Finite Group Databasebeta

← #20254681

Subgroups — #20254681

Order 6016.

320 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#15689750C211yesmaximal, characteristic, complemented
2#15689742C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689519C211yesmaximal, characteristic, complemented
5#15689477C211yesmaximal, characteristic, complemented
6#15689463C211yesmaximal, characteristic, complemented
7#15689452C211yesmaximal, characteristic, complemented
8#15689445C211yesmaximal, characteristic
9#15689440C211yesmaximal, characteristic
10#15689432C211yesmaximal, characteristic, complemented
11#15689421C211yesmaximal, characteristic, complemented
12#15689411C211yesmaximal, characteristic, complemented
13#15689406C211yesmaximal, characteristic, complemented
14#15689185C211yesmaximal, characteristic, complemented
15C47×#489C211yesmaximal, characteristic, complemented
16#13094024C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094022—21no—
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094014—21no—
23#13094010—21no—
24#13094008—21no—
25#13094002—21no—
26#13094001—21no—
27#13094000—21no—
28#13094000C2211yescharacteristic
29#13093995C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093956C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#124×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64C2×C4×D47—21no—
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C22⋊C4×C47—21no—
74C22⋊C4×C47—21no—
75C42×C47C2311yescharacteristic
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4D411yescharacteristic
81(C2×D47)⋊C4D411yescharacteristic
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
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⋊C4D411yescharacteristic
96Dic47⋊C4D411yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47—21no—
103C22×D47C2×D411yescharacteristic
104Q8×C47—21no—
105Q8×C47—21no—
106Q8×C47—81no—
107D4×C47—21no—
108D4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C22⋊D47—81no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—81no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C4×D47—21no—
125C4×D47—21no—
126C4×D47—81no—
127Dic94—81no—
128Dic94—81no—
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—21no—
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#3244—471nomaximal, Sylow
155C2×C47—81no—
156C2×C47#53611yescharacteristic
157C2×C47#57711yescharacteristic
158C2×C47#57711yescharacteristic
159D47—41no—
160#544—471no—
161#542—471no—
162#501—471no—
163#498—471no—
164#489D4711yescharacteristic, complemented
165#488—471no—
166#485—471no—
167#483—471no—
168#482—471no—
169#481—471no—
170#479—471no—
171#478—471no—
172#476—471no—
173#475—471no—
174#433—471no—
175C47#324411yescharacteristic, complemented, Sylow
176C4⋊Q8—471no—
177C4⋊Q8—471no—
178C4⋊Q8—941no—
179C4⋊Q8C2×D4711yescharacteristic
180#126—941no—
181#125—471no—
182#125—471no—
183#125—941no—
184#124—941no—
185#124C2×D4711yescharacteristic
186#123—941no—
187C22⋊Q8—471no—
188C22⋊Q8—941no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191#121—471no—
192C4×Q8—471no—
193C4×D4—471no—
194#117—471no—
195#117—471no—
196C2×C4⋊C4—471no—
197#107—471no—
198#107—471no—
199#106—471no—
200#106—471no—
201#106—471no—
202#106—471no—
203#106—471no—
204#106—471no—
205C4⋊C8—471no—
206C4⋊C8—471no—
207#103—471no—
208#103—471no—
209#103C2×D4711yescharacteristic
210#103C2×D4711yescharacteristic
211#102—471no—
212#102—471no—
213#102C2×D4711yescharacteristic
214#102C2×D4711yescharacteristic
215C22⋊C8—471no—
216C22⋊C8—471no—
217#97C2×D4711yescharacteristic
218C4×C8—471no—
219C2×Q8—21no—
220C2×Q8—941no—
221C2×Q8—941no—
222C2×Q8C22×D4711yescharacteristic
223C2×D4—941no—
224C2×D4C22×D4711yescharacteristic
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—471no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—471no—
253C22⋊C4—471no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C42—471no—
259C42—941no—
260C42—941no—
261C42C22×D4711yescharacteristic
262C23—21no—
263C23—471no—
264Q8—21no—
265Q8—21no—
266Q8—81no—
267Q8—3761no—
268Q8—3761no—
269D4—21no—
270D4—21no—
271D4—3761no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—471no—
276C2×C4—471no—
277C2×C4—471no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—3761no—
285C2×C4—3761no—
286C2×C4D4×D4711yescharacteristic
287C2×C4D4×D4711yescharacteristic
288C2×C4C23×D4711yescharacteristic
289C8—21no—
290C8—21no—
291C8—941no—
292C8—941no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—941no—
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#1309407111yescharacteristic
314C2—81no—
315C2—1881no—
316C2#1568969311yescharacteristic
317C2#1568993211yescharacteristic
318C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3244
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689532C2semidirect
4. #15689519C2semidirect
5. #15689477C2semidirect
6. #15689463C2semidirect
7. #15689452C2semidirect
10. #15689432C2semidirect
11. #15689421C2semidirect
12. #15689411C2semidirect
13. #15689406C2semidirect
14. #15689185C2semidirect
15. C47×#489C2semidirect
164. #489D47semidirect
175. C47#3244semidirect