Finite Group Databasebeta

← #20257370

Subgroups — #20257370

Order 6016.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689852C211yesmaximal, characteristic, complemented
2#15689842C213yesmaximal, complemented
3#15689830C213yesmaximal, complemented
4#15689825C213yesmaximal, complemented
5#15689815C213yesmaximal, complemented
6Q8×C22⋊D47C211yesmaximal, characteristic, complemented
7#15689780C211yesmaximal, characteristic, complemented
8#15689742C213yesmaximal, complemented
9#15689733C213yesmaximal, complemented
10#15689654C213yesmaximal, complemented
11#15689653C213yesmaximal, complemented
12#15689606C211yesmaximal, characteristic, complemented
13#15689599C211yesmaximal, characteristic, complemented
14C2×Q8×Dic47C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17#13094024C2213yes—
18#13094022C2213yes—
19#13094019C2213yes—
20#13094017C2216yes—
21#13094017C2216yes—
22#13094017C2213yes—
23#13094015C2216yes—
24#13094015C2213yes—
25#13094015C2213yes—
26#13094014C2213yes—
27#13094011C2213yes—
28#13094010C2213yes—
29#13094008C2216yes—
30#13094008C2211yescharacteristic
31#13094005C2213yes—
32#13094003C2213yes—
33#13094003C2213yes—
34#13094001C2216yes—
35#13094001C2213yes—
36#13094000C2213yes—
37#13093996C2213yes—
38#13093995C2213yes—
39Q8×Dic47C2213yes—
40Q8×Dic47C2211yescharacteristic
41Q8×Dic47C2211yescharacteristic
42Q8×Dic47C2213yes—
43Q8×Dic47C2211yescharacteristic
44C4×Dic94C2213yes—
45C4×Dic94C2213yes—
46#13093989C2213yes—
47D4×Dic47C2213yes—
48D4×Dic47C2216yes—
49D4×Dic47C2213yes—
50C4×C22⋊D47C2213yes—
51C4×C22⋊D47C2213yes—
52#13093983C2213yes—
53#13093982C2213yes—
54#13093981C2213yes—
55#13093980C2216yes—
56C2×C4⋊Dic47C2213yes—
57C2×C4⋊Dic47C2213yes—
58C2×C4×Dic47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C22×Q8×C47C2211yescharacteristic
61#124×C47C2213yes—
62C22⋊Q8×C47C2213yes—
63#121×C47C2213yes—
64C4×Q8×C47C2211yescharacteristic
65C4×D4×C47C2213yes—
66#41×C47—24no—
67C2×Q8×C47—24no—
68C2×Q8×C47C2313yes—
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47C2313yes—
71C2×D4×C47C2313yes—
72C22×C4×C47C2313yes—
73C22×C4×C47C2313yes—
74C2×C22⋊D47C2311yescharacteristic
75C2×C22⋊D47C2313yes—
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2313yes—
78C22×Dic47C2316yes—
79Q8×D47—24no—
80C2×C4×D47C2313yes—
81C2×Dic94C2313yes—
82C2×Dic94C2313yes—
83C4⋊C4×C47C2313yes—
84C4⋊C4×C47C2313yes—
85C22⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47C2313yes—
87C22⋊C4×C47C2316yes—
88C42×C47C2313yes—
89C22⋊Dic47C2313yes—
90C22⋊Dic47C2313yes—
91C22⋊Dic47C2313yes—
92C22⋊Dic47C2313yes—
93C22⋊Dic47C2316yes—
94(C2×D47)⋊C4C2311yescharacteristic
95(C2×D47)⋊C4C2313yes—
96(C2×D47)⋊C4C2311yescharacteristic
97(C2×D47)⋊C4C2313yes—
98C4⋊Dic47C2313yes—
99C4⋊Dic47C2313yes—
100C4⋊Dic47C2313yes—
101C4⋊Dic47C2313yes—
102C4⋊Dic47C2316yes—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2316yes—
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4C2313yes—
107Dic47⋊C4C2316yes—
108Dic47⋊C4C2313yes—
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2313yes—
111Dic47⋊C4C2313yes—
112Dic47⋊C4C2313yes—
113C4×Dic47C2313yes—
114C4×Dic47C2313yes—
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2316yes—
118C4×Dic47C2313yes—
119C23×C47C2413yes—
120C23×C47C2411yescharacteristic
121C22×D47C2411yescharacteristic
122Q8×C47—26no—
123Q8×C47#4114yes—
124D4×C47—26no—
125D4×C47—26no—
126C2×C4×C47—26no—
127C2×C4×C47—26no—
128C2×C4×C47C2413yes—
129C2×C4×C47C2413yes—
130C2×C4×C47C2411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C2×C4×C47C2413yes—
133C22⋊D47—22no—
134C22⋊D47—43no—
135C2×Dic47—22no—
136C2×Dic47—46no—
137C2×Dic47—43no—
138C2×Dic47C2411yescharacteristic
139C2×Dic47C2411yescharacteristic
140C2×Dic47C2413yes—
141C2×Dic47C2411yescharacteristic
142C2×Dic47C2413yes—
143C2×Dic47C2413yes—
144C2×Dic47C2413yes—
145C4×D47—26no—
146Dic94—26no—
147Dic94—43no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—23no—
151C22×C47—23no—
152C22×C47—23no—
153C22×C472−1+412yes—
154C22×C47C2511yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—21no—
158C4×C47—21no—
159C4×C47—23no—
160C4×C47—23no—
161C4×C47—21no—
162C4×C47C2×#4116yes—
163Dic47—23no—
164Dic47—21no—
165Dic47—21no—
166Dic47—21no—
167Dic47—23no—
168Dic47—23no—
169Dic47—23no—
170#3516—471nomaximal, Sylow
171C2×C47—22no—
172C2×C47—43no—
173C2×C47C22×#4111yescharacteristic
174C2×C47C2×2−1+411yescharacteristic
175C2×C47#58511yescharacteristic
176D47—41no—
177#557—471no—
178#556—473no—
179#554—473no—
180#553—473no—
181#552—473no—
182D4×Q8—471no—
183#548—471no—
184#548D4711yescharacteristic, complemented
185#542—473no—
186#541—473no—
187#529—473no—
188#529—473no—
189#520—471no—
190#519—471no—
191C2×C4×Q8—471no—
192C47#351611yescharacteristic, complemented, Sylow
193C2×#41C2×D4711yescharacteristic
194C22×Q8—471no—
195C22×Q8C2×D4711yescharacteristic
196C4⋊Q8—473no—
197C4⋊Q8—473no—
198#126—473no—
199#126—476no—
200#126—473no—
201#126—476no—
202#125—473no—
203#125—473no—
204#125—476no—
205#125—473no—
206#124—473no—
207#124—473no—
208#124C2×D4713yes—
209#123—473no—
210#123—471no—
211#123—476no—
212C22⋊Q8—473no—
213C22⋊Q8—473no—
214C22⋊Q8—473no—
215C22⋊Q8—473no—
216C22⋊Q8—476no—
217C22⋊Q8C2×D4713yes—
218#121—473no—
219#121—473no—
220#121C2×D4713yes—
221C4×Q8—471no—
222C4×Q8—473no—
223C4×Q8—471no—
224C4×Q8—473no—
225C4×Q8—471no—
226C4×Q8—473no—
227C4×Q8—473no—
228C4×Q8—473no—
229C4×Q8C2×D4711yescharacteristic
230C4×D4—473no—
231C4×D4—473no—
232C4×D4—476no—
233C4×D4—473no—
234C4×D4—473no—
235C4×D4C2×D4713yes—
236#117—473no—
237#117—473no—
238#117—476no—
239#117—473no—
240C2×C4⋊C4—473no—
241C2×C4⋊C4—473no—
242C2×C42—473no—
243#41—24no—
244C2×Q8—24no—
245C2×Q8—473no—
246C2×Q8—473no—
247C2×Q8—944no—
248C2×Q8C22×D4713yes—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—473no—
252C2×D4C22×D4713yes—
253C2×D4C22×D4713yes—
254C22×C4—471no—
255C22×C4—473no—
256C22×C4—476no—
257C22×C4—473no—
258C22×C4C22×D4713yes—
259C22×C4C22×D4713yes—
260C4⋊C4—473no—
261C4⋊C4—473no—
262C4⋊C4—473no—
263C4⋊C4—476no—
264C4⋊C4—473no—
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⋊C4—476no—
274C4⋊C4—471no—
275C4⋊C4C22×D4713yes—
276C4⋊C4C22×D4713yes—
277C22⋊C4—473no—
278C22⋊C4—473no—
279C22⋊C4—473no—
280C22⋊C4—473no—
281C22⋊C4—476no—
282C22⋊C4—473no—
283C22⋊C4—471no—
284C22⋊C4—471no—
285C22⋊C4—473no—
286C22⋊C4C22×D4716yes—
287C22⋊C4C22×D4711yescharacteristic
288C22⋊C4C22×D4713yes—
289C42—473no—
290C42—473no—
291C42—473no—
292C42—473no—
293C42—476no—
294C42—473no—
295C42C22×D4713yes—
296C23—471no—
297C23C23×D4713yes—
298C23C23×D4711yescharacteristic
299Q8—26no—
300Q8—946no—
301Q8—1883no—
302Q8#1062535214yes—
303D4—26no—
304D4—26no—
305D4—942no—
306D4—1883no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—473no—
312C2×C4—471no—
313C2×C4—473no—
314C2×C4—473no—
315C2×C4—473no—
316C2×C4—942no—
317C2×C4—946no—
318C2×C4—1886no—
319C2×C4—1883no—
320C2×C4C23×D4713yes—
321C2×C4C23×D4713yes—
322C2×C4C23×D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C2×C4C23×D4713yes—
325C22—21no—
326C22—21no—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—941no—
331C22—941no—
332C22—941no—
333C22#1309407112yes—
334C22C24×D4711yescharacteristic
335C4—21no—
336C4—23no—
337C4—23no—
338C4—21no—
339C4—943no—
340C4—941no—
341C4—941no—
342C4—941no—
343C4—943no—
344C4—943no—
345C4—943no—
346C4C2×#1062535216yes—
347C2—22no—
348C2—43no—
349C2—1881no—
350C2C22×#1062535211yescharacteristic
351C2C2×#1309407111yescharacteristic
352C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3516
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689852C2semidirect
2. #15689842C2semidirect
3. #15689830C2semidirect
4. #15689825C2semidirect
5. #15689815C2semidirect
6. Q8×C22⋊D47C2semidirect
7. #15689780C2semidirect
8. #15689742C2semidirect
9. #15689733C2semidirect
10. #15689654C2semidirect
11. #15689653C2semidirect
12. #15689606C2semidirect
13. #15689599C2semidirect
14. C2×Q8×Dic47C2semidirect
15. C47×#548C2semidirect
184. #548D47semidirect
192. C47#3516semidirect