Finite Group Databasebeta

← #20255652

Subgroups — #20255652

Order 6016.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689812C211yesmaximal, characteristic, complemented
2#15689784C211yesmaximal, characteristic
3#15689479C211yesmaximal, characteristic, complemented
4#15689457C211yesmaximal, characteristic, complemented
5#15689447C211yesmaximal, characteristic, complemented
6#15689432C211yesmaximal, characteristic, complemented
7#15689380C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689348C211yesmaximal, characteristic, complemented
10#15689288C211yesmaximal, characteristic, complemented
11#15689279C211yesmaximal, characteristic, complemented
12#15689215C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689123C211yesmaximal, characteristic, complemented
15C47×#419C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094017—21no—
22#13094016—21no—
23#13094015C2211yescharacteristic
24#13094013—21no—
25#13094013C2211yescharacteristic
26#13094006—21no—
27#13094004C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094000—21no—
30#13094000C2211yescharacteristic
31#13093998—21no—
32#13093998C2211yescharacteristic
33Q8×Dic47C2211yescharacteristic
34#13093989C2211yescharacteristic
35C4×C22⋊D47—21no—
36C4×C22⋊D47C2211yescharacteristic
37#13093981—21no—
38C4⋊C4×D47C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—22no—
61C2×Q8×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47D411yescharacteristic
68#10625354—22no—
69#10625354—41no—
70C2×D188—21no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76M16×C47—41no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C42×C47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47D411yescharacteristic
85#10625337—22no—
86#10625337—41no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625325—41no—
110#10625324—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—42no—
118Q8×C47#4112yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—42no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—41no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—21no—
137D188—21no—
138D188—42no—
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—42no—
142C4×D47—42no—
143Dic94—21no—
144Dic94—21no—
145C8×C47—21no—
146C8×C47—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47C22×D411yescharacteristic
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—22no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C47H(5,𝔽2)11yescharacteristic
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172#3327—471nomaximal, Sylow
173C2×C47—41no—
174C2×C47#54611yescharacteristic
175C2×C47#57511yescharacteristic
176C2×C47#57811yescharacteristic
177D47—41no—
178D47—81no—
179#552—471no—
180#548—471no—
181#488—471no—
182#484—471no—
183#482—471no—
184#479—471no—
185#470—471no—
186#468—471no—
187#464—471no—
188#452—471no—
189#451—471no—
190C4×Q16—471no—
191#436—471no—
192#419D4711yescharacteristic, complemented
193#417—471no—
194C47#332711yescharacteristic, complemented, Sylow
195C2×#41—471no—
196C22×Q8C2×D4711yescharacteristic
197C2×Q16—471no—
198C2×Q16—471no—
199C2×SD16—471no—
200C2×M16—471no—
201C2×M16C2×D4711yescharacteristic
202#126—941no—
203#125—471no—
204#125—941no—
205#124—471no—
206#124—941no—
207#123—941no—
208C22⋊Q8—471no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212#121—471no—
213#121—941no—
214C4×Q8—471no—
215C4×Q8—471no—
216C4×D4—471no—
217C4×D4—941no—
218#117—941no—
219#117C2×D4711yescharacteristic
220C2×C4⋊C4—471no—
221#107—471no—
222#107—471no—
223#106—471no—
224C4⋊C8—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103C2×D4711yescharacteristic
229#103C2×D4711yescharacteristic
230#103C2×D4711yescharacteristic
231#103C2×D4711yescharacteristic
232#102—471no—
233#102—471no—
234#102—471no—
235C22⋊C8—471no—
236C22⋊C8—471no—
237C4×C8—471no—
238#41—942no—
239#41—1881no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—471no—
244C2×Q8C22×D4711yescharacteristic
245C2×Q8C22×D4711yescharacteristic
246C2×D4—471no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4—941no—
250C22×C4—21no—
251C22×C4—471no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4C22×D4711yescharacteristic
255Q16—942no—
256Q16—1881no—
257SD16—1881no—
258M16—41no—
259M16—1881no—
260C2×C8—471no—
261C2×C8—471no—
262C2×C8C22×D4711yescharacteristic
263C2×C8C22×D4711yescharacteristic
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—471no—
279C22⋊C4—471no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—21no—
287C42—471no—
288C42—941no—
289C42—941no—
290C23—471no—
291C23—941no—
292C23D4×D4711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—941no—
298Q8—941no—
299Q8#1062535012yes—
300D4—941no—
301D4—941no—
302D4—1882no—
303D4—1881no—
304D4—1882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4D4×D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C8—21no—
325C8—21no—
326C8—941no—
327C8—941no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—941no—
332C22—941no—
333C22—941no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—941no—
344C4—941no—
345C4—941no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4C2×#1062535011yescharacteristic
350C4#1309406911yescharacteristic
351C2—41no—
352C2—3761no—
353C2—1881no—
354C2#1568976311yescharacteristic
355C2#1568992211yescharacteristic
356C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3327
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #15689812C2semidirect
3. #15689479C2semidirect
4. #15689457C2semidirect
5. #15689447C2semidirect
6. #15689432C2semidirect
7. #15689380C2semidirect
8. #15689369C2semidirect
9. #15689348C2semidirect
10. #15689288C2semidirect
11. #15689279C2semidirect
12. #15689215C2semidirect
13. #15689199C2semidirect
14. #15689123C2semidirect
15. C47×#419C2semidirect
192. #419D47semidirect
194. C47#3327semidirect