Finite Group Databasebeta

← #20257195

Subgroups — #20257195

Order 6016.

964 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic94C211yesmaximal, characteristic, complemented
2#15689853C213yesmaximal, complemented
3#15689851C213yesmaximal, complemented
4#15689850C213yesmaximal, complemented
5#15689850C213yesmaximal, complemented
6#15689849C211yesmaximal, characteristic, complemented
7#15689849C211yesmaximal, characteristic, complemented
8#15689753C213yesmaximal
9#15689750C213yesmaximal
10#15689679C213yesmaximal
11#15689677C213yesmaximal
12#15689599C211yesmaximal, characteristic
13#15689599C211yesmaximal, characteristic
14C4×Q8×D47C211yesmaximal, characteristic
15C47×#557C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17#13094024C2213yes—
18#13094023C2213yes—
19#13094023C2213yes—
20#13094023C2216yes—
21#13094023C2213yes—
22#13094023C2213yes—
23#13094023C2213yes—
24#13094022C2216yes—
25#13094022C2213yes—
26#13094016C2213yes—
27#13094016C2213yes—
28#13094015C2213yes—
29#13094015C2213yes—
30#13094014C2216yes—
31#13094014C2216yes—
32#13094014C2213yes—
33#13094014C2213yes—
34#13094004C2213yes—
35#13094002C2216yes—
36#13094002C2211yescharacteristic
37#13094002C2213yes—
38#13094000C2213yes—
39Q8×Dic47C2211yescharacteristic
40Q8×Dic47C2211yescharacteristic
41Q8×Dic47C2211yescharacteristic
42C4×Dic94C2213yes—
43C4×Dic94C2213yes—
44C4×Dic94C2213yes—
45C4×Dic94C2213yes—
46C4×Dic94C2213yes—
47C4×Dic94C2213yes—
48#13093989C2213yes—
49#13093989C2213yes—
50#13093989C2216yes—
51#13093989C2213yes—
52#13093989C2216yes—
53#13093982C2213yes—
54#13093982C2213yes—
55#13093981C2213yes—
56#13093981C2213yes—
57C4⋊C4×D47C2213yes—
58C42×D47C2213yes—
59C4⋊Q8×C47C2213yes—
60#125×C47C2213yes—
61#125×C47C2213yes—
62C4×Q8×C47C2211yescharacteristic
63C4×Q8×C47C2211yescharacteristic
64C4×Q8×C47C2213yes—
65C4×Q8×C47C2211yescharacteristic
66C2×Q8×C47C2313yes—
67C2×Q8×C47C2311yescharacteristic
68Q8×D47Q818yescomplemented
69C2×C4×D47C2311yescharacteristic
70C2×C4×D47C2313yes—
71C2×C4×D47C2313yes—
72C2×Dic94C2313yes—
73C2×Dic94C2311yescharacteristic
74C2×Dic94C2316yes—
75C2×Dic94C2313yes—
76C2×Dic94C2313yes—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2313yes—
79C4⋊C4×C47C2313yes—
80C4⋊C4×C47C2313yes—
81C4⋊C4×C47C2313yes—
82C4⋊C4×C47C2313yes—
83C4⋊C4×C47C2316yes—
84C42×C47C2313yes—
85C42×C47C2313yes—
86C42×C47C2313yes—
87(C2×D47)⋊C4C2311yescharacteristic
88(C2×D47)⋊C4C2311yescharacteristic
89(C2×D47)⋊C4C2313yes—
90(C2×D47)⋊C4C2313yes—
91C4⋊Dic47C2313yes—
92C4⋊Dic47C2313yes—
93C4⋊Dic47C2313yes—
94C4⋊Dic47C2313yes—
95C4⋊Dic47C2313yes—
96C4⋊Dic47C2313yes—
97Dic47⋊C4C2316yes—
98Dic47⋊C4C2313yes—
99Dic47⋊C4C2313yes—
100Dic47⋊C4C2313yes—
101Dic47⋊C4C2313yes—
102Dic47⋊C4C2313yes—
103Dic47⋊C4C2313yes—
104Dic47⋊C4C2316yes—
105Dic47⋊C4C2316yes—
106Dic47⋊C4C2311yescharacteristic
107Dic47⋊C4C2311yescharacteristic
108Dic47⋊C4C2313yes—
109Dic47⋊C4C2313yes—
110C4×Dic47C2313yes—
111C4×Dic47C2313yes—
112C4×Dic47C2313yes—
113C4×Dic47C2313yes—
114C4×Dic47C2313yes—
115C4×Dic47C2316yes—
116C4×Dic47C2316yes—
117C22×D47C2411yescharacteristic
118Q8×C47—43no—
119Q8×C47C2×Q814yes—
120C2×C4×C47C2411yescharacteristic
121C2×C4×C47C2413yes—
122C2×C4×C47C2413yes—
123C2×C4×C47C2413yes—
124C2×C4×C47C2411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C2×C4×C47C2413yes—
127C2×Dic47C2411yescharacteristic
128C2×Dic47C2413yes—
129C2×Dic47C2411yescharacteristic
130C2×Dic47C2413yes—
131C2×Dic47C2413yes—
132C2×Dic47C2413yes—
133C2×Dic47C2411yescharacteristic
134C4×D47—22no—
135C4×D47—43no—
136C4×D47C2×Q8112yes—
137Dic94—26no—
138Dic94—22no—
139Dic94—43no—
140Dic94—46no—
141Dic94C2×Q8112yes—
142C22×C47C2511yescharacteristic
143C2×D47—21no—
144C2×D47—21no—
145C2×D47C22×Q812yes—
146C4×C47—23no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—23no—
150C4×C47—23no—
151C4×C47—21no—
152C4×C47C22×Q816yes—
153Dic47—23no—
154Dic47—21no—
155Dic47—21no—
156Dic47—23no—
157Dic47—23no—
158Dic47C22×Q816yes—
159Dic472−1+412yes—
160#3502—471nomaximal, Sylow
161C2×C47C23×Q811yescharacteristic
162C2×C47C2×2−1+411yescharacteristic
163C2×C47#58511yescharacteristic
164D47—22no—
165Q82—473no—
166Q82—471no—
167#557—473no—
168#557—473no—
169#557—471no—
170#557—471no—
171#557—473no—
172#557D4711yescharacteristic, complemented
173#544—473no—
174#544—473no—
175#533—473no—
176#533—473no—
177#519—471no—
178#519—471no—
179C2×C4×Q8—471no—
180C47#350211yescharacteristic, complemented, Sylow
181C22×Q8—471no—
182C4⋊Q8—473no—
183C4⋊Q8—476no—
184C4⋊Q8—473no—
185C4⋊Q8—473no—
186C4⋊Q8—473no—
187C4⋊Q8—476no—
188C4⋊Q8—473no—
189C4⋊Q8—473no—
190C4⋊Q8—473no—
191C4⋊Q8C2×D4713yes—
192#125—473no—
193#125—473no—
194#125—476no—
195#125—476no—
196#125—473no—
197#125—473no—
198#125—473no—
199#125—473no—
200#125C2×D4713yes—
201#125C2×D4713yes—
202C22⋊Q8—473no—
203C22⋊Q8—473no—
204C22⋊Q8—471no—
205C22⋊Q8—476no—
206C22⋊Q8—473no—
207C4×Q8—471no—
208C4×Q8—471no—
209C4×Q8—471no—
210C4×Q8—473no—
211C4×Q8—473no—
212C4×Q8—473no—
213C4×Q8—476no—
214C4×Q8—476no—
215C4×Q8—473no—
216C4×Q8—473no—
217C4×Q8—473no—
218C4×Q8—473no—
219C4×Q8—473no—
220C4×Q8—473no—
221C4×Q8C2×D4711yescharacteristic
222C4×Q8C2×D4711yescharacteristic
223C4×Q8C2×D4711yescharacteristic
224C4×Q8C2×D4713yes—
225#117—473no—
226#117—473no—
227#117—473no—
228#117—473no—
229C2×C4⋊C4—473no—
230C2×C42—473no—
231C2×Q8—478no—
232C2×Q8—473no—
233C2×Q8—473no—
234C2×Q8—471no—
235C2×Q8—473no—
236C2×Q8—476no—
237C2×Q8C22×D4713yes—
238C2×Q8C22×D4711yescharacteristic
239C22×C4—473no—
240C22×C4—471no—
241C22×C4—473no—
242C4⋊C4—476no—
243C4⋊C4—473no—
244C4⋊C4—473no—
245C4⋊C4—473no—
246C4⋊C4—473no—
247C4⋊C4—473no—
248C4⋊C4—471no—
249C4⋊C4—473no—
250C4⋊C4—471no—
251C4⋊C4—476no—
252C4⋊C4—476no—
253C4⋊C4—473no—
254C4⋊C4—473no—
255C4⋊C4—473no—
256C4⋊C4—473no—
257C4⋊C4—473no—
258C4⋊C4—473no—
259C4⋊C4—473no—
260C4⋊C4—473no—
261C4⋊C4C22×D4713yes—
262C4⋊C4C22×D4713yes—
263C4⋊C4C22×D4713yes—
264C4⋊C4C22×D4713yes—
265C4⋊C4C22×D4716yes—
266C4⋊C4C22×D4711yescharacteristic
267C4⋊C4C22×D4713yes—
268C22⋊C4—473no—
269C22⋊C4—471no—
270C22⋊C4—473no—
271C22⋊C4—471no—
272C42—473no—
273C42—473no—
274C42—473no—
275C42—476no—
276C42—476no—
277C42—473no—
278C42—473no—
279C42C22×D4713yes—
280C42C22×D4713yes—
281C42C22×D4713yes—
282C23—471no—
283Q8—43no—
284Q8—4712no—
285Q8—946no—
286Q8—942no—
287Q8—1883no—
288Q8—1886no—
289Q8Q8×D4714yes—
290C2×C4—473no—
291C2×C4—471no—
292C2×C4—4712no—
293C2×C4—471no—
294C2×C4—473no—
295C2×C4—471no—
296C2×C4—473no—
297C2×C4—473no—
298C2×C4—942no—
299C2×C4—1883no—
300C2×C4C23×D4711yescharacteristic
301C2×C4C23×D4713yes—
302C2×C4C23×D4713yes—
303C2×C4C23×D4713yes—
304C2×C4C23×D4711yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C2×C4C23×D4713yes—
307C22—472no—
308C22—941no—
309C22—941no—
310C22C24×D4711yescharacteristic
311C4—21no—
312C4—23no—
313C4—21no—
314C4—23no—
315C4—21no—
316C4—23no—
317C4—476no—
318C4—472no—
319C4—941no—
320C4—943no—
321C4—943no—
322C4—941no—
323C4—943no—
324C4C2×Q8×D4716yes—
325C2—942no—
326C2C22×Q8×D4711yescharacteristic
327C22−1+4×D4711yescharacteristic
328C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#557C2
hypercenter#557D47
hypocenterC47#3502
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
2. #15689853C2semidirect
3. #15689851C2semidirect
4. #15689850C2semidirect
5. #15689850C2semidirect
6. #15689849C2semidirect
7. #15689849C2semidirect
15. C47×#557C2semidirect
68. Q8×D47Q8semidirect
172. #557D47semidirect
180. C47#3502semidirect