Finite Group Databasebeta

← #20254656

Subgroups — #20254656

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#15689735C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689522C211yesmaximal, characteristic, complemented
4#15689493C211yesmaximal, characteristic, complemented
5#15689475C211yesmaximal, characteristic, complemented
6#15689464C211yesmaximal, characteristic
7#15689464C211yesmaximal, characteristic
8#15689458C211yesmaximal, characteristic
9#15689453C211yesmaximal, characteristic
10#15689427C211yesmaximal, characteristic, complemented
11#15689427C211yesmaximal, characteristic, complemented
12#15689415C211yesmaximal, characteristic, complemented
13#15689405C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic
15C47×#544C211yesmaximal, characteristic
16#13094024C2211yescharacteristic
17#13094017—21no—
18#13094017—21no—
19#13094016C2211yescharacteristic
20#13094014—21no—
21#13094014—21no—
22#13094003C2211yescharacteristic
23#13094003C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093957C2211yescharacteristic
27#13093957C2211yescharacteristic
28#13093957C2211yescharacteristic
29#13093957C2211yescharacteristic
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#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
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×Dic94C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C4⋊C4×C47—21no—
66C4⋊C4×C47—21no—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47D411yescharacteristic
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊C4×C47D411yescharacteristic
80C22⋊C4×C47D411yescharacteristic
81C42×C47—21no—
82C42×C47C2311yescharacteristic
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C2×C47⋊C8C2311yescharacteristic
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47C2×D411yescharacteristic
103Q8×C47—81no—
104Q8×C47—81no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—81no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122Dic94—21no—
123Dic94—21no—
124Dic94—21no—
125Dic94—21no—
126C47⋊C8—21no—
127C47⋊C8—21no—
128C47⋊C8—21no—
129C47⋊C8—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—21no—
133C22×C47C22×D411yescharacteristic
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—21no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C472−1+411yescharacteristic
144C4×C472−1+411yescharacteristic
145Dic47—41no—
146Dic47—41no—
147Dic47—41no—
148Dic47—41no—
149#3242—471nomaximal, Sylow
150C2×C47—41no—
151C2×C47#53611yescharacteristic
152C2×C47#57711yescharacteristic
153C2×C47#57811yescharacteristic
154#544D4711yescharacteristic
155#541—471no—
156#501—471no—
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—21no—
171C4⋊Q8—471no—
172C4⋊Q8C2×D4711yescharacteristic
173C4⋊Q8C2×D4711yescharacteristic
174#126—941no—
175#126—941no—
176#125—21no—
177#125—471no—
178#125—941no—
179#125—941no—
180#125C2×D4711yescharacteristic
181#125C2×D4711yescharacteristic
182C22⋊Q8—21no—
183C22⋊Q8—21no—
184C22⋊Q8—471no—
185C22⋊Q8—471no—
186C4×Q8—471no—
187C4×Q8—471no—
188#117C2×D4711yescharacteristic
189#117C2×D4711yescharacteristic
190C2×C4⋊C4C2×D4711yescharacteristic
191#107—471no—
192#107—471no—
193#107—471no—
194#107—471no—
195#106—471no—
196#106—471no—
197#106—471no—
198#106—471no—
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#97—471no—
212C4×C8—471no—
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—471no—
216C2×Q8—471no—
217C22×C4—21no—
218C22×C4C22×D4711yescharacteristic
219C2×C8—471no—
220C2×C8—471no—
221C2×C8—471no—
222C2×C8—471no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—471no—
231C4⋊C4—471no—
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⋊C4C22⋊D4711yescharacteristic
241C4⋊C4C22⋊D4711yescharacteristic
242C4⋊C4C22×D4711yescharacteristic
243C4⋊C4C22×D4711yescharacteristic
244C4⋊C4C22×D4711yescharacteristic
245C4⋊C4C22×D4711yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—941no—
248C22⋊C4—941no—
249C22⋊C4C22⋊D4711yescharacteristic
250C22⋊C4C22⋊D4711yescharacteristic
251C42—21no—
252C42—941no—
253C42—941no—
254C42C22×D4711yescharacteristic
255C42C22×D4711yescharacteristic
256C23C2×C22⋊D4711yescharacteristic
257Q8—81no—
258Q8—81no—
259Q8—941no—
260Q8—941no—
261Q8—941no—
262Q8—941no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—81no—
270C2×C4—941no—
271C2×C4—941no—
272C2×C4—941no—
273C2×C4—941no—
274C2×C4C2×C22⋊D4711yescharacteristic
275C2×C4C2×C22⋊D4711yescharacteristic
276C2×C4C2×C22⋊D4711yescharacteristic
277C2×C4C2×C22⋊D4711yescharacteristic
278C2×C4C2×C22⋊D4711yescharacteristic
279C2×C4C23×D4711yescharacteristic
280C8—941no—
281C8—941no—
282C8—941no—
283C8—941no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×C22⋊D4711yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—1881no—
298C4—1881no—
299C4—1881no—
300C4—1881no—
301C4#1309407211yescharacteristic
302C4#1309407211yescharacteristic
303C2—41no—
304C2#1568969711yescharacteristic
305C2#1568993411yescharacteristic
306C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#544C2
socleC22×C47C22×D4
hypercenter#544D47
hypocenterC47#3242
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. #15689529C2semidirect
3. #15689522C2semidirect
4. #15689493C2semidirect
5. #15689475C2semidirect
10. #15689427C2semidirect
11. #15689427C2semidirect
12. #15689415C2semidirect
13. #15689405C2semidirect
169. C47#3242semidirect