Finite Group Databasebeta

← #20256288

Subgroups — #20256288

Order 6016.

374 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
1#15689832C211yesmaximal, characteristic, complemented
2D4×Dic94C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689530C211yesmaximal, characteristic, complemented
5#15689520C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689421C211yesmaximal, characteristic, complemented
8#15689413C211yesmaximal, characteristic, complemented
9#15689411C211yesmaximal, characteristic, complemented
10#15689411C211yesmaximal, characteristic, complemented
11#15689401C211yesmaximal, characteristic, complemented
12#15689251C211yesmaximal, characteristic, complemented
13#15689235C211yesmaximal, characteristic
14D8×Dic47C211yesmaximal, characteristic
15C47×#442C211yesmaximal, characteristic
16C22×Dic94—21no—
17#13094024C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094003—21no—
24#13094003—21no—
25#13094001—21no—
26#13094001—21no—
27#13094001—21no—
28#13094001—21no—
29C4×Dic94C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34C2×Dic47⋊C4—21no—
35#13093958C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94—44no—
72C2×Dic94D411yescharacteristic
73D8×C47Q814yescomplemented
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47D411yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47C2311yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C23×C47—21no—
105C23×C47—21no—
106D4×C47—21no—
107D4×C47—21no—
108D4×C47C2×Q812yes—
109D4×C47C2×Q812yescomplemented
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—42no—
113C2×C4×C47—81no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—42no—
122C2×Dic47—42no—
123C2×Dic47—42no—
124C2×Dic47—81no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129Dic94—22no—
130Dic94—42no—
131Dic94—42no—
132Dic94—42no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47C2×Q812yescomplemented
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47—22no—
139C22×C47—22no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47C22×D411yescharacteristic
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47C22×Q811yescharacteristic
150C4×C472−1+411yescharacteristic
151Dic47—21no—
152Dic47—21no—
153Dic47—21no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47AGL(1,ℤ/8)12yes—
159#3384—471nomaximal, Sylow
160C2×C47—42no—
161C2×C47—42no—
162C2×C47D4×Q811yescharacteristic
163C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C47#57711yescharacteristic
165#554—471no—
166D4×Q8—471no—
167#501—471no—
168#501—471no—
169#498—471no—
170#478—471no—
171#478—471no—
172#476—471no—
173#476—471no—
174#476—471no—
175#474—471no—
176#446—471no—
177#442—471no—
178#442D4711yescharacteristic
179C4×D8—471no—
180C47#338411yescharacteristic, complemented, Sylow
181C22×Q8—941no—
182C2×D8C2×D4711yescharacteristic
183C4⋊Q8—471no—
184C4⋊Q8—471no—
185C4⋊Q8—471no—
186C4⋊Q8—471no—
187#125—471no—
188#125—471no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C22⋊Q8—941no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C4×Q8—471no—
196C4×D4—471no—
197C4×D4—471no—
198C4×D4—471no—
199C4×D4—471no—
200C4×D4C2×D4711yescharacteristic
201C4×D4C2×D4711yescharacteristic
202C2×C4⋊C4—941no—
203#107—471no—
204#107—471no—
205#107—471no—
206#106—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211#106C2×D4711yescharacteristic
212C4⋊C8—471no—
213C4⋊C8—471no—
214C4⋊C8—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102C2×D4711yescharacteristic
220#102C2×D4711yescharacteristic
221#97—471no—
222#97C2×D4711yescharacteristic
223C4×C8—471no—
224C2×Q8—471no—
225C2×Q8—941no—
226C2×Q8—941no—
227C2×Q8—941no—
228C2×Q8—941no—
229C2×Q8—1884no—
230C2×D4C22×D4711yescharacteristic
231C2×D4C22×D4711yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238D8Dic9414yescomplemented
239C2×C8—471no—
240C2×C8—471no—
241C2×C8C22×D4711yescharacteristic
242C2×C8C22×D4711yescharacteristic
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C42—471no—
267C42—471no—
268C42C22×D4711yescharacteristic
269C23—21no—
270C23—21no—
271Q8—942no—
272Q8—3761no—
273Q8—1882no—
274Q8—1882no—
275Q8—1882no—
276D4—21no—
277D4—21no—
278D4C2×Dic9412yes—
279D4C2×Dic9412yescomplemented
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—471no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—3761no—
293C2×C4—1882no—
294C2×C4—1882no—
295C2×C4—1882no—
296C2×C4D4×D4711yescharacteristic
297C2×C4D4×D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—941no—
301C8—941no—
302C8C2×Dic9412yescomplemented
303C22—22no—
304C22—22no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D4711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—472no—
315C4—941no—
316C4—941no—
317C4—941no—
318C4—1881no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4C22×Dic9411yescharacteristic
323C4#1309407111yescharacteristic
324C2—42no—
325C2—42no—
326C2D4×Dic9411yescharacteristic
327C2AGL(1,ℤ/8)×D4711yescharacteristic
328C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3384
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689832C2semidirect
2. D4×Dic94C2semidirect
3. #15689532C2semidirect
4. #15689530C2semidirect
5. #15689520C2semidirect
6. #15689423C2semidirect
7. #15689421C2semidirect
8. #15689413C2semidirect
9. #15689411C2semidirect
10. #15689411C2semidirect
11. #15689401C2semidirect
12. #15689251C2semidirect
73. D8×C47Q8semidirect
109. D4×C47C2×Q8semidirect
135. C8×C47C2×Q8semidirect
180. C47#3384semidirect
238. D8Dic94semidirect
279. D4C2×Dic94semidirect
302. C8C2×Dic94semidirect