Finite Group Databasebeta

← #20257478

Subgroups — #20257478

Order 6016.

992 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689851C213yesmaximal, complemented
2#15689849C211yesmaximal, characteristic, complemented
3#15689841C213yesmaximal, complemented
4#15689814C213yesmaximal, complemented
5#15689812C213yesmaximal, complemented
6Q8×D188C211yesmaximal, characteristic, complemented
7Q8×C22⋊D47C211yesmaximal, characteristic, complemented
8Q8×C22⋊D47C211yesmaximal, characteristic, complemented
9#15689735C213yesmaximal, complemented
10#15689731C213yesmaximal, complemented
11#15689677C213yesmaximal, complemented
12#15689651C213yesmaximal
13#15689599C211yesmaximal, characteristic, complemented
14C4×Q8×D47C211yesmaximal, characteristic, complemented
15C47×#519C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094024C2213yes—
19#13094023C2213yes—
20#13094022C2213yes—
21#13094022C2213yes—
22#13094019C2213yes—
23#13094018C2216yes—
24#13094017C2213yes—
25#13094017C2216yes—
26#13094016C2216yes—
27#13094016C2213yes—
28#13094015C2213yes—
29#13094014C2216yes—
30#13094014C2216yes—
31#13094014C2213yes—
32#13094010C2213yes—
33#13094009C2213yes—
34#13094006C2213yes—
35#13094004C2213yes—
36#13094004C2213yes—
37#13094003C2213yes—
38#13094003C2213yes—
39#13094002C2213yes—
40#13094000C2213yes—
41#13094000C2213yes—
42#13093997C2211yescharacteristic
43Q8×Dic47C2211yescharacteristic
44Q8×Dic47C2211yescharacteristic
45C4×Dic94C2213yes—
46C4×Dic94C2213yes—
47C4×Dic94C2216yes—
48C4×Dic94C2213yes—
49#13093989C2213yes—
50#13093989C2213yes—
51C4×D188C2213yes—
52C4×C22⋊D47C2213yes—
53C4×C22⋊D47C2213yes—
54#13093982C2213yes—
55#13093981C2213yes—
56#13093981C2216yes—
57C4⋊C4×D47C2213yes—
58C42×D47C2213yes—
59C22×Q8×C47C2211yescharacteristic
60C4×Q8×C47C2213yes—
61C4×Q8×C47C2211yescharacteristic
62C4×Q8×C47C2213yes—
63C4×Q8×C47C2211yescharacteristic
64#117×C47C2213yes—
65#117×C47C2213yes—
66C2×Q8×C47—24no—
67C2×Q8×C47C2313yes—
68C2×Q8×C47C2311yescharacteristic
69C22×C4×C47C2313yes—
70C2×C22⋊D47C2311yescharacteristic
71C2×C22⋊D47C2311yescharacteristic
72Q8×D47—24no—
73Q8×D47—24no—
74C2×D188C2311yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2313yes—
77C2×C4×D47C2313yes—
78C2×C4×D47C2313yes—
79C2×Dic94C2313yes—
80C2×Dic94C2313yes—
81C2×Dic94C2313yes—
82C4⋊C4×C47C2313yes—
83C4⋊C4×C47C2313yes—
84C4⋊C4×C47C2313yes—
85C4⋊C4×C47C2313yes—
86C22⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47C2313yes—
88C42×C47C2313yes—
89C42×C47C2316yes—
90C42×C47C2313yes—
91C22⋊Dic47C2313yes—
92C22⋊Dic47C2313yes—
93(C2×D47)⋊C4C2311yescharacteristic
94(C2×D47)⋊C4C2313yes—
95(C2×D47)⋊C4C2313yes—
96(C2×D47)⋊C4C2313yes—
97(C2×D47)⋊C4C2313yes—
98(C2×D47)⋊C4C2313yes—
99C4⋊Dic47C2313yes—
100C4⋊Dic47C2313yes—
101C4⋊Dic47C2313yes—
102C4⋊Dic47C2316yes—
103C4⋊Dic47C2313yes—
104Dic47⋊C4C2316yes—
105Dic47⋊C4C2313yes—
106Dic47⋊C4C2313yes—
107Dic47⋊C4C2316yes—
108Dic47⋊C4C2316yes—
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2313yes—
111Dic47⋊C4C2311yescharacteristic
112Dic47⋊C4C2316yes—
113Dic47⋊C4C2313yes—
114C4×Dic47C2313yes—
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2316yes—
118C4×Dic47C2313yes—
119C23×C47C2411yescharacteristic
120C22×D47C2411yescharacteristic
121C22×D47C2411yescharacteristic
122Q8×C47—26no—
123Q8×C47#4114yes—
124C2×C4×C47—26no—
125C2×C4×C47C2413yes—
126C2×C4×C47C2411yescharacteristic
127C2×C4×C47C2413yes—
128C2×C4×C47C2411yescharacteristic
129C2×C4×C47C2413yes—
130C2×C4×C47C2413yes—
131C22⋊D47—22no—
132C22⋊D47—22no—
133C2×Dic47C2411yescharacteristic
134C2×Dic47C2413yes—
135C2×Dic47C2413yes—
136C2×Dic47C2413yes—
137C2×Dic47C2413yes—
138C2×Dic47C2411yescharacteristic
139D188—22no—
140C4×D47—26no—
141C4×D47—26no—
142C4×D47—26no—
143C4×D47—22no—
144Dic94—26no—
145Dic94—26no—
146Dic94—26no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47C2511yescharacteristic
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—21no—
156C2×D472−1+412yes—
157C4×C47—23no—
158C4×C47—23no—
159C4×C47—23no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47C2×#4116yes—
163Dic47—23no—
164Dic47—23no—
165Dic47—23no—
166Dic47—23no—
167Dic47—21no—
168Dic472−1+412yes—
169#3523—471nomaximal, Sylow
170C2×C47—41no—
171C2×C47C22×#4111yescharacteristic
172C2×C47C2×2−1+411yescharacteristic
173C2×C47C2×2−1+411yescharacteristic
174D47—22no—
175D47—41no—
176#557—471no—
177#557—473no—
178#556—473no—
179#552—473no—
180#552—473no—
181D4×Q8—471no—
182D4×Q8—471no—
183D4×Q8—471no—
184#541—473no—
185#541—473no—
186#533—473no—
187#529—473no—
188#519—471no—
189#519D4711yescharacteristic, complemented
190C2×C4×Q8—471no—
191C47#352311yescharacteristic, complemented, Sylow
192C22×Q8—471no—
193C22×Q8—471no—
194C22×Q8C2×D4711yescharacteristic
195C4⋊Q8—473no—
196C4⋊Q8—473no—
197C4⋊Q8—473no—
198C4⋊Q8—473no—
199#126—473no—
200#126—473no—
201#126—476no—
202#126—476no—
203#125—473no—
204#125—476no—
205#125—476no—
206#125—473no—
207#125—476no—
208#125—473no—
209#124—473no—
210#123—473no—
211#123—473no—
212C22⋊Q8—473no—
213C22⋊Q8—473no—
214C22⋊Q8—473no—
215C22⋊Q8—473no—
216C22⋊Q8—473no—
217C22⋊Q8—473no—
218C22⋊Q8—473no—
219#121—471no—
220C4×Q8—471no—
221C4×Q8—471no—
222C4×Q8—473no—
223C4×Q8—473no—
224C4×Q8—473no—
225C4×Q8—473no—
226C4×Q8—473no—
227C4×Q8—476no—
228C4×Q8C2×D4711yescharacteristic
229C4×Q8C2×D4713yes—
230C4×Q8C2×D4711yescharacteristic
231C4×Q8C2×D4713yes—
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—473no—
235#117—473no—
236#117—473no—
237#117—476no—
238#117C2×D4713yes—
239#117C2×D4713yes—
240C2×C4⋊C4—473no—
241C2×C42—473no—
242C2×Q8—24no—
243C2×Q8—473no—
244C2×Q8—473no—
245C2×Q8—473no—
246C2×Q8—944no—
247C2×Q8—944no—
248C2×Q8C22×D4713yes—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—471no—
253C22×C4—471no—
254C22×C4—473no—
255C22×C4—473no—
256C22×C4—473no—
257C22×C4C22×D4713yes—
258C4⋊C4—476no—
259C4⋊C4—473no—
260C4⋊C4—473no—
261C4⋊C4—476no—
262C4⋊C4—476no—
263C4⋊C4—473no—
264C4⋊C4—473no—
265C4⋊C4—471no—
266C4⋊C4—476no—
267C4⋊C4—473no—
268C4⋊C4—473no—
269C4⋊C4—473no—
270C4⋊C4—473no—
271C4⋊C4—476no—
272C4⋊C4—473no—
273C4⋊C4C22×D4713yes—
274C4⋊C4C22×D4713yes—
275C4⋊C4C22×D4713yes—
276C4⋊C4C22×D4713yes—
277C22⋊C4—473no—
278C22⋊C4—473no—
279C22⋊C4—471no—
280C22⋊C4—473no—
281C22⋊C4—473no—
282C22⋊C4—473no—
283C22⋊C4—473no—
284C22⋊C4—473no—
285C22⋊C4C22×D4711yescharacteristic
286C22⋊C4C22×D4713yes—
287C42—473no—
288C42—473no—
289C42—473no—
290C42—476no—
291C42—473no—
292C42C22×D4713yes—
293C42C22×D4716yes—
294C42C22×D4713yes—
295C23—471no—
296C23—471no—
297C23C23×D4711yescharacteristic
298Q8—26no—
299Q8—946no—
300Q8—946no—
301Q8—946no—
302Q8#1062535014yes—
303D4—942no—
304D4—942no—
305D4—942no—
306C2×C4—26no—
307C2×C4—471no—
308C2×C4—473no—
309C2×C4—471no—
310C2×C4—473no—
311C2×C4—473no—
312C2×C4—473no—
313C2×C4—942no—
314C2×C4—946no—
315C2×C4—946no—
316C2×C4—946no—
317C2×C4C23×D4713yes—
318C2×C4C23×D4711yescharacteristic
319C2×C4C23×D4713yes—
320C2×C4C23×D4711yescharacteristic
321C2×C4C23×D4713yes—
322C2×C4C23×D4713yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—472no—
327C22—941no—
328C22—941no—
329C22—941no—
330C22—941no—
331C22—941no—
332C22C24×D4711yescharacteristic
333C4—23no—
334C4—21no—
335C4—23no—
336C4—21no—
337C4—23no—
338C4—472no—
339C4—943no—
340C4—943no—
341C4—943no—
342C4—941no—
343C4—943no—
344C4C2×#1062535016yes—
345C2—41no—
346C2—942no—
347C2—1881no—
348C2C22×#1062535011yescharacteristic
349C22−1+4×D4711yescharacteristic
350C22−1+4×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#519C2
hypercenter#519D47
hypocenterC47#3523
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #15689851C2semidirect
2. #15689849C2semidirect
3. #15689841C2semidirect
4. #15689814C2semidirect
5. #15689812C2semidirect
6. Q8×D188C2semidirect
7. Q8×C22⋊D47C2semidirect
8. Q8×C22⋊D47C2semidirect
9. #15689735C2semidirect
10. #15689731C2semidirect
11. #15689677C2semidirect
13. #15689599C2semidirect
14. C4×Q8×D47C2semidirect
15. C47×#519C2semidirect
189. #519D47semidirect
191. C47#3523semidirect