Finite Group Databasebeta

← #20255281

Subgroups — #20255281

Order 6016.

386 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#15689815C211yesmaximal, characteristic, complemented
2#15689779C211yesmaximal, characteristic
3#15689476C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689434C211yesmaximal, characteristic, complemented
6#15689433C211yesmaximal, characteristic, complemented
7#15689363C211yesmaximal, characteristic, complemented
8#15689343C211yesmaximal, characteristic, complemented
9#15689282C211yesmaximal, characteristic, complemented
10#15689278C211yesmaximal, characteristic, complemented
11#15689215C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14C2×#13093949C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094019—21no—
22#13094015—21no—
23#13094015C2211yescharacteristic
24#13094011C2211yescharacteristic
25#13094010—21no—
26#13094008—21no—
27#13094004C2211yescharacteristic
28#13094001—21no—
29#13094000C2211yescharacteristic
30#13093996—21no—
31Q8×Dic47C2211yescharacteristic
32#13093989C2211yescharacteristic
33D4×Dic47—21no—
34C4×C22⋊D47C2211yescharacteristic
35#13093982C2211yescharacteristic
36#13093980—21no—
37C2×C4⋊Dic47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625352—22no—
69#10625352—41no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—22no—
72C2×Dic94—21no—
73C2×Dic94—41no—
74C2×Dic94C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76SD16×C47—41no—
77C2×C8×C47—41no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625337—22no—
89#10625337—41no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—42no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—22no—
127C22⋊D47—42no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—42no—
133C2×Dic47—42no—
134C2×Dic47—42no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C4×D47—21no—
139C4×D47—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—21no—
143Dic94—42no—
144Dic94#4112yes—
145C8×C47—21no—
146C8×C47—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47#13512yes—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47H(5,𝔽2)11yescharacteristic
165Dic47—22no—
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172#3300—471nomaximal, Sylow
173C2×C47—22no—
174C2×C47—81no—
175C2×C47#54611yescharacteristic
176C2×C47C2×#13511yescharacteristic
177C2×C47#57811yescharacteristic
178D47—41no—
179#552—471no—
180#548—471no—
181#488—471no—
182#485—471no—
183#480—471no—
184#479—471no—
185#467—471no—
186#465D4711yescharacteristic, complemented
187#464—471no—
188#452—471no—
189#451—471no—
190C4×Q16—471no—
191C8×D4—471no—
192#416—471no—
193C2×#103—471no—
194C47#330011yescharacteristic, complemented, Sylow
195C2×#41—471no—
196C22×Q8—471no—
197C2×Q16—471no—
198C2×Q16—471no—
199C2×SD16C2×D4711yescharacteristic
200C22×C8—471no—
201C22×C8C2×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—941no—
211C22⋊Q8C2×D4711yescharacteristic
212#121—941no—
213#121C2×D4711yescharacteristic
214C4×Q8—471no—
215C4×Q8—471no—
216C4×D4—471no—
217C4×D4—941no—
218#117—471no—
219#117—941no—
220C2×C4⋊C4—471no—
221#107—471no—
222#107—471no—
223#106C2×D4711yescharacteristic
224C4⋊C8—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103C2×D4711yescharacteristic
232#102—471no—
233#102—471no—
234#102C2×D4711yescharacteristic
235C22⋊C8—471no—
236C22⋊C8—471no—
237C4×C8—471no—
238#41—942no—
239#41—1881no—
240C2×Q8—471no—
241C2×Q8—471no—
242C2×Q8—942no—
243C2×Q8—941no—
244C2×Q8—1881no—
245C2×Q8C22×D4711yescharacteristic
246C2×D4—21no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C22×C4—471no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4C22×D4711yescharacteristic
255Q16—942no—
256Q16—1881no—
257SD16—41no—
258C2×C8—41no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—1881no—
262C2×C8C22×D4711yescharacteristic
263C2×C8C22×D4711yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
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—21no—
279C22⋊C4—471no—
280C22⋊C4—471no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C42—941no—
288C42—941no—
289C42—941no—
290C23—21no—
291C23—471no—
292C23D4×D4711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—472no—
296Q8—941no—
297Q8—941no—
298Q8—941no—
299Q8—1882no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—942no—
304D4—1882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—1882no—
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—41no—
331C22—41no—
332C22—41no—
333C22—941no—
334C22—941no—
335C22—941no—
336C22#1309404512yes—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—941no—
343C4—942no—
344C4—941no—
345C4—941no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4#41×D4711yescharacteristic
350C4#1309406911yescharacteristic
351C2—22no—
352C2—81no—
353C2—1881no—
354C2#1568976211yescharacteristic
355C2C2×#1309404511yescharacteristic
356C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3300
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689815C2semidirect
3. #15689476C2semidirect
4. #15689467C2semidirect
5. #15689434C2semidirect
6. #15689433C2semidirect
7. #15689363C2semidirect
8. #15689343C2semidirect
9. #15689282C2semidirect
10. #15689278C2semidirect
11. #15689215C2semidirect
12. C8×C22⋊D47C2semidirect
13. #15689116C2semidirect
14. C2×#13093949C2semidirect
15. C47×#465C2semidirect
186. #465D47semidirect
194. C47#3300semidirect