Finite Group Databasebeta

← #20257213

Subgroups — #20257213

Order 6016.

988 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689852C211yesmaximal, characteristic, complemented
2#15689849C211yesmaximal, characteristic, complemented
3#15689849C211yesmaximal, characteristic, complemented
4#15689834C213yesmaximal, complemented
5#15689833C213yesmaximal, complemented
6#15689829C213yesmaximal, complemented
7#15689829C213yesmaximal, complemented
8#15689753C213yesmaximal, complemented
9#15689750C213yesmaximal, complemented
10#15689677C213yesmaximal, complemented
11#125×D47C213yesmaximal, complemented
12#15689605C211yesmaximal, characteristic
13#15689605C211yesmaximal, characteristic
14C4×#10625354C211yesmaximal, characteristic
15C47×#557C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17#13094024C2213yes—
18#13094023C2213yes—
19#13094023C2213yes—
20#13094023C2213yes—
21#13094022C2213yes—
22#13094016C2213yes—
23#13094016C2213yes—
24#13094015C2213yes—
25#13094015C2213yes—
26#13094015C2213yes—
27#13094015C2213yes—
28#13094014C2216yes—
29#13094014C2213yes—
30#13094014C2211yescharacteristic
31#13094004C2216yes—
32#13094004C2213yes—
33#13094002C2216yes—
34#13094002C2216yes—
35#13094002C2213yes—
36#13094002C2213yes—
37#13094000C2216yes—
38#13094000C2213yes—
39Q8×Dic47C2211yescharacteristic
40Q8×Dic47C2211yescharacteristic
41Q8×Dic47C2211yescharacteristic
42C4×Dic94C2213yes—
43C4×Dic94C2213yes—
44C4×Dic94C2213yes—
45C4×D188C2213yes—
46C4×D188C2213yes—
47C4×D188C2213yes—
48#13093986C2213yes—
49#13093986C2213yes—
50#13093986C2213yes—
51#13093982C2213yes—
52#13093981C2213yes—
53#13093981C2213yes—
54C4⋊C4×D47C2213yes—
55C4⋊C4×D47C2213yes—
56C4⋊C4×D47C2216yes—
57C4⋊C4×D47C2216yes—
58C42×D47C2213yes—
59C4⋊Q8×C47C2213yes—
60#125×C47C2213yes—
61#125×C47C2213yes—
62C4×Q8×C47C2213yes—
63C4×Q8×C47C2211yescharacteristic
64C4×Q8×C47C2211yescharacteristic
65C4×Q8×C47C2211yescharacteristic
66C2×Q8×C47C2313yes—
67C2×Q8×C47C2311yescharacteristic
68#10625354Q818yescomplemented
69C2×D188C2313yes—
70C2×C4×D47C2313yes—
71C2×C4×D47C2313yes—
72C2×C4×D47C2316yes—
73C2×C4×D47C2316yes—
74C2×C4×D47C2313yes—
75C2×Dic94C2313yes—
76C2×Dic94C2313yes—
77C2×Dic94C2313yes—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2313yes—
80C4⋊C4×C47C2313yes—
81C4⋊C4×C47C2313yes—
82C4⋊C4×C47C2313yes—
83C4⋊C4×C47C2313yes—
84C4⋊C4×C47C2316yes—
85C42×C47C2313yes—
86C42×C47C2313yes—
87C42×C47C2313yes—
88(C2×D47)⋊C4C2313yes—
89(C2×D47)⋊C4C2313yes—
90(C2×D47)⋊C4C2313yes—
91(C2×D47)⋊C4C2313yes—
92(C2×D47)⋊C4C2316yes—
93C4⋊Dic47C2313yes—
94C4⋊Dic47C2313yes—
95C4⋊Dic47C2313yes—
96C4⋊Dic47C2316yes—
97C4⋊Dic47C2313yes—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2313yes—
100Dic47⋊C4C2313yes—
101Dic47⋊C4C2313yes—
102Dic47⋊C4C2313yes—
103Dic47⋊C4C2313yes—
104Dic47⋊C4C2316yes—
105Dic47⋊C4C2316yes—
106Dic47⋊C4C2311yescharacteristic
107Dic47⋊C4C2311yescharacteristic
108Dic47⋊C4C2311yescharacteristic
109Dic47⋊C4C2311yescharacteristic
110Dic47⋊C4C2313yes—
111Dic47⋊C4C2313yes—
112C4×Dic47C2311yescharacteristic
113C4×Dic47C2313yes—
114C4×Dic47C2313yes—
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C22×D47C2413yes—
118Q8×C47—43no—
119Q8×C47C2×Q814yes—
120C2×C4×C47C2411yescharacteristic
121C2×C4×C47C2413yes—
122C2×C4×C47C2411yescharacteristic
123C2×C4×C47C2413yes—
124C2×C4×C47C2413yes—
125C2×C4×C47C2411yescharacteristic
126C2×C4×C47C2413yes—
127C2×Dic47C2411yescharacteristic
128C2×Dic47C2411yescharacteristic
129C2×Dic47C2411yescharacteristic
130C2×Dic47C2413yes—
131C2×Dic47C2413yes—
132C2×Dic47C2413yes—
133C2×Dic47C2411yescharacteristic
134D188C2×Q8112yes—
135C4×D47—43no—
136C4×D47—46no—
137C4×D47—46no—
138C4×D47—43no—
139C4×D47C2×Q8112yes—
140Dic94—43no—
141Dic94—43no—
142Dic94—43no—
143C22×C47C2511yescharacteristic
144C2×D47—23no—
145C2×D47—23no—
146C2×D47C22×Q816yes—
147C4×C47—21no—
148C4×C47—23no—
149C4×C47—23no—
150C4×C47—21no—
151C4×C47—23no—
152C4×C47—21no—
153C4×C47C22×Q816yes—
154Dic47—21no—
155Dic47—21no—
156Dic47—23no—
157Dic47—23no—
158Dic47—23no—
159Dic47—21no—
160Dic47C22×Q812yes—
161#3504—471nomaximal, Sylow
162C2×C47C23×Q811yescharacteristic
163C2×C47#58511yescharacteristic
164C2×C47#58511yescharacteristic
165D47—26no—
166#557—471no—
167#557—471no—
168#557—471no—
169#557D4711yescharacteristic, complemented
170#554—473no—
171#554—473no—
172#554—473no—
173#554—473no—
174#544—473no—
175#544—473no—
176#533—473no—
177C2×#125—473no—
178#520—471no—
179#520—471no—
180C4×#41—471no—
181C47#350411yescharacteristic, complemented, Sylow
182C2×#41—471no—
183C4⋊Q8—473no—
184C4⋊Q8—473no—
185C4⋊Q8—473no—
186C4⋊Q8—473no—
187C4⋊Q8—473no—
188C4⋊Q8C2×D4713yes—
189#125—473no—
190#125—476no—
191#125—473no—
192#125—473no—
193#125—471no—
194#125—473no—
195#125—473no—
196#125—473no—
197#125—473no—
198#125C2×D4713yes—
199#125C2×D4713yes—
200C22⋊Q8—473no—
201C22⋊Q8—476no—
202C22⋊Q8—473no—
203C22⋊Q8—473no—
204C22⋊Q8—473no—
205C22⋊Q8—476no—
206C22⋊Q8—476no—
207C22⋊Q8—476no—
208C4×Q8—471no—
209C4×Q8—471no—
210C4×Q8—471no—
211C4×Q8—473no—
212C4×Q8—473no—
213C4×Q8—473no—
214C4×Q8C2×D4711yescharacteristic
215C4×Q8C2×D4711yescharacteristic
216C4×Q8C2×D4711yescharacteristic
217C4×Q8C2×D4713yes—
218C4×D4—473no—
219C4×D4—473no—
220C4×D4—473no—
221C4×D4—473no—
222C4×D4—473no—
223C4×D4—473no—
224#117—473no—
225#117—473no—
226#117—473no—
227C2×C4⋊C4—473no—
228C2×C4⋊C4—473no—
229C2×C4⋊C4—476no—
230C2×C4⋊C4—476no—
231C2×C42—473no—
232#41—478no—
233C2×Q8—473no—
234C2×Q8—473no—
235C2×Q8—473no—
236C2×Q8C22×D4713yes—
237C2×Q8C22×D4711yescharacteristic
238C2×D4—473no—
239C22×C4—473no—
240C22×C4—473no—
241C22×C4—473no—
242C22×C4—476no—
243C22×C4—476no—
244C4⋊C4—473no—
245C4⋊C4—473no—
246C4⋊C4—473no—
247C4⋊C4—473no—
248C4⋊C4—476no—
249C4⋊C4—476no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—473no—
255C4⋊C4—473no—
256C4⋊C4—473no—
257C4⋊C4—473no—
258C4⋊C4—473no—
259C4⋊C4—476no—
260C4⋊C4—473no—
261C4⋊C4—471no—
262C4⋊C4—473no—
263C4⋊C4C22×D4713yes—
264C4⋊C4C22×D4713yes—
265C4⋊C4C22×D4713yes—
266C4⋊C4C22×D4716yes—
267C4⋊C4C22×D4713yes—
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4713yes—
270C22⋊C4—473no—
271C22⋊C4—473no—
272C22⋊C4—476no—
273C22⋊C4—473no—
274C22⋊C4—473no—
275C42—471no—
276C42—473no—
277C42—473no—
278C42—473no—
279C42—473no—
280C42C22×D4713yes—
281C42C22×D4713yes—
282C42C22×D4713yes—
283C23—473no—
284Q8—43no—
285Q8—1883no—
286Q8—1883no—
287Q8—1883no—
288Q8Q8×D4714yes—
289D4—4712no—
290C2×C4—471no—
291C2×C4—4712no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—473no—
296C2×C4—473no—
297C2×C4—473no—
298C2×C4—1886no—
299C2×C4—1883no—
300C2×C4—1883no—
301C2×C4—1886no—
302C2×C4C23×D4711yescharacteristic
303C2×C4C23×D4713yes—
304C2×C4C23×D4711yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C2×C4C23×D4713yes—
307C2×C4C23×D4713yes—
308C2×C4C23×D4713yes—
309C22—476no—
310C22—943no—
311C22—943no—
312C22C24×D4711yescharacteristic
313C4—23no—
314C4—23no—
315C4—21no—
316C4—21no—
317C4—23no—
318C4—21no—
319C4—472no—
320C4—941no—
321C4—943no—
322C4—941no—
323C4—943no—
324C4—943no—
325C4—941no—
326C4C2×Q8×D4716yes—
327C2—946no—
328C2C22×Q8×D4711yescharacteristic
329C2#1568995911yescharacteristic
330C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#557C2
hypercenter#557D47
hypocenterC47#3504
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #15689852C2semidirect
2. #15689849C2semidirect
3. #15689849C2semidirect
4. #15689834C2semidirect
5. #15689833C2semidirect
6. #15689829C2semidirect
7. #15689829C2semidirect
8. #15689753C2semidirect
9. #15689750C2semidirect
10. #15689677C2semidirect
11. #125×D47C2semidirect
15. C47×#557C2semidirect
68. #10625354Q8semidirect
169. #557D47semidirect
181. C47#3504semidirect