Finite Group Databasebeta

← #20254689

Subgroups — #20254689

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#15689750C211yesmaximal, characteristic, complemented
2#15689747C211yesmaximal, characteristic
3#15689529C211yesmaximal, characteristic, complemented
4#15689485C211yesmaximal, characteristic, complemented
5#15689478C211yesmaximal, characteristic, complemented
6#15689467C211yesmaximal, characteristic, complemented
7#15689455C211yesmaximal, characteristic, complemented
8#15689449C211yesmaximal, characteristic
9#15689443C211yesmaximal, characteristic
10#15689433C211yesmaximal, characteristic, complemented
11#15689422C211yesmaximal, characteristic, complemented
12#15689412C211yesmaximal, characteristic, complemented
13#15689407C211yesmaximal, characteristic, complemented
14#15689182C211yesmaximal, characteristic, complemented
15C47×#498C211yesmaximal, characteristic, complemented
16#13094023C2211yescharacteristic
17#13094022—21no—
18#13094019—21no—
19#13094016C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094014—21no—
22#13094013—21no—
23#13094012C2211yescharacteristic
24#13094009—21no—
25#13094004C2211yescharacteristic
26#13094002—21no—
27#13094000—21no—
28#13094000—21no—
29#13093999C2211yescharacteristic
30#13093989C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35#13093957C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093955C2211yescharacteristic
38#13093955C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4⋊Q8×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×D188—21no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C42×C47C2311yescharacteristic
77(C2×D47)⋊C4—21no—
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)⋊C4D411yescharacteristic
84(C2×D47)⋊C4D411yescharacteristic
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4D411yescharacteristic
96Dic47⋊C4D411yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C22×D47—21no—
103C22×D47C2×D411yescharacteristic
104Q8×C47—81no—
105Q8×C47—81no—
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—81no—
122C4×D47—21no—
123C4×D47—21no—
124C4×D47—81no—
125C4×D47—81no—
126Dic94—21no—
127Dic94—21no—
128Dic94—81no—
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#3244—471nomaximal, Sylow
155C2×C47#53611yescharacteristic
156C2×C47#57711yescharacteristic
157C2×C47#57711yescharacteristic
158D47—41no—
159D47—81no—
160#544—471no—
161#542—471no—
162#501—471no—
163#498D4711yescharacteristic, complemented
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—471no—
177C4⋊Q8—941no—
178C4⋊Q8C2×D4711yescharacteristic
179C4⋊Q8C2×D4711yescharacteristic
180#126—941no—
181#125—471no—
182#125—471no—
183#125—941no—
184#124—471no—
185#124—941no—
186#123—941no—
187C22⋊Q8—471no—
188C22⋊Q8—941no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191#121—471no—
192C4×Q8—471no—
193C4×D4—471no—
194#117—471no—
195#117—471no—
196C2×C4⋊C4—471no—
197#107—471no—
198#107—471no—
199#106—471no—
200#106—471no—
201#106C2×D4711yescharacteristic
202#106C2×D4711yescharacteristic
203#106C2×D4711yescharacteristic
204#106C2×D4711yescharacteristic
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×C8C2×D4711yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—471no—
222C2×Q8—941no—
223C2×D4—471no—
224C2×D4—941no—
225C22×C4—471no—
226C22×C4—941no—
227C22×C4—941no—
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—471no—
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⋊C4—941no—
246C4⋊C4C22×D4711yescharacteristic
247C4⋊C4C22×D4711yescharacteristic
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C22⋊C4—471no—
251C22⋊C4—471no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C42—471no—
259C42—941no—
260C42—941no—
261C42C22×D4711yescharacteristic
262C23—471no—
263C23—941no—
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—471no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—3761no—
285C2×C4—3761no—
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#1309407211yescharacteristic
313C4#1309407211yescharacteristic
314C2—3761no—
315C2—1881no—
316C2#1568969811yescharacteristic
317C2#1568992911yescharacteristic
318C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#498C2
socleC22×C47C22×D4
hypercenter#498D47
hypocenterC47#3244
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689529C2semidirect
4. #15689485C2semidirect
5. #15689478C2semidirect
6. #15689467C2semidirect
7. #15689455C2semidirect
10. #15689433C2semidirect
11. #15689422C2semidirect
12. #15689412C2semidirect
13. #15689407C2semidirect
14. #15689182C2semidirect
15. C47×#498C2semidirect
163. #498D47semidirect
175. C47#3244semidirect