Finite Group Databasebeta

← #20257489

Subgroups — #20257489

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#15689856C213yesmaximal, complemented
2#15689852C211yesmaximal, characteristic, complemented
3#15689838C213yesmaximal, complemented
4#15689821C213yesmaximal, complemented
5#15689808C213yesmaximal, complemented
6#15689792C211yesmaximal, characteristic, complemented
7#15689785C211yesmaximal, characteristic, complemented
8#15689780C211yesmaximal, characteristic, complemented
9#15689744C213yesmaximal, complemented
10#15689724C213yesmaximal, complemented
11#15689655C213yesmaximal, complemented
12#15689651C213yesmaximal, complemented
13#15689599C211yesmaximal, characteristic, complemented
14C4×#10625354C211yesmaximal, characteristic, complemented
15C47×#520C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094024C2213yes—
19#13094020C2213yes—
20#13094019C2216yes—
21#13094019C2211yescharacteristic
22#13094017C2213yes—
23#13094015C2213yes—
24#13094015C2213yes—
25#13094014C2213yes—
26#13094012C2213yes—
27#13094011C2213yes—
28#13094010C2216yes—
29#13094010C2213yes—
30#13094009C2213yes—
31#13094007C2216yes—
32#13094006C2216yes—
33#13094006C2213yes—
34#13094004C2213yes—
35#13094003C2213yes—
36#13094002C2213yes—
37#13093999C2213yes—
38#13093998C2213yes—
39#13093998C2216yes—
40#13093997C2213yes—
41#13093995C2213yes—
42#13093995C2213yes—
43Q8×Dic47C2211yescharacteristic
44Q8×Dic47C2211yescharacteristic
45C4×Dic94C2213yes—
46C4×Dic94C2213yes—
47#13093989C2213yes—
48C4×D188C2213yes—
49C4×D188C2213yes—
50#13093986C2213yes—
51C4×C22⋊D47C2213yes—
52C4×C22⋊D47C2213yes—
53C4×C22⋊D47C2216yes—
54#13093983C2216yes—
55#13093982C2213yes—
56#13093982C2213yes—
57#13093981C2213yes—
58C42×D47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C4×Q8×C47C2211yescharacteristic
61C4×Q8×C47C2211yescharacteristic
62C4×D4×C47C2213yes—
63C4×D4×C47C2213yes—
64#117×C47C2213yes—
65C2×C4⋊C4×C47C2213yes—
66#41×C47—24no—
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47C2313yes—
69C22×C4×C47C2313yes—
70C22×C4×C47C2316yes—
71C2×C22⋊D47C2313yes—
72C2×C22⋊D47C2316yes—
73C2×C22⋊D47C2313yes—
74#10625354—24no—
75Q8×D47—24no—
76C2×D188C2313yes—
77C2×D188C2313yes—
78C2×C4×D47C2313yes—
79C2×C4×D47C2313yes—
80C2×C4×D47C2313yes—
81C2×C4×D47C2313yes—
82C2×Dic94C2313yes—
83C2×Dic94C2313yes—
84C4⋊C4×C47C2313yes—
85C4⋊C4×C47C2313yes—
86C4⋊C4×C47C2313yes—
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47C2313yes—
89C22⋊C4×C47C2313yes—
90C42×C47C2313yes—
91C42×C47C2313yes—
92C22⋊Dic47C2313yes—
93C22⋊Dic47C2316yes—
94C22⋊Dic47C2313yes—
95(C2×D47)⋊C4C2311yescharacteristic
96(C2×D47)⋊C4C2313yes—
97(C2×D47)⋊C4C2316yes—
98(C2×D47)⋊C4C2311yescharacteristic
99(C2×D47)⋊C4C2313yes—
100(C2×D47)⋊C4C2316yes—
101(C2×D47)⋊C4C2311yescharacteristic
102(C2×D47)⋊C4C2313yes—
103C4⋊Dic47C2313yes—
104C4⋊Dic47C2313yes—
105C4⋊Dic47C2313yes—
106C4⋊Dic47C2316yes—
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4C2313yes—
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2311yescharacteristic
111Dic47⋊C4C2313yes—
112Dic47⋊C4C2313yes—
113Dic47⋊C4C2313yes—
114C4×Dic47C2311yescharacteristic
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2313yes—
118C4×Dic47C2316yes—
119C23×C47C2413yes—
120C22×D47C2411yescharacteristic
121C22×D47C2413yes—
122Q8×C47#4114yes—
123D4×C47—26no—
124C2×C4×C47—26no—
125C2×C4×C47—46no—
126C2×C4×C47C2413yes—
127C2×C4×C47C2411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C2×C4×C47C2413yes—
130C2×C4×C47C2411yescharacteristic
131C2×C4×C47C2413yes—
132C22⋊D47—43no—
133C22⋊D47—46no—
134C22⋊D47—43no—
135C2×Dic47C2411yescharacteristic
136C2×Dic47C2411yescharacteristic
137C2×Dic47C2411yescharacteristic
138C2×Dic47C2413yes—
139C2×Dic47C2413yes—
140C2×Dic47C2413yes—
141D188—26no—
142D188—43no—
143C4×D47—26no—
144C4×D47—26no—
145C4×D47—43no—
146C4×D47—43no—
147Dic94—26no—
148Dic94—43no—
149C22×C47—23no—
150C22×C47—23no—
151C22×C47—23no—
152C22×C47C2511yescharacteristic
153C2×D47—21no—
154C2×D47—23no—
155C2×D47—23no—
156C2×D47—23no—
157C2×D47—21no—
158C2×D47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—23no—
163C4×C47—23no—
164C4×C47C2×#4116yes—
165Dic47—23no—
166Dic47—21no—
167Dic47—23no—
168Dic47—23no—
169Dic47—21no—
170Dic47—21no—
171#3524—471nomaximal, Sylow
172C2×C47—43no—
173C2×C47C22×#4111yescharacteristic
174C2×C47#58511yescharacteristic
175C2×C47#58511yescharacteristic
176D47—41no—
177D47—43no—
178#559—473no—
179#557—471no—
180#555—473no—
181#553—473no—
182#552—473no—
183#550—471no—
184#548—471no—
185#548—471no—
186#542—473no—
187#540—473no—
188#529—473no—
189#529—473no—
190#520D4711yescharacteristic, complemented
191#519—471no—
192C4×#41—471no—
193C47#352411yescharacteristic, complemented, Sylow
194C2×#41—471no—
195C2×#41C2×D4711yescharacteristic
196C22×Q8—471no—
197C4⋊Q8—473no—
198#127—473no—
199#126—471no—
200#126—476no—
201#126—473no—
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—476no—
219#121—473no—
220#121—473no—
221#121—473no—
222C4×Q8—471no—
223C4×Q8—471no—
224C4×Q8—473no—
225C4×Q8—473no—
226C4×Q8—473no—
227C4×Q8C2×D4711yescharacteristic
228C4×Q8C2×D4711yescharacteristic
229C4×D4—473no—
230C4×D4—473no—
231C4×D4—476no—
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—473no—
235C4×D4C2×D4713yes—
236C4×D4C2×D4713yes—
237#117—476no—
238#117—473no—
239#117—473no—
240#117—473no—
241#117C2×D4713yes—
242C2×C4⋊C4C2×D4713yes—
243C2×C42—473no—
244#41—24no—
245#41—944no—
246C2×Q8—473no—
247C2×Q8—473no—
248C2×Q8—944no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—473no—
251C2×D4—476no—
252C2×D4—473no—
253C2×D4—473no—
254C2×D4—473no—
255C2×D4C22×D4713yes—
256C22×C4—473no—
257C22×C4—473no—
258C22×C4—473no—
259C22×C4—473no—
260C22×C4C22×D4713yes—
261C22×C4C22×D4716yes—
262C4⋊C4—473no—
263C4⋊C4—473no—
264C4⋊C4—471no—
265C4⋊C4—473no—
266C4⋊C4—473no—
267C4⋊C4—473no—
268C4⋊C4—473no—
269C4⋊C4—473no—
270C4⋊C4—473no—
271C4⋊C4—476no—
272C4⋊C4—471no—
273C4⋊C4C22×D4713yes—
274C4⋊C4C22×D4713yes—
275C4⋊C4C22×D4713yes—
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—473no—
278C22⋊C4—476no—
279C22⋊C4—473no—
280C22⋊C4—471no—
281C22⋊C4—473no—
282C22⋊C4—476no—
283C22⋊C4—471no—
284C22⋊C4—471no—
285C22⋊C4—473no—
286C22⋊C4—476no—
287C22⋊C4—473no—
288C22⋊C4C22×D4713yes—
289C22⋊C4C22×D4713yes—
290C42—471no—
291C42—473no—
292C42—473no—
293C42—476no—
294C42—473no—
295C42C22×D4713yes—
296C42C22×D4713yes—
297C23—471no—
298C23—473no—
299C23C23×D4713yes—
300Q8—946no—
301Q8—1883no—
302Q8#1062535014yes—
303D4—26no—
304D4—946no—
305D4—1883no—
306D4—1883no—
307D4—1883no—
308D4—1886no—
309C2×C4—26no—
310C2×C4—46no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—473no—
314C2×C4—471no—
315C2×C4—473no—
316C2×C4—473no—
317C2×C4—946no—
318C2×C4—946no—
319C2×C4—1883no—
320C2×C4—1883no—
321C2×C4C23×D4713yes—
322C2×C4C23×D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C2×C4C23×D4713yes—
325C2×C4C23×D4711yescharacteristic
326C2×C4C23×D4713yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—941no—
331C22—943no—
332C22—943no—
333C22—941no—
334C22—943no—
335C22—941no—
336C22C24×D4711yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—21no—
342C4—941no—
343C4—943no—
344C4—941no—
345C4—941no—
346C4—943no—
347C4—943no—
348C4C2×#1062535016yes—
349C2—43no—
350C2—1881no—
351C2—1883no—
352C2C22×#1062535011yescharacteristic
353C2#1568995811yescharacteristic
354C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#520C2
hypercenter#520D47
hypocenterC47#3524
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #15689856C2semidirect
2. #15689852C2semidirect
3. #15689838C2semidirect
4. #15689821C2semidirect
5. #15689808C2semidirect
6. #15689792C2semidirect
7. #15689785C2semidirect
8. #15689780C2semidirect
9. #15689744C2semidirect
10. #15689724C2semidirect
11. #15689655C2semidirect
12. #15689651C2semidirect
13. #15689599C2semidirect
14. C4×#10625354C2semidirect
15. C47×#520C2semidirect
190. #520D47semidirect
193. C47#3524semidirect