Finite Group Databasebeta

← #20254665

Subgroups — #20254665

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#15689751C211yesmaximal, characteristic, complemented
2#15689529C211yesmaximal, characteristic, complemented
3#15689526C211yesmaximal, characteristic, complemented
4#15689482C211yesmaximal, characteristic, complemented
5#15689477C211yesmaximal, characteristic, complemented
6#15689461C211yesmaximal, characteristic, complemented
7#15689456C211yesmaximal, characteristic, complemented
8#15689444C211yesmaximal, characteristic
9#15689434C211yesmaximal, characteristic
10#15689430C211yesmaximal, characteristic, complemented
11#15689423C211yesmaximal, characteristic, complemented
12#15689418C211yesmaximal, characteristic, complemented
13#15689403C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#542C211yesmaximal, characteristic
16#13094024C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094023—21no—
19#13094016C2211yescharacteristic
20#13094016C2211yescharacteristic
21#13094015—21no—
22#13094001—21no—
23#13094001—21no—
24#13093983C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26#13093957C2211yescharacteristic
27#13093957C2211yescharacteristic
28#13093957C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52#123×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C22×Dic47—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47D411yescharacteristic
72C4⋊C4×C47D411yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47D411yescharacteristic
81C22⋊C4×C47D411yescharacteristic
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C2×C47⋊C8C2311yescharacteristic
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47—21no—
103C23×C47C2×D411yescharacteristic
104Q8×C47—21no—
105Q8×C47—21no—
106Q8×C47—81no—
107D4×C47—21no—
108D4×C47—21no—
109D4×C47—81no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—81no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—81no—
127Dic94—81no—
128Dic94—81no—
129C47⋊C8—21no—
130C47⋊C8—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—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C472−1+411yescharacteristic
149C4×C472−1+411yescharacteristic
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3243—471nomaximal, Sylow
155C2×C47—41no—
156C2×C47—81no—
157C2×C47#53611yescharacteristic
158C2×C47#57611yescharacteristic
159C2×C47#57811yescharacteristic
160#544—471no—
161#542D4711yescharacteristic
162#501—471no—
163#500—471no—
164#489—471no—
165#488—471no—
166#485—471no—
167#484—471no—
168#482—471no—
169#480—471no—
170#479—471no—
171#478—471no—
172#477—471no—
173#474—471no—
174#433—471no—
175C47#324311yescharacteristic, complemented, Sylow
176C4⋊Q8—471no—
177C4⋊Q8—471no—
178C4⋊Q8—941no—
179C4⋊Q8C2×D4711yescharacteristic
180#126—21no—
181#125—471no—
182#125—471no—
183#125—941no—
184#124—21no—
185#124C2×D4711yescharacteristic
186#123—21no—
187C22⋊Q8—21no—
188C22⋊Q8—941no—
189C22⋊Q8—941no—
190C22⋊Q8C2×D4711yescharacteristic
191#121C2×D4711yescharacteristic
192C4×Q8C2×D4711yescharacteristic
193C4×D4C2×D4711yescharacteristic
194#117—471no—
195#117C2×D4711yescharacteristic
196C2×C4⋊C4—471no—
197#107—471no—
198#107—471no—
199#107—471no—
200#107—471no—
201#107—471no—
202#107—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—941no—
221C2×Q8—941no—
222C2×Q8C22×D4711yescharacteristic
223C2×D4—21no—
224C2×D4C22×D4711yescharacteristic
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—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⋊C4C22⋊D4711yescharacteristic
247C4⋊C4C22⋊D4711yescharacteristic
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—941no—
256C22⋊C4C22⋊D4711yescharacteristic
257C22⋊C4C22⋊D4711yescharacteristic
258C42—21no—
259C42—941no—
260C42C22×D4711yescharacteristic
261C42C22×D4711yescharacteristic
262C23—21no—
263C23C2×C22⋊D4711yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—81no—
267Q8—3761no—
268Q8—3761no—
269D4—21no—
270D4—21no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—941no—
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—41no—
297C22—41no—
298C22—41no—
299C22C22×C22⋊D4711yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4#1309407111yescharacteristic
313C4#1309407111yescharacteristic
314C2—41no—
315C2—81no—
316C2#1568969411yescharacteristic
317C2#1568992611yescharacteristic
318C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#542C2
socleC22×C47C22×D4
hypercenter#542D47
hypocenterC47#3243
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #15689751C2semidirect
2. #15689529C2semidirect
3. #15689526C2semidirect
4. #15689482C2semidirect
5. #15689477C2semidirect
6. #15689461C2semidirect
7. #15689456C2semidirect
10. #15689430C2semidirect
11. #15689423C2semidirect
12. #15689418C2semidirect
13. #15689403C2semidirect
14. #15689184C2semidirect
175. C47#3243semidirect