Finite Group Databasebeta

← #20254686

Subgroups — #20254686

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#15689744C211yesmaximal, characteristic
2#15689533C211yesmaximal, characteristic, complemented
3#15689519C211yesmaximal, characteristic, complemented
4#15689485C211yesmaximal, characteristic, complemented
5#15689480C211yesmaximal, characteristic, complemented
6#15689464C211yesmaximal, characteristic, complemented
7#15689453C211yesmaximal, characteristic, complemented
8#15689447C211yesmaximal, characteristic
9#15689441C211yesmaximal, characteristic
10#15689427C211yesmaximal, characteristic, complemented
11#15689420C211yesmaximal, characteristic, complemented
12#15689410C211yesmaximal, characteristic, complemented
13#15689405C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#544C211yesmaximal, characteristic, complemented
16#13094024C2211yescharacteristic
17#13094019—21no—
18#13094012C2211yescharacteristic
19#13094010—21no—
20#13094006—21no—
21#13094003C2211yescharacteristic
22#13094002—21no—
23#13093998C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25C4×D188C2211yescharacteristic
26#13093957C2211yescharacteristic
27#13093957C2211yescharacteristic
28#13093955C2211yescharacteristic
29#13093955C2211yescharacteristic
30#13093955C2211yescharacteristic
31#13093955C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47—21no—
49C4⋊Q8×C47C2211yescharacteristic
50C4⋊Q8×C47C2211yescharacteristic
51#125×C47—21no—
52#125×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47—21no—
56#117×C47C2211yescharacteristic
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C2×C47⋊C8C2311yescharacteristic
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47C2×D411yescharacteristic
103C22×D47—21no—
104Q8×C47—81no—
105Q8×C47—81no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—81no—
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C22⋊D47—81no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123D188—21no—
124D188—21no—
125C4×D47—81no—
126Dic94—21no—
127Dic94—21no—
128Dic94—81no—
129C47⋊C8—21no—
130C47⋊C8—21no—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C22×C47—21no—
134C22×C47—21no—
135C22×C47—21no—
136C22×C47C22×D411yescharacteristic
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C472−1+411yescharacteristic
150C4×C472−1+411yescharacteristic
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3244—471nomaximal, Sylow
155C2×C47—41no—
156C2×C47#53611yescharacteristic
157C2×C47#57711yescharacteristic
158C2×C47#57711yescharacteristic
159D47—81no—
160#544D4711yescharacteristic, complemented
161#542—471no—
162#501—471no—
163#498—471no—
164#489—471no—
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—21no—
177C4⋊Q8—471no—
178C4⋊Q8C2×D4711yescharacteristic
179C4⋊Q8C2×D4711yescharacteristic
180#126—941no—
181#125—21no—
182#125C2×D4711yescharacteristic
183#125C2×D4711yescharacteristic
184#124—471no—
185#124—941no—
186#123—941no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8—471no—
190C22⋊Q8—941no—
191#121—471no—
192C4×Q8—471no—
193C4×D4—471no—
194#117C2×D4711yescharacteristic
195#117C2×D4711yescharacteristic
196C2×C4⋊C4C2×D4711yescharacteristic
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#103—471no—
210#103—471no—
211#102—471no—
212#102—471no—
213#102—471no—
214#102—471no—
215C22⋊C8—471no—
216C22⋊C8—471no—
217#97—471no—
218C4×C8—471no—
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—471no—
222C2×Q8—941no—
223C2×D4—471no—
224C2×D4—941no—
225C22×C4—21no—
226C22×C4—941no—
227C22×C4C22×D4711yescharacteristic
228C2×C8—471no—
229C2×C8—471no—
230C2×C8—471no—
231C2×C8—471no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4C22⋊D4711yescharacteristic
245C4⋊C4C22⋊D4711yescharacteristic
246C4⋊C4C22×D4711yescharacteristic
247C4⋊C4C22×D4711yescharacteristic
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4C22⋊D4711yescharacteristic
257C22⋊C4C22⋊D4711yescharacteristic
258C42—21no—
259C42—941no—
260C42C22×D4711yescharacteristic
261C42C22×D4711yescharacteristic
262C23—941no—
263C23C2×C22⋊D4711yescharacteristic
264Q8—81no—
265Q8—81no—
266Q8—941no—
267Q8—941no—
268Q8—3761no—
269D4—941no—
270D4—941no—
271D4—3761no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—81no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—3761no—
283C2×C4C2×C22⋊D4711yescharacteristic
284C2×C4C2×C22⋊D4711yescharacteristic
285C2×C4C2×C22⋊D4711yescharacteristic
286C2×C4C2×C22⋊D4711yescharacteristic
287C2×C4C2×C22⋊D4711yescharacteristic
288C2×C4C23×D4711yescharacteristic
289C8—941no—
290C8—941no—
291C8—941no—
292C8—941no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—1881no—
297C22—1881no—
298C22—1881no—
299C22C22×C22⋊D4711yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4#1309407211yescharacteristic
313C4#1309407211yescharacteristic
314C2—41no—
315C2—3761no—
316C2#1568969711yescharacteristic
317C2#1568993111yescharacteristic
318C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#544C2
socleC22×C47C22×D4
hypercenter#544D47
hypocenterC47#3244
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689519C2semidirect
4. #15689485C2semidirect
5. #15689480C2semidirect
6. #15689464C2semidirect
7. #15689453C2semidirect
10. #15689427C2semidirect
11. #15689420C2semidirect
12. #15689410C2semidirect
13. #15689405C2semidirect
14. #15689184C2semidirect
15. C47×#544C2semidirect
160. #544D47semidirect
175. C47#3244semidirect