Finite Group Databasebeta

← #20254633

Subgroups — #20254633

Order 6016.

328 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#15689679C211yesmaximal, characteristic, complemented
2#15689660C211yesmaximal, characteristic
3#15689531C211yesmaximal, characteristic, complemented
4#15689530C211yesmaximal, characteristic, complemented
5#15689484C211yesmaximal, characteristic, complemented
6#15689484C211yesmaximal, characteristic, complemented
7#15689463C211yesmaximal, characteristic, complemented
8#15689462C211yesmaximal, characteristic, complemented
9#15689450C211yesmaximal, characteristic
10#15689449C211yesmaximal, characteristic
11#15689430C211yesmaximal, characteristic, complemented
12#15689424C211yesmaximal, characteristic, complemented
13#15689420C211yesmaximal, characteristic, complemented
14#15689179C211yesmaximal, characteristic, complemented
15C47×#479C211yesmaximal, characteristic, complemented
16#13094023C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094019—21no—
19#13094016C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094013C2211yescharacteristic
22#13094009—21no—
23#13094002—21no—
24#13094002—21no—
25#13094000C2211yescharacteristic
26#13093999C2211yescharacteristic
27#13093989—21no—
28#13093989—21no—
29C4×D188—21no—
30C4×D188C2211yescharacteristic
31#13093982C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981—21no—
34C42×D47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D188—21no—
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47D411yescharacteristic
64C2×C4×D47D411yescharacteristic
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C42×C47—21no—
77C42×C47C2311yescharacteristic
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47D411yescharacteristic
98C4×Dic47D411yescharacteristic
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C22×D47—21no—
103C22×D47C2×D411yescharacteristic
104Q8×C47—21no—
105Q8×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47C2×D411yescharacteristic
117C2×Dic47C2×D411yescharacteristic
118C2×Dic47C2×D411yescharacteristic
119D188—21no—
120D188—21no—
121D188—42no—
122C4×D47—21no—
123C4×D47—21no—
124C4×D47—41no—
125C4×D47—41no—
126C4×D47—42no—
127Dic94—42no—
128Dic94—42no—
129C8×C47—21no—
130C8×C47—21no—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C22×C47C22×D411yescharacteristic
134C2×D47—21no—
135C2×D47—21no—
136C2×D47—21no—
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C472−1+411yescharacteristic
147C4×C472−1+411yescharacteristic
148Dic47—21no—
149Dic47—21no—
150Dic47—21no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3240—471nomaximal, Sylow
155C2×C47#53611yescharacteristic
156C2×C47#57511yescharacteristic
157C2×C47#57511yescharacteristic
158D47—41no—
159D47—81no—
160#533—471no—
161#529—471no—
162#501—471no—
163#501—471no—
164#489—471no—
165#489—471no—
166#485—471no—
167#485—471no—
168#482—471no—
169#482—471no—
170#479—471no—
171#479D4711yescharacteristic, complemented
172#478—471no—
173#478—471no—
174#432—471no—
175C47#324011yescharacteristic, complemented, Sylow
176C4⋊Q8—471no—
177C4⋊Q8—471no—
178#126—941no—
179#125—471no—
180#125—471no—
181#125C2×D4711yescharacteristic
182#124—471no—
183#123—941no—
184C22⋊Q8—471no—
185C22⋊Q8—941no—
186C22⋊Q8—941no—
187#121—471no—
188C4×Q8—941no—
189C4×Q8—941no—
190C4×Q8C2×D4711yescharacteristic
191C4×D4—471no—
192C4×D4—941no—
193#117—471no—
194#117—471no—
195#117—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#103C2×D4711yescharacteristic
210#103C2×D4711yescharacteristic
211#102—471no—
212#102—471no—
213#102—471no—
214#102—471no—
215C22⋊C8—471no—
216C22⋊C8—471no—
217#97—471no—
218#97—471no—
219C2×Q8—941no—
220C2×Q8—941no—
221C2×Q8C22×D4711yescharacteristic
222C2×D4—471no—
223C2×D4—941no—
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—941no—
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
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—941no—
249C22⋊C4—941no—
250C22⋊C4—941no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—21no—
256C42—471no—
257C42—471no—
258C42—471no—
259C42—941no—
260C42—941no—
261C42C22×D4711yescharacteristic
262C23—471no—
263C23—941no—
264Q8—21no—
265Q8—21no—
266Q8—1882no—
267Q8—1882no—
268D4—941no—
269D4—941no—
270D4—1882no—
271C2×C4—21no—
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—1881no—
284C2×C4—1881no—
285C2×C4—1882no—
286C2×C4D4×D4711yescharacteristic
287C2×C4D4×D4711yescharacteristic
288C2×C4C23×D4711yescharacteristic
289C8—21no—
290C8—21no—
291C8—941no—
292C8—941no—
293C22—941no—
294C22—941no—
295C22—941no—
296C22—1881no—
297C22—1881no—
298C22—1881no—
299C22C2×D4×D4711yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—941no—
307C4—941no—
308C4—941no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4#1309407111yescharacteristic
313C4#1309407211yescharacteristic
314C2—3761no—
315C2—1881no—
316C2#1568969611yescharacteristic
317C2#1568992011yescharacteristic
318C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3240
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #15689679C2semidirect
3. #15689531C2semidirect
4. #15689530C2semidirect
5. #15689484C2semidirect
6. #15689484C2semidirect
7. #15689463C2semidirect
8. #15689462C2semidirect
11. #15689430C2semidirect
12. #15689424C2semidirect
13. #15689420C2semidirect
14. #15689179C2semidirect
15. C47×#479C2semidirect
171. #479D47semidirect
175. C47#3240semidirect