Finite Group Databasebeta

← #20256290

Subgroups — #20256290

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#15689829C211yesmaximal, characteristic, complemented
2D4×Dic94C211yesmaximal, characteristic, complemented
3#15689533C211yesmaximal, characteristic, complemented
4#15689531C211yesmaximal, characteristic, complemented
5#15689520C211yesmaximal, characteristic, complemented
6#15689425C211yesmaximal, characteristic, complemented
7#15689414C211yesmaximal, characteristic, complemented
8#15689412C211yesmaximal, characteristic, complemented
9#15689411C211yesmaximal, characteristic, complemented
10#15689402C211yesmaximal, characteristic, complemented
11#15689252C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic
13#15689232C211yesmaximal, characteristic
14#15689203C211yesmaximal, characteristic
15C47×#478C211yesmaximal, characteristic, complemented
16C22×Dic94—21no—
17C2×#10625334C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094004—21no—
24#13094003—21no—
25#13094002—21no—
26#13094002—21no—
27#13094001—21no—
28#13094001—21no—
29C4×Dic94C2211yescharacteristic
30C4×D188C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35C4⋊C4×D47—21no—
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94—44no—
72C2×Dic94D411yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84#10625334Q814yescomplemented
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47D411yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
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—
105C22×D47—21no—
106D4×C47—21no—
107D4×C47C2×Q812yes—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—42no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—42no—
119C2×Dic47—42no—
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188C2×Q812yescomplemented
126C4×D47—42no—
127C4×D47—81no—
128C4×D47—81no—
129Dic94—22no—
130Dic94—42no—
131Dic94—42no—
132Dic94—42no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47—21no—
136C47⋊C8—21no—
137C47⋊C8C2×Q812yescomplemented
138C22×C47—22no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47C22×D411yescharacteristic
142C2×D47—22no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47C22×Q811yescharacteristic
151C4×C472−1+411yescharacteristic
152Dic47—21no—
153Dic47—21no—
154Dic47—21no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47AGL(1,ℤ/8)12yes—
159#3384—471nomaximal, Sylow
160C2×C47—42no—
161C2×C47D4×Q811yescharacteristic
162C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C47#57711yescharacteristic
164D47—42no—
165#554—471no—
166D4×Q8—471no—
167#501—471no—
168#501—471no—
169#498—471no—
170#478—471no—
171#478D4711yescharacteristic, complemented
172#476—471no—
173#476—471no—
174#476—471no—
175#474—471no—
176#446—471no—
177#442—471no—
178#442—471no—
179C4×D8—471no—
180C47#338411yescharacteristic, complemented, Sylow
181C22×Q8—941no—
182C2×D8—471no—
183C4⋊Q8—471no—
184C4⋊Q8—471no—
185C4⋊Q8—471no—
186C4⋊Q8—471no—
187#125—471no—
188#125C2×D4711yescharacteristic
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×D4—471no—
201C4×D4C2×D4711yescharacteristic
202C2×C4⋊C4—941no—
203#107—471no—
204#107—471no—
205#107C2×D4711yescharacteristic
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⋊C8C2×D4711yescharacteristic
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102C2×D4711yescharacteristic
220#102C2×D4711yescharacteristic
221#97—471no—
222#97—471no—
223C4×C8—471no—
224C2×Q8—471no—
225C2×Q8—941no—
226C2×Q8—941no—
227C2×Q8—941no—
228C2×Q8—941no—
229C2×Q8—1884no—
230C2×D4—471no—
231C2×D4C22×D4711yescharacteristic
232C22×C4—21no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238D8—474no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8C22×D4711yescharacteristic
242C2×C8C22×D4711yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4C22×D4711yescharacteristic
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C42—471no—
267C42—471no—
268C42C22×D4711yescharacteristic
269C23—21no—
270C23—941no—
271Q8—942no—
272Q8—3761no—
273Q8—1882no—
274Q8—1882no—
275Q8—1882no—
276D4—21no—
277D4—472no—
278D4—941no—
279D4Q8×D4712yes—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—471no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—3761no—
292C2×C4—3761no—
293C2×C4—1882no—
294C2×C4—1882no—
295C2×C4—1882no—
296C2×C4D4×D4711yescharacteristic
297C2×C4D4×D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—21no—
301C8—472no—
302C8—941no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—942no—
307C22—1881no—
308C22—1881no—
309C22C2×D4×D4711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—472no—
316C4—941no—
317C4—941no—
318C4—941no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4C2×Q8×D4711yescharacteristic
323C4#1309407111yescharacteristic
324C2—42no—
325C2—1882no—
326C2#1568978611yescharacteristic
327C2AGL(1,ℤ/8)×D4711yescharacteristic
328C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3384
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689829C2semidirect
2. D4×Dic94C2semidirect
3. #15689533C2semidirect
4. #15689531C2semidirect
5. #15689520C2semidirect
6. #15689425C2semidirect
7. #15689414C2semidirect
8. #15689412C2semidirect
9. #15689411C2semidirect
10. #15689402C2semidirect
11. #15689252C2semidirect
15. C47×#478C2semidirect
84. #10625334Q8semidirect
125. D188C2×Q8semidirect
137. C47⋊C8C2×Q8semidirect
171. #478D47semidirect
180. C47#3384semidirect