Finite Group Databasebeta

← #20257486

Subgroups — #20257486

Order 6016.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689859C213yesmaximal, complemented
2#15689849C211yesmaximal, characteristic, complemented
3#15689837C213yesmaximal, complemented
4#15689825C213yesmaximal, complemented
5#15689813C213yesmaximal, complemented
6#15689780C211yesmaximal, characteristic, complemented
7#15689780C211yesmaximal, characteristic, complemented
8#15689740C213yesmaximal, complemented
9#15689727C213yesmaximal, complemented
10#15689654C213yesmaximal, complemented
11#15689653C213yesmaximal, complemented
12#15689606C211yesmaximal, characteristic, complemented
13#15689599C211yesmaximal, characteristic, complemented
14#41×Dic47C211yesmaximal, characteristic, complemented
15C47×#550C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17#13094023C2213yes—
18#13094019C2211yescharacteristic
19#13094017C2216yes—
20#13094017C2213yes—
21#13094016C2213yes—
22#13094015C2213yes—
23#13094014C2213yes—
24#13094011C2213yes—
25#13094011C2216yes—
26#13094011C2213yes—
27#13094010C2213yes—
28#13094008C2213yes—
29#13094005C2216yes—
30#13094005C2216yes—
31#13094005C2213yes—
32#13094003C2213yes—
33#13094003C2213yes—
34#13094001C2213yes—
35#13093996C2216yes—
36#13093996C2213yes—
37#13093995C2213yes—
38#13093995C2213yes—
39Q8×Dic47C2211yescharacteristic
40Q8×Dic47C2211yescharacteristic
41Q8×Dic47C2211yescharacteristic
42C4×Dic94C2213yes—
43C4×Dic94C2213yes—
44#13093989C2213yes—
45D4×Dic47C2213yes—
46D4×Dic47C2213yes—
47D4×Dic47C2216yes—
48D4×Dic47C2213yes—
49D4×Dic47C2213yes—
50C4×C22⋊D47C2213yes—
51C4×C22⋊D47C2213yes—
52#13093983C2213yes—
53#13093983C2213yes—
54#13093982C2213yes—
55#13093981C2213yes—
56#13093980C2216yes—
57C2×C4⋊Dic47C2213yes—
58C2×C4×Dic47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C2×#41×C47C2211yescharacteristic
61#127×C47C2213yes—
62#121×C47C2213yes—
63#121×C47C2213yes—
64C4×Q8×C47C2211yescharacteristic
65C4×D4×C47C2213yes—
66#41×C47—24no—
67#41×C47—24no—
68C2×Q8×C47C2311yescharacteristic
69C2×D4×C47C2313yes—
70C2×D4×C47C2313yes—
71C2×D4×C47C2313yes—
72C2×D4×C47C2316yes—
73C22×C4×C47C2313yes—
74C22×C4×C47C2313yes—
75C2×C22⋊D47C2313yes—
76C2×C22⋊D47C2313yes—
77C22×Dic47C2313yes—
78C22×Dic47C2313yes—
79C22×Dic47C2316yes—
80Q8×D47—24no—
81C2×C4×D47C2313yes—
82C2×Dic94C2313yes—
83C2×Dic94C2313yes—
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2313yes—
86C22⋊C4×C47C2313yes—
87C22⋊C4×C47C2313yes—
88C42×C47C2313yes—
89C22⋊Dic47C2316yes—
90C22⋊Dic47C2313yes—
91C22⋊Dic47C2316yes—
92C22⋊Dic47C2313yes—
93C22⋊Dic47C2313yes—
94C22⋊Dic47C2313yes—
95C22⋊Dic47C2316yes—
96(C2×D47)⋊C4C2311yescharacteristic
97(C2×D47)⋊C4C2313yes—
98(C2×D47)⋊C4C2311yescharacteristic
99(C2×D47)⋊C4C2311yescharacteristic
100C4⋊Dic47C2313yes—
101C4⋊Dic47C2313yes—
102C4⋊Dic47C2313yes—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2313yes—
105C4⋊Dic47C2313yes—
106Dic47⋊C4C2313yes—
107Dic47⋊C4C2316yes—
108Dic47⋊C4C2313yes—
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2313yes—
111Dic47⋊C4C2311yescharacteristic
112Dic47⋊C4C2313yes—
113C4×Dic47C2311yescharacteristic
114C4×Dic47C2313yes—
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2316yes—
118C4×Dic47C2313yes—
119C23×C47C2413yes—
120C23×C47C2413yes—
121C22×D47C2411yescharacteristic
122Q8×C47#4114yes—
123D4×C47—26no—
124D4×C47—26no—
125D4×C47—46no—
126D4×C47—43no—
127C2×C4×C47—26no—
128C2×C4×C47—26no—
129C2×C4×C47C2411yescharacteristic
130C2×C4×C47C2413yes—
131C2×C4×C47C2411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C2×C4×C47C2413yes—
134C22⋊D47—43no—
135C22⋊D47—43no—
136C2×Dic47—43no—
137C2×Dic47—43no—
138C2×Dic47—46no—
139C2×Dic47C2411yescharacteristic
140C2×Dic47C2411yescharacteristic
141C2×Dic47C2413yes—
142C2×Dic47C2411yescharacteristic
143C2×Dic47C2413yes—
144C2×Dic47C2413yes—
145C2×Dic47C2413yes—
146C4×D47—26no—
147Dic94—26no—
148Dic94—43no—
149C22×C47—23no—
150C22×C47—23no—
151C22×C47—23no—
152C22×C47—23no—
153C22×C47—23no—
154C22×C47—23no—
155C22×C47C2511yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—23no—
162C4×C47—21no—
163C4×C47C2×#4116yes—
164Dic47—23no—
165Dic47—21no—
166Dic47—23no—
167Dic47—21no—
168Dic47—21no—
169Dic47—23no—
170Dic47—23no—
171#3524—471nomaximal, Sylow
172C2×C47—43no—
173C2×C47—43no—
174C2×C47C22×#4111yescharacteristic
175C2×C47#58511yescharacteristic
176C2×C47#58511yescharacteristic
177D47—41no—
178#559—473no—
179#557—471no—
180#555—473no—
181#553—473no—
182#552—473no—
183#550D4711yescharacteristic, complemented
184#548—471no—
185#548—471no—
186#542—473no—
187#540—473no—
188#529—473no—
189#529—473no—
190#520—471no—
191#519—471no—
192C4×#41—471no—
193C47#352411yescharacteristic, complemented, Sylow
194C2×#41C2×D4711yescharacteristic
195C2×#41C2×D4711yescharacteristic
196C22×Q8—471no—
197C4⋊Q8—473no—
198#127C2×D4713yes—
199#126—471no—
200#126—473no—
201#126—476no—
202#125—473no—
203#125—473no—
204#125—473no—
205#124—473no—
206#124—473no—
207#124—476no—
208#124—473no—
209#123—476no—
210#123—473no—
211#123—476no—
212#123—473no—
213C22⋊Q8—473no—
214C22⋊Q8—473no—
215C22⋊Q8—473no—
216#121—473no—
217#121—473no—
218#121—473no—
219#121—476no—
220#121C2×D4713yes—
221#121C2×D4713yes—
222C4×Q8—471no—
223C4×Q8—471no—
224C4×Q8—471no—
225C4×Q8—473no—
226C4×Q8—473no—
227C4×Q8—473no—
228C4×Q8C2×D4711yescharacteristic
229C4×D4—473no—
230C4×D4—473no—
231C4×D4—473no—
232C4×D4—473no—
233C4×D4—476no—
234C4×D4—473no—
235C4×D4—473no—
236C4×D4C2×D4713yes—
237#117—473no—
238#117—473no—
239#117—473no—
240#117—476no—
241#117—473no—
242C2×C4⋊C4—473no—
243C2×C42—473no—
244#41—24no—
245#41—24no—
246C2×Q8—473no—
247C2×Q8—473no—
248C2×Q8—944no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—473no—
251C2×D4—473no—
252C2×D4C22×D4713yes—
253C2×D4C22×D4713yes—
254C2×D4C22×D4716yes—
255C2×D4C22×D4713yes—
256C22×C4—473no—
257C22×C4—473no—
258C22×C4—476no—
259C22×C4—473no—
260C22×C4C22×D4713yes—
261C22×C4C22×D4713yes—
262C4⋊C4—473no—
263C4⋊C4—473no—
264C4⋊C4—473no—
265C4⋊C4—476no—
266C4⋊C4—473no—
267C4⋊C4—471no—
268C4⋊C4—473no—
269C4⋊C4—473no—
270C4⋊C4—473no—
271C4⋊C4—473no—
272C4⋊C4—471no—
273C4⋊C4—473no—
274C4⋊C4—473no—
275C4⋊C4C22×D4713yes—
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—473no—
278C22⋊C4—476no—
279C22⋊C4—473no—
280C22⋊C4—476no—
281C22⋊C4—473no—
282C22⋊C4—476no—
283C22⋊C4—473no—
284C22⋊C4—471no—
285C22⋊C4—473no—
286C22⋊C4—471no—
287C22⋊C4—471no—
288C22⋊C4C22×D4713yes—
289C22⋊C4C22×D4713yes—
290C42—471no—
291C42—473no—
292C42—473no—
293C42—473no—
294C42—476no—
295C42—473no—
296C42C22×D4713yes—
297C23—471no—
298C23C23×D4713yes—
299C23C23×D4713yes—
300Q8—946no—
301Q8—1883no—
302Q8#1062535214yes—
303D4—26no—
304D4—26no—
305D4—46no—
306D4—43no—
307D4—1883no—
308D4—1883no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—473no—
314C2×C4—471no—
315C2×C4—473no—
316C2×C4—473no—
317C2×C4—473no—
318C2×C4—946no—
319C2×C4—1883no—
320C2×C4—1883no—
321C2×C4—1886no—
322C2×C4C23×D4711yescharacteristic
323C2×C4C23×D4713yes—
324C2×C4C23×D4711yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C2×C4C23×D4713yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—23no—
331C22—23no—
332C22—23no—
333C22—941no—
334C22—941no—
335C22—941no—
336C22C24×D4711yescharacteristic
337C4—21no—
338C4—21no—
339C4—23no—
340C4—21no—
341C4—943no—
342C4—941no—
343C4—943no—
344C4—941no—
345C4—941no—
346C4—943no—
347C4—943no—
348C4C2×#1062535216yes—
349C2—43no—
350C2—43no—
351C2—1881no—
352C2C22×#1062535211yescharacteristic
353C2#1568995811yescharacteristic
354C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#550C2
hypercenter#550D47
hypocenterC47#3524
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #15689859C2semidirect
2. #15689849C2semidirect
3. #15689837C2semidirect
4. #15689825C2semidirect
5. #15689813C2semidirect
6. #15689780C2semidirect
7. #15689780C2semidirect
8. #15689740C2semidirect
9. #15689727C2semidirect
10. #15689654C2semidirect
11. #15689653C2semidirect
12. #15689606C2semidirect
13. #15689599C2semidirect
14. #41×Dic47C2semidirect
15. C47×#550C2semidirect
183. #550D47semidirect
193. C47#3524semidirect