Finite Group Databasebeta

← #20254657

Subgroups — #20254657

Order 6016.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689750C211yesmaximal, characteristic
2#15689736C211yesmaximal, characteristic
3#15689522C211yesmaximal, characteristic, complemented
4#15689492C211yesmaximal, characteristic, complemented
5#15689475C211yesmaximal, characteristic, complemented
6#15689467C211yesmaximal, characteristic
7#15689466C211yesmaximal, characteristic
8#15689460C211yesmaximal, characteristic
9#15689455C211yesmaximal, characteristic
10#15689433C211yesmaximal, characteristic, complemented
11#15689429C211yesmaximal, characteristic, complemented
12#15689417C211yesmaximal, characteristic, complemented
13#15689407C211yesmaximal, characteristic, complemented
14#15689185C211yesmaximal, characteristic
15C47×#501C211yesmaximal, characteristic, complemented
16#13094024C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094022—21no—
19#13094019—21no—
20#13094019—21no—
21#13094016C2211yescharacteristic
22#13094015—21no—
23#13094015—21no—
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094004C2211yescharacteristic
27#13094004C2211yescharacteristic
28#13094002—21no—
29#13094000—21no—
30#13093989C2211yescharacteristic
31#13093989C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35#13093957C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093955C2211yescharacteristic
38#13093955C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×C4×D47—21no—
61C2×C4×D47C2311yescharacteristic
62C2×Dic94—21no—
63C2×Dic94C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C2×C8×C47C2311yescharacteristic
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47C2311yescharacteristic
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C42×C47C2311yescharacteristic
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4D411yescharacteristic
79(C2×D47)⋊C4D411yescharacteristic
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4D411yescharacteristic
95Dic47⋊C4D411yescharacteristic
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C22×D47C2×D411yescharacteristic
103Q8×C47—81no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2411yescharacteristic
111C2×Dic47—21no—
112C2×Dic47—21no—
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47C2×D411yescharacteristic
116C2×Dic47C2×D411yescharacteristic
117C2×Dic47C2×D411yescharacteristic
118C4×D47—21no—
119C4×D47—21no—
120C4×D47—81no—
121Dic94—21no—
122Dic94—21no—
123Dic94—21no—
124Dic94—21no—
125Dic94—81no—
126C8×C47—21no—
127C8×C47—21no—
128C47⋊C8—21no—
129C47⋊C8—21no—
130C22×C47C22×D411yescharacteristic
131C2×D47—21no—
132C2×D47—21no—
133C2×D47—21no—
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—41no—
137C4×C47—41no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C472−1+411yescharacteristic
141C4×C472−1+411yescharacteristic
142Dic47—21no—
143Dic47—21no—
144Dic47—21no—
145Dic47—41no—
146Dic47—41no—
147Dic47—41no—
148Dic47—41no—
149#3242—471nomaximal, Sylow
150C2×C47#53611yescharacteristic
151C2×C47#57711yescharacteristic
152C2×C47#57811yescharacteristic
153D47—41no—
154#544—471no—
155#541—471no—
156#501D4711yescharacteristic, complemented
157#499—471no—
158#491—471no—
159#487—471no—
160#485—471no—
161#485—471no—
162#484—471no—
163#483—471no—
164#479—471no—
165#479—471no—
166#477—471no—
167#475—471no—
168#433—471no—
169C47#324211yescharacteristic, complemented, Sylow
170C4⋊Q8—471no—
171C4⋊Q8—471no—
172C4⋊Q8—941no—
173C4⋊Q8C2×D4711yescharacteristic
174#126—941no—
175#126—941no—
176#125—471no—
177#125—471no—
178#125—941no—
179#125—941no—
180#125—941no—
181#125C2×D4711yescharacteristic
182C22⋊Q8—471no—
183C22⋊Q8—471no—
184C22⋊Q8—941no—
185C22⋊Q8—941no—
186C4×Q8—471no—
187C4×Q8—471no—
188#117—471no—
189#117—471no—
190C2×C4⋊C4—471no—
191#107—471no—
192#107—471no—
193#107C2×D4711yescharacteristic
194#107C2×D4711yescharacteristic
195#106—471no—
196#106—471no—
197#106C2×D4711yescharacteristic
198#106C2×D4711yescharacteristic
199C4⋊C8—471no—
200C4⋊C8—471no—
201#103—471no—
202#103—471no—
203#103—471no—
204#103—471no—
205#103—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209C22⋊C8—471no—
210C22⋊C8—471no—
211#97C2×D4711yescharacteristic
212C4×C8—471no—
213C2×Q8—21no—
214C2×Q8—471no—
215C2×Q8—471no—
216C2×Q8—941no—
217C22×C4—471no—
218C22×C4—941no—
219C2×C8—471no—
220C2×C8—471no—
221C2×C8C22×D4711yescharacteristic
222C2×C8C22×D4711yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—471no—
227C4⋊C4—471no—
228C4⋊C4—471no—
229C4⋊C4—471no—
230C4⋊C4—941no—
231C4⋊C4—941no—
232C4⋊C4—941no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4—941no—
236C4⋊C4—941no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4C22×D4711yescharacteristic
243C4⋊C4C22×D4711yescharacteristic
244C4⋊C4C22×D4711yescharacteristic
245C4⋊C4C22×D4711yescharacteristic
246C22⋊C4—471no—
247C22⋊C4—471no—
248C22⋊C4—941no—
249C22⋊C4—941no—
250C22⋊C4—941no—
251C42—471no—
252C42—941no—
253C42—941no—
254C42—941no—
255C42C22×D4711yescharacteristic
256C23—471no—
257Q8—81no—
258Q8—941no—
259Q8—941no—
260Q8—941no—
261Q8—941no—
262Q8—3761no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—471no—
268C2×C4—471no—
269C2×C4—471no—
270C2×C4—941no—
271C2×C4—941no—
272C2×C4—941no—
273C2×C4—941no—
274C2×C4—941no—
275C2×C4—941no—
276C2×C4—3761no—
277C2×C4D4×D4711yescharacteristic
278C2×C4D4×D4711yescharacteristic
279C2×C4C23×D4711yescharacteristic
280C8—21no—
281C8—21no—
282C8—941no—
283C8—941no—
284C22—941no—
285C22—941no—
286C22—941no—
287C22C2×D4×D4711yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—941no—
295C4—941no—
296C4—941no—
297C4—1881no—
298C4—1881no—
299C4—1881no—
300C4—1881no—
301C4#1309407211yescharacteristic
302C4#1309407211yescharacteristic
303C2—1881no—
304C2#1568969811yescharacteristic
305C2#1568993311yescharacteristic
306C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3242
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #15689522C2semidirect
4. #15689492C2semidirect
5. #15689475C2semidirect
10. #15689433C2semidirect
11. #15689429C2semidirect
12. #15689417C2semidirect
13. #15689407C2semidirect
15. C47×#501C2semidirect
156. #501D47semidirect
169. C47#3242semidirect