485—471no—
168#482—471no—
169#482D4711yescharacteristic
170#477—471no—
171#476—471no—
172#475—471no—
173#474—471no—
174#431—471no—
175C47#323311yescharacteristic, complemented, Sylow
176C4⋊Q8—471no—
177C4⋊Q8—471no—
178#126—941no—
179#125—471no—
180#125—471no—
181#125—471no—
182#124—471no—
183#123—941no—
184C22⋊Q8—471no—
185C22⋊Q8—941no—
186C22⋊Q8—941no—
187#121C2×D4711yescharacteristic
188C4×Q8—471no—
189C4×Q8—941no—
190C4×Q8—941no—
191C4×D4—471no—
192C4×D4—941no—
193#117—471no—
194#117—941no—
195#117C2×D4711yescharacteristic
196C2×C42—471no—
197#107—471no—
198#107—471no—
199#107—471no—
200#107C2×D4711yescharacteristic
201#106—471no—
202#106—471no—
203#106—471no—
204#106C2×D4711yescharacteristic
205C4⋊C8—471no—
206C4⋊C8—471no—
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#102—471no—
212#102—471no—
213#102C2×D4711yescharacteristic
214#102C2×D4711yescharacteristic
215C22⋊C8—471no—
216C22⋊C8C2×D4711yescharacteristic
217C4×C8—471no—
218C4×C8—471no—
219C2×Q8—471no—
220C2×Q8—941no—
221C2×Q8—941no—
222C2×D4—21no—
223C2×D4C22×D4711yescharacteristic
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—941no—
227C22×C4C22×D4711yescharacteristic
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—471no—
233C4⋊C4—471no—
234C4⋊C4—471no—
235C4⋊C4—941no—
236C4⋊C4—941no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4C22×D4711yescharacteristic
246C4⋊C4C22×D4711yescharacteristic
247C4⋊C4C22×D4711yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—21no—
250C22⋊C4—941no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—21no—
256C42—471no—
257C42—471no—
258C42—471no—
259C42—471no—
260C42—941no—
261C42—941no—
262C23—21no—
263C23D4×D4711yescharacteristic
264Q8—941no—
265Q8—941no—
266Q8—1882no—
267Q8—1882no—
268D4—21no—
269D4—21no—
270D4—42no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—471no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—471no—
280C2×C4—942no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—1882no—
286C2×C4—1881no—
287C2×C4D4×D4711yescharacteristic
288C2×C4C23×D4711yescharacteristic
289C8—21no—
290C8—21no—
291C8—941no—
292C8—941no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C2×D4×D4711yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—472no—
305C4—941no—
306C4—941no—
307C4—941no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4#1309407111yescharacteristic
313C4#1309407111yescharacteristic
314C2—41no—
315C2—81no—
316C2#1568969511yescharacteristic
317C2#135×D4711yescharacteristic
318C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3233
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689676C2semidirect
3. #15689524C2semidirect
4. #15689523C2semidirect
5. #15689476C2semidirect
6. #15689476C2semidirect
7. #15689465C2semidirect
8. #15689464C2semidirect
10. #15689417C2semidirect
11. #15689411C2semidirect
12. #15689407C2semidirect
13. #15689401C2semidirect
14. #15689173C2semidirect
175. C47#3233semidirect