Finite Group Databasebeta

← #20254554

Subgroups — #20254554

Order 6016.

334 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#15689655C211yesmaximal, characteristic
2#125×D47C211yesmaximal, characteristic, complemented
3#15689524C211yesmaximal, characteristic, complemented
4#15689523C211yesmaximal, characteristic, complemented
5#15689476C211yesmaximal, characteristic, complemented
6#15689476C211yesmaximal, characteristic, complemented
7#15689460C211yesmaximal, characteristic, complemented
8#15689455C211yesmaximal, characteristic, complemented
9#15689440C211yesmaximal, characteristic
10#15689435C211yesmaximal, characteristic
11#15689431C211yesmaximal, characteristic, complemented
12#15689427C211yesmaximal, characteristic, complemented
13#15689423C211yesmaximal, characteristic, complemented
14#15689175C211yesmaximal, characteristic, complemented
15C47×#478C211yesmaximal, characteristic, complemented
16#13094017—21no—
17#13094016C2211yescharacteristic
18#13094015C2211yescharacteristic
19#13094015C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094014—21no—
22#13094014—21no—
23#13094011C2211yescharacteristic
24#13094006—21no—
25#13094004C2211yescharacteristic
26#13093995C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28C4×C22⋊D47—21no—
29#13093983—21no—
30C4⋊C4×D47—21no—
31C4⋊C4×D47—21no—
32C4⋊C4×D47C2211yescharacteristic
33C4⋊C4×D47C2211yescharacteristic
34C42×D47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C2×C22⋊D47—21no—
62C2×C4×D47—21no—
63C2×C4×D47—21no—
64C2×C4×D47D411yescharacteristic
65C2×C4×D47D411yescharacteristic
66C2×C4×D47C2311yescharacteristic
67C2×Dic94C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
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—
79C22⋊Dic47—21no—
80(C2×D47)⋊C4—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96C4×Dic47—21no—
97C4×Dic47D411yescharacteristic
98C4×Dic47D411yescharacteristic
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47—21no—
103C22×D47C2×D411yescharacteristic
104D4×C47—21no—
105D4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—42no—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C22⋊D47—42no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121C4×D47—22no—
122C4×D47—21no—
123C4×D47—21no—
124C4×D47—41no—
125C4×D47—42no—
126C4×D47—42no—
127Dic94—21no—
128Dic94—21no—
129C8×C47—21no—
130C8×C47—21no—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C22×C47—41no—
134C22×C47—41no—
135C22×C47—41no—
136C22×C47C22×D411yescharacteristic
137C2×D47—21no—
138C2×D47—21no—
139C2×D47#13512yes—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C472−1+411yescharacteristic
146C4×C472−1+411yescharacteristic
147Dic47—21no—
148Dic47—21no—
149Dic47—21no—
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3232—471nomaximal, Sylow
155C2×C47—81no—
156C2×C47#53611yescharacteristic
157C2×C47C2×#13511yescharacteristic
158C2×C47#57511yescharacteristic
159D47—22no—
160#529—471no—
161C2×#125—471no—
162#499—471no—
163#499—471no—
164#488—471no—
165#488—471no—
166#484—471no—
167#483—471no—
168#481—471no—
169#480—471no—
170#479—471no—
171#479—471no—
172#478—471no—
173#478D4711yescharacteristic, complemented
174#431—471no—
175C47#323211yescharacteristic, complemented, Sylow
176#126—941no—
177#125—471no—
178#125—471no—
179#125—471no—
180#125—471no—
181#125—941no—
182#125—941no—
183#125C2×D4711yescharacteristic
184#124—471no—
185#123—941no—
186C22⋊Q8—471no—
187#121—471no—
188C4×Q8—471no—
189C4×D4—941no—
190C4×D4C2×D4711yescharacteristic
191#117—941no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4—941no—
195C2×C4⋊C4—941no—
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⋊C8C2×D4711yescharacteristic
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⋊C8—471no—
217C4×C8—471no—
218C4×C8—471no—
219C2×Q8—471no—
220C2×D4—941no—
221C2×D4C22×D4711yescharacteristic
222C22×C4—21no—
223C22×C4—471no—
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—941no—
227C22×C4—941no—
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—471no—
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⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4C22×D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C42—471no—
258C42—471no—
259C42—471no—
260C42—941no—
261C42C22×D4711yescharacteristic
262C23—21no—
263C23—471no—
264Q8—941no—
265Q8—941no—
266D4—21no—
267D4—21no—
268D4—1882no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—471no—
274C2×C4—471no—
275C2×C4—471no—
276C2×C4—942no—
277C2×C4—941no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—1881no—
284C2×C4—1882no—
285C2×C4—1882no—
286C2×C4D4×D4711yescharacteristic
287C2×C4D4×D4711yescharacteristic
288C2×C4C23×D4711yescharacteristic
289C8—21no—
290C8—21no—
291C8—941no—
292C8—941no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—472no—
297C22—941no—
298C22—941no—
299C22C2×D4×D4711yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—941no—
306C4—941no—
307C4—941no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4#1309407111yescharacteristic
313C4#1309407211yescharacteristic
314C2—81no—
315C2—942no—
316C2#1568969611yescharacteristic
317C2#135×D4711yescharacteristic
318C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3232
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
2. #125×D47C2semidirect
3. #15689524C2semidirect
4. #15689523C2semidirect
5. #15689476C2semidirect
6. #15689476C2semidirect
7. #15689460C2semidirect
8. #15689455C2semidirect
11. #15689431C2semidirect
12. #15689427C2semidirect
13. #15689423C2semidirect
14. #15689175C2semidirect
15. C47×#478C2semidirect
173. #478D47semidirect
175. C47#3232semidirect