Finite Group Databasebeta

← #20253682

Subgroups — #20253682

Order 6016.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689733C211yesmaximal, characteristic
2#15689601C211yesmaximal, characteristic
3#15689465C211yesmaximal, characteristic
4#15689461C211yesmaximal, characteristic
5#15689432C211yesmaximal, characteristic, complemented
6#15689428C211yesmaximal, characteristic, complemented
7#15689331C211yesmaximal, characteristic, complemented
8#15689331C211yesmaximal, characteristic, complemented
9#15689279C211yesmaximal, characteristic
10#15689230C211yesmaximal, characteristic, complemented
11#15689227C211yesmaximal, characteristic, complemented
12Q16×Dic47C211yesmaximal, characteristic, complemented
13#15689215C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic
15C47×#451C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18#13094022C2211yescharacteristic
19#13094017—21no—
20#13094017—21no—
21#13094015—21no—
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094003C2211yescharacteristic
25Q8×Dic47—21no—
26Q8×Dic47—21no—
27Q8×Dic47C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32#13093989C2211yescharacteristic
33#13093983—21no—
34#13093983—21no—
35#13093983C2211yescharacteristic
36#13093983C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×Q16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47—22no—
60C2×Q8×C47—22no—
61C2×Q8×C47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×Dic94C2311yescharacteristic
68Q16×C47—22no—
69Q16×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C22⋊Dic47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47D411yescharacteristic
78C22⋊Dic47D411yescharacteristic
79#10625337—22no—
80#10625337—22no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47D411yescharacteristic
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47C2×D411yescharacteristic
109Q8×C47—24no—
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47#4112yes—
115Q8×C47#4112yes—
116C2×C4×C47—24no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133Dic94—21no—
134Dic94—21no—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47C22×D411yescharacteristic
143C4×C47—22no—
144C4×C47—22no—
145C4×C47—21no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47C2×#4111yescharacteristic
149C4×C47C2×#4111yescharacteristic
150Dic47—21no—
151Dic47—21no—
152Dic47—21no—
153Dic47—21no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158#3127—471nomaximal, Sylow
159C2×C47—41no—
160C2×C47#52511yescharacteristic
161C2×C47#57811yescharacteristic
162C2×C47#57811yescharacteristic
163#541—471no—
164#519—471no—
165#485—471no—
166#485—471no—
167#479—471no—
168#479—471no—
169#462—471no—
170#462—471no—
171#451—471no—
172#451D4711yescharacteristic
173#441—471no—
174#441—471no—
175C4×Q16—471no—
176C4×Q16—471no—
177#433—471no—
178C47#312711yescharacteristic, complemented, Sylow
179C22×Q8C2×D4711yescharacteristic
180C2×Q16—471no—
181C2×Q16—471no—
182C2×Q16C2×D4711yescharacteristic
183C2×Q16C2×D4711yescharacteristic
184C4⋊Q8—471no—
185#126—941no—
186#126—941no—
187#125—471no—
188#125—941no—
189#125—941no—
190C22⋊Q8—471no—
191C22⋊Q8C2×D4711yescharacteristic
192C4×Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—471no—
196C4×Q8—471no—
197C4×Q8—471no—
198C4×Q8—941no—
199C4×Q8—941no—
200#117—471no—
201#117—471no—
202#117—941no—
203#117—941no—
204#107—471no—
205#107—471no—
206#106—471no—
207#106—471no—
208C4⋊C8—471no—
209C4⋊C8—471no—
210#103—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103C2×D4711yescharacteristic
217#103C2×D4711yescharacteristic
218C22⋊C8—471no—
219C22⋊C8C2×D4711yescharacteristic
220#97—471no—
221C4×C8—471no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—21no—
225C2×Q8—471no—
226C2×Q8C22×D4711yescharacteristic
227C2×Q8C22×D4711yescharacteristic
228C2×Q8C22×D4711yescharacteristic
229C22×C4—21no—
230C22×C4C22×D4711yescharacteristic
231Q16—22no—
232Q16—22no—
233Q16—942no—
234Q16—942no—
235C2×C8—471no—
236C2×C8—471no—
237C2×C8C22×D4711yescharacteristic
238C2×C8C22×D4711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—471no—
259C22⋊C4—471no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C42—471no—
263C42—471no—
264C42—941no—
265C42—941no—
266C42—941no—
267C42—941no—
268C42—941no—
269C42—941no—
270C42—941no—
271C23D4×D4711yescharacteristic
272Q8—24no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—21no—
277Q8—941no—
278Q8—941no—
279Q8#1062535212yes—
280Q8#1062535212yes—
281C2×C4—24no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—471no—
291C2×C4—471no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4D4×D4711yescharacteristic
297C2×C4C23×D4711yescharacteristic
298C8—21no—
299C8—21no—
300C8—941no—
301C8—941no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22C2×D4×D4711yescharacteristic
306C4—22no—
307C4—22no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—941no—
312C4—941no—
313C4—941no—
314C4—941no—
315C4—1881no—
316C4—1881no—
317C4—1881no—
318C4—1881no—
319C4C2×#1062535211yescharacteristic
320C4C2×#1062535211yescharacteristic
321C2—41no—
322C2#1568962911yescharacteristic
323C2#1568993611yescharacteristic
324C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3127
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #15689432C2semidirect
6. #15689428C2semidirect
7. #15689331C2semidirect
8. #15689331C2semidirect
10. #15689230C2semidirect
11. #15689227C2semidirect
12. Q16×Dic47C2semidirect
13. #15689215C2semidirect
178. C47#3127semidirect