Finite Group Databasebeta

← #20255959

Subgroups — #20255959

Order 6016.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689812C211yesmaximal, characteristic
2#15689808C211yesmaximal, characteristic
3#15689523C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689464C211yesmaximal, characteristic, complemented
6#15689460C211yesmaximal, characteristic, complemented
7#15689458C211yesmaximal, characteristic, complemented
8#15689433C211yesmaximal, characteristic, complemented
9#15689429C211yesmaximal, characteristic, complemented
10#15689382C211yesmaximal, characteristic, complemented
11#15689381C211yesmaximal, characteristic, complemented
12#15689217C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic
14#15689164C211yesmaximal, characteristic, complemented
15C47×#428C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18#13094019—21no—
19#13094017—21no—
20#13094016—21no—
21#13094015C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094007—21no—
25#13094006—21no—
26#13094004C2211yescharacteristic
27#13094004C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094003C2211yescharacteristic
30#13093989C2211yescharacteristic
31#13093989C2211yescharacteristic
32C4×C22⋊D47C2211yescharacteristic
33#13093983—21no—
34#13093982C2211yescharacteristic
35#13093981—21no—
36C4⋊C4×D47C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47D411yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2311yescharacteristic
66M16×C47—22no—
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47C2311yescharacteristic
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C42×C47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47D411yescharacteristic
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4D411yescharacteristic
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
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⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103Dic188—22no—
104#10625324—22no—
105C23×C47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—42no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2411yescharacteristic
116C22⋊D47—41no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C4×D47—21no—
125C4×D47—21no—
126C4×D47—42no—
127Dic94—21no—
128Dic94—21no—
129Dic94—21no—
130Dic94—21no—
131C8×C47—21no—
132C8×C47#4112yes—
133C47⋊C8—21no—
134C47⋊C8—21no—
135C22×C47—21no—
136C22×C47—21no—
137C22×C47—21no—
138C22×C47C22×D411yescharacteristic
139C2×D47—21no—
140C2×D47—21no—
141C2×D47—21no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47C2×#4111yescharacteristic
148C4×C472−1+411yescharacteristic
149Dic47—21no—
150Dic47—21no—
151Dic47—21no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156#3352—471nomaximal, Sylow
157C2×C47—41no—
158C2×C47#54711yescharacteristic
159C2×C47#57511yescharacteristic
160C2×C47#57811yescharacteristic
161D47—41no—
162#552—471no—
163#552—471no—
164#499—471no—
165#485—471no—
166#485—471no—
167#484—471no—
168#484—471no—
169#479—471no—
170#479—471no—
171#470—471no—
172#470—471no—
173C4×Q16—471no—
174#436—471no—
175#428—471no—
176#428D4711yescharacteristic, complemented
177C47#335211yescharacteristic, complemented, Sylow
178C2×Q16—471no—
179C2×M16—471no—
180C2×M16C2×D4711yescharacteristic
181#126—941no—
182#126—941no—
183#125—471no—
184#125—471no—
185#125—941no—
186#125—941no—
187#123—941no—
188#123—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×D4—471no—
196#117—471no—
197#117—941no—
198#117—941no—
199#117C2×D4711yescharacteristic
200C2×C4⋊C4—471no—
201C2×C4⋊C4C2×D4711yescharacteristic
202#107—471no—
203#107—471no—
204#107—471no—
205#107C2×D4711yescharacteristic
206#107C2×D4711yescharacteristic
207#106—471no—
208#106—471no—
209#106C2×D4711yescharacteristic
210#106C2×D4711yescharacteristic
211C4⋊C8—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218C22⋊C8—471no—
219C22⋊C8—471no—
220C4×C8—471no—
221C2×Q8—471no—
222C2×Q8—471no—
223C2×D4—471no—
224C22×C4—21no—
225C22×C4—471no—
226C22×C4—941no—
227C22×C4C22×D4711yescharacteristic
228Q16—942no—
229M16—22no—
230M16—942no—
231C2×C8—471no—
232C2×C8—471no—
233C2×C8C22×D4711yescharacteristic
234C2×C8C22×D4711yescharacteristic
235C4⋊C4—21no—
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⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4C22×D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C4⋊C4C22×D4711yescharacteristic
253C4⋊C4C22×D4711yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—471no—
256C22⋊C4—471no—
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C42—21no—
263C42—471no—
264C42—941no—
265C42—941no—
266C42—941no—
267C23—471no—
268C23D4×D4711yescharacteristic
269Q8—941no—
270Q8—941no—
271Q8—941no—
272Q8—941no—
273D4—1881no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—471no—
282C2×C4—471no—
283C2×C4—471no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—1882no—
291C2×C4D4×D4711yescharacteristic
292C2×C4C23×D4711yescharacteristic
293C8—21no—
294C8—941no—
295C8—941no—
296C8#1062535012yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—941no—
301C22—941no—
302C22—941no—
303C22C2×D4×D4711yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—941no—
310C4—941no—
311C4—941no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4C2×#1062535011yescharacteristic
317C4#1309407211yescharacteristic
318C2—41no—
319C2—1881no—
320C2#1568977411yescharacteristic
321C2#1568991911yescharacteristic
322C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3352
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #15689523C2semidirect
4. #15689467C2semidirect
5. #15689464C2semidirect
6. #15689460C2semidirect
7. #15689458C2semidirect
8. #15689433C2semidirect
9. #15689429C2semidirect
10. #15689382C2semidirect
11. #15689381C2semidirect
12. #15689217C2semidirect
14. #15689164C2semidirect
15. C47×#428C2semidirect
176. #428D47semidirect
177. C47#3352semidirect