Finite Group Databasebeta

← #20257384

Subgroups — #20257384

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#15689846C213yesmaximal, complemented
2#15689834C213yesmaximal, complemented
3#15689826C213yesmaximal, complemented
4#15689811C213yesmaximal, complemented
5Q8×D188C211yesmaximal, characteristic, complemented
6#15689785C211yesmaximal, characteristic, complemented
7#15689785C211yesmaximal, characteristic, complemented
8#15689747C213yesmaximal, complemented
9#15689736C213yesmaximal, complemented
10#15689660C213yesmaximal, complemented
11#15689658C213yesmaximal, complemented
12#15689605C211yesmaximal, characteristic, complemented
13#15689599C211yesmaximal, characteristic, complemented
14C4×Q8×D47C211yesmaximal, characteristic, complemented
15C47×#557C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic
19#13094024C2213yes—
20#13094019C2216yes—
21#13094019C2216yes—
22#13094019C2213yes—
23#13094019C2213yes—
24#13094015C2213yes—
25#13094015C2216yes—
26#13094013C2213yes—
27#13094012C2213yes—
28#13094012C2213yes—
29#13094009C2216yes—
30#13094009C2213yes—
31#13094009C2211yescharacteristic
32#13094004C2213yes—
33#13094004C2213yes—
34#13094004C2213yes—
35#13094004C2213yes—
36#13094000C2216yes—
37#13094000C2213yes—
38#13093999C2213yes—
39#13093999C2213yes—
40#13093999C2213yes—
41Q8×Dic47C2211yescharacteristic
42C4×Dic94C2213yes—
43C4×Dic94C2213yes—
44#13093989C2213yes—
45#13093989C2213yes—
46C4×D188C2213yes—
47C4×D188C2213yes—
48C4×D188C2213yes—
49C4×D188C2213yes—
50#13093986C2213yes—
51#13093986C2216yes—
52#13093982C2213yes—
53#13093982C2216yes—
54#13093981C2213yes—
55#13093981C2213yes—
56C4⋊C4×D47C2213yes—
57C4⋊C4×D47C2213yes—
58C42×D47C2213yes—
59C4⋊Q8×C47C2213yes—
60#125×C47C2213yes—
61#125×C47C2213yes—
62C4×Q8×C47C2211yescharacteristic
63C4×Q8×C47C2211yescharacteristic
64C4×Q8×C47C2211yescharacteristic
65C4×Q8×C47C2213yes—
66C2×Q8×C47C2313yes—
67C2×Q8×C47C2311yescharacteristic
68#10625354—24no—
69Q8×D47—24no—
70Q8×D47—24no—
71C2×D188C2313yes—
72C2×D188C2313yes—
73C2×D188C2311yescharacteristic
74C2×D188C2313yes—
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2313yes—
77C2×C4×D47C2313yes—
78C2×C4×D47C2313yes—
79C2×C4×D47C2313yes—
80C2×C4×D47C2316yes—
81C2×Dic94C2313yes—
82C2×Dic94C2313yes—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2313yes—
85C4⋊C4×C47C2313yes—
86C4⋊C4×C47C2313yes—
87C4⋊C4×C47C2313yes—
88C4⋊C4×C47C2313yes—
89C4⋊C4×C47C2316yes—
90C42×C47C2313yes—
91C42×C47C2313yes—
92C42×C47C2313yes—
93(C2×D47)⋊C4C2311yescharacteristic
94(C2×D47)⋊C4C2313yes—
95(C2×D47)⋊C4C2313yes—
96(C2×D47)⋊C4C2313yes—
97(C2×D47)⋊C4C2313yes—
98(C2×D47)⋊C4C2316yes—
99(C2×D47)⋊C4C2313yes—
100(C2×D47)⋊C4C2316yes—
101(C2×D47)⋊C4C2311yescharacteristic
102(C2×D47)⋊C4C2311yescharacteristic
103(C2×D47)⋊C4C2313yes—
104(C2×D47)⋊C4C2313yes—
105C4⋊Dic47C2313yes—
106C4⋊Dic47C2316yes—
107C4⋊Dic47C2313yes—
108C4⋊Dic47C2313yes—
109C4⋊Dic47C2313yes—
110Dic47⋊C4C2313yes—
111Dic47⋊C4C2316yes—
112Dic47⋊C4C2311yescharacteristic
113Dic47⋊C4C2313yes—
114Dic47⋊C4C2313yes—
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2313yes—
118C4×Dic47C2316yes—
119C22×D47C2411yescharacteristic
120C22×D47C2413yes—
121C22×D47C2411yescharacteristic
122Q8×C47—43no—
123Q8×C47#4114yes—
124C2×C4×C47C2411yescharacteristic
125C2×C4×C47C2413yes—
126C2×C4×C47C2413yes—
127C2×C4×C47C2411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C2×C4×C47C2413yes—
130C2×C4×C47C2413yes—
131C2×Dic47C2411yescharacteristic
132C2×Dic47C2413yes—
133C2×Dic47C2413yes—
134C2×Dic47C2413yes—
135C2×Dic47C2411yescharacteristic
136D188—26no—
137D188—22no—
138D188—26no—
139D188—43no—
140C4×D47—22no—
141C4×D47—26no—
142C4×D47—26no—
143C4×D47—26no—
144C4×D47—46no—
145C4×D47—43no—
146Dic94—26no—
147Dic94—26no—
148C22×C47C2511yescharacteristic
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—23no—
153C2×D47—21no—
154C2×D47—23no—
155C2×D47—23no—
156C2×D47—21no—
157C2×D472−1+412yes—
158C4×C47—21no—
159C4×C47—23no—
160C4×C47—21no—
161C4×C47—23no—
162C4×C47—23no—
163C4×C47—21no—
164C4×C47C2×#4116yes—
165Dic47—23no—
166Dic47—23no—
167Dic47—21no—
168Dic47—21no—
169Dic47—23no—
170#3516—471nomaximal, Sylow
171C2×C47C22×#4111yescharacteristic
172C2×C47C2×2−1+411yescharacteristic
173C2×C47#58511yescharacteristic
174D47—22no—
175D47—41no—
176D47—43no—
177#557D4711yescharacteristic, complemented
178#556—473no—
179#554—473no—
180#553—473no—
181#552—473no—
182D4×Q8—471no—
183#548—471no—
184#548—471no—
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×#41—471no—
194C22×Q8—471no—
195C22×Q8—471no—
196C4⋊Q8—473no—
197C4⋊Q8C2×D4713yes—
198#126—476no—
199#126—473no—
200#126—473no—
201#126—476no—
202#125—473no—
203#125—476no—
204#125C2×D4713yes—
205#125C2×D4713yes—
206#124—473no—
207#124—473no—
208#124—473no—
209#123—471no—
210#123—473no—
211#123—476no—
212C22⋊Q8—473no—
213C22⋊Q8—476no—
214C22⋊Q8—473no—
215C22⋊Q8—473no—
216C22⋊Q8—473no—
217C22⋊Q8—473no—
218#121—473no—
219#121—473no—
220#121—473no—
221C4×Q8—471no—
222C4×Q8—473no—
223C4×Q8—473no—
224C4×Q8—473no—
225C4×Q8—473no—
226C4×Q8C2×D4711yescharacteristic
227C4×Q8C2×D4711yescharacteristic
228C4×Q8C2×D4711yescharacteristic
229C4×Q8C2×D4713yes—
230C4×D4—473no—
231C4×D4—476no—
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—473no—
235C4×D4—473no—
236#117—473no—
237#117—476no—
238#117—473no—
239#117—473no—
240C2×C4⋊C4—473no—
241C2×C4⋊C4—473no—
242C2×C42—473no—
243#41—944no—
244C2×Q8—473no—
245C2×Q8—473no—
246C2×Q8—944no—
247C2×Q8—944no—
248C2×Q8C22×D4713yes—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—473no—
251C2×D4—471no—
252C2×D4—473no—
253C2×D4—473no—
254C22×C4—471no—
255C22×C4—473no—
256C22×C4—473no—
257C22×C4—473no—
258C22×C4—473no—
259C22×C4—476no—
260C4⋊C4—473no—
261C4⋊C4—476no—
262C4⋊C4—471no—
263C4⋊C4—473no—
264C4⋊C4—473no—
265C4⋊C4—473no—
266C4⋊C4—476no—
267C4⋊C4—473no—
268C4⋊C4—473no—
269C4⋊C4—473no—
270C4⋊C4C22×D4713yes—
271C4⋊C4C22×D4713yes—
272C4⋊C4C22×D4713yes—
273C4⋊C4C22×D4713yes—
274C4⋊C4C22×D4716yes—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4713yes—
277C22⋊C4—473no—
278C22⋊C4—471no—
279C22⋊C4—473no—
280C22⋊C4—473no—
281C22⋊C4—473no—
282C22⋊C4—476no—
283C22⋊C4—473no—
284C22⋊C4—471no—
285C22⋊C4—471no—
286C22⋊C4—476no—
287C22⋊C4—473no—
288C22⋊C4—473no—
289C42—473no—
290C42—473no—
291C42—473no—
292C42—476no—
293C42C22×D4713yes—
294C42C22×D4713yes—
295C42C22×D4713yes—
296C23—471no—
297C23—471no—
298C23—473no—
299Q8—43no—
300Q8—946no—
301Q8—946no—
302Q8#1062535414yes—
303D4—946no—
304D4—942no—
305D4—946no—
306D4—1883no—
307C2×C4—471no—
308C2×C4—473no—
309C2×C4—473no—
310C2×C4—473no—
311C2×C4—471no—
312C2×C4—942no—
313C2×C4—946no—
314C2×C4—946no—
315C2×C4—946no—
316C2×C4—1886no—
317C2×C4—1883no—
318C2×C4C23×D4711yescharacteristic
319C2×C4C23×D4713yes—
320C2×C4C23×D4713yes—
321C2×C4C23×D4711yescharacteristic
322C2×C4C23×D4711yescharacteristic
323C2×C4C23×D4713yes—
324C2×C4C23×D4713yes—
325C22—472no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22—943no—
330C22—941no—
331C22—943no—
332C22—943no—
333C22—941no—
334C22C24×D4711yescharacteristic
335C4—21no—
336C4—23no—
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—941no—
342C4—943no—
343C4—943no—
344C4—941no—
345C4—943no—
346C4C2×#1062535416yes—
347C2—942no—
348C2—1881no—
349C2—1883no—
350C2C22×#1062535411yescharacteristic
351C22−1+4×D4711yescharacteristic
352C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#557C2
hypercenter#557D47
hypocenterC47#3516
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #15689846C2semidirect
2. #15689834C2semidirect
3. #15689826C2semidirect
4. #15689811C2semidirect
5. Q8×D188C2semidirect
6. #15689785C2semidirect
7. #15689785C2semidirect
8. #15689747C2semidirect
9. #15689736C2semidirect
10. #15689660C2semidirect
11. #15689658C2semidirect
12. #15689605C2semidirect
13. #15689599C2semidirect
14. C4×Q8×D47C2semidirect
15. C47×#557C2semidirect
177. #557D47semidirect
192. C47#3516semidirect