Finite Group Databasebeta

← #20253175

Subgroups — #20253175

Order 6016.

388 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#15689679C211yesmaximal, characteristic, complemented
2C4×#10625354C211yesmaximal, characteristic
3#15689430C211yesmaximal, characteristic, complemented
4#15689424C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689416C211yesmaximal, characteristic, complemented
7#15689412C211yesmaximal, characteristic, complemented
8#15689406C211yesmaximal, characteristic, complemented
9#15689402C211yesmaximal, characteristic, complemented
10#15689160C211yesmaximal, characteristic, complemented
11#15689158C211yesmaximal, characteristic, complemented
12C4⋊C8×D47C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic
14#15689118C211yesmaximal, characteristic
15C47×#479C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×C8×D47C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094002—21no—
23#13094002—21no—
24Q8×Dic47C2211yescharacteristic
25#13093989—21no—
26#13093989—21no—
27C4×D188—21no—
28C4×D188C2211yescharacteristic
29#13093986—21no—
30#13093986C2211yescharacteristic
31#13093982—21no—
32#13093982C2211yescharacteristic
33#13093982C2211yescharacteristic
34#13093982C2211yescharacteristic
35C42×D47—21no—
36C42×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60#10625354—22no—
61#10625354Q814yescomplemented
62C2×D188—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47D411yescharacteristic
68C2×C4×D47D411yescharacteristic
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×Dic94—21no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C42×C47—21no—
81C42×C47C2311yescharacteristic
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47D411yescharacteristic
100C4×Dic47D411yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C8×D47—22no—
105C8×D47—22no—
106C22×D47—21no—
107C22×D47C2×D411yescharacteristic
108Q8×C47—21no—
109Q8×C47C2×Q812yes—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123D188—24no—
124D188—21no—
125D188C2×Q812yes—
126C4×D47—24no—
127C4×D47—22no—
128C4×D47—41no—
129C4×D47—42no—
130C4×D47—42no—
131C4×D47C2×Q812yes—
132C4×D47#4112yes—
133Dic94—42no—
134Dic94—42no—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C22×C47C22×D411yescharacteristic
140C2×D47—21no—
141C2×D47—21no—
142C2×D47—22no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47C22⋊Q812yes—
146C4×C47—22no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C22×Q811yescharacteristic
153C4×C47C2×#4111yescharacteristic
154Dic47—21no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47C22⋊Q812yes—
159Dic47#13512yes—
160#3076—471nomaximal, Sylow
161C2×C47C2×C22⋊Q811yescharacteristic
162C2×C47C2×#13511yescharacteristic
163C2×C47#57511yescharacteristic
164D47—22no—
165D47—42no—
166#533—471no—
167C4×#41—471no—
168#479—471no—
169#479D4711yescharacteristic, complemented
170#478—471no—
171#478—471no—
172#477—471no—
173#476—471no—
174#475—471no—
175#474—471no—
176#427—471no—
177#427—471no—
178C2×C4⋊C8—471no—
179#416—471no—
180#416—471no—
181C47#307611yescharacteristic, complemented, Sylow
182C2×#41—471no—
183C22×C8—471no—
184C22×C8—471no—
185C4⋊Q8—471no—
186C4⋊Q8—471no—
187#125—471no—
188#125C2×D4711yescharacteristic
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C4×Q8—471no—
192C4×Q8—941no—
193C4×Q8—941no—
194C4×Q8C2×D4711yescharacteristic
195C4×D4—471no—
196C4×D4—471no—
197C4×D4—941no—
198C4×D4—941no—
199#117—471no—
200#117—471no—
201#117—471no—
202#117—941no—
203C2×C42—471no—
204C2×C42—941no—
205#107—471no—
206#107—471no—
207#107—471no—
208#107C2×D4711yescharacteristic
209#106—471no—
210#106—471no—
211#106—471no—
212#106C2×D4711yescharacteristic
213C4⋊C8—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8C2×D4711yescharacteristic
217#103—471no—
218#103—471no—
219#103C2×D4711yescharacteristic
220#103C2×D4711yescharacteristic
221#102—471no—
222#102—471no—
223#102—471no—
224#102—471no—
225#41—474no—
226#41—942no—
227C2×Q8—941no—
228C2×Q8—941no—
229C2×Q8C22×D4711yescharacteristic
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C2×C8—471no—
239C2×C8—471no—
240C2×C8—942no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
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⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C42—21no—
264C42—471no—
265C42—471no—
266C42—471no—
267C42—941no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42C22×D4711yescharacteristic
272C23—471no—
273C23—941no—
274Q8—21no—
275Q8—1882no—
276Q8—1882no—
277Q8Q8×D4712yes—
278D4—472no—
279D4—944no—
280D4—941no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—472no—
288C2×C4—472no—
289C2×C4—471no—
290C2×C4—942no—
291C2×C4—944no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—1881no—
296C2×C4—1882no—
297C2×C4—1882no—
298C2×C4D4×D4711yescharacteristic
299C2×C4D4×D4711yescharacteristic
300C2×C4C23×D4711yescharacteristic
301C8—21no—
302C8—21no—
303C8—941no—
304C8—941no—
305C22—472no—
306C22—941no—
307C22—941no—
308C22—942no—
309C22—1881no—
310C22—1881no—
311C22C2×D4×D4711yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—472no—
319C4—472no—
320C4—941no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4C2×Q8×D4711yescharacteristic
325C4#41×D4711yescharacteristic
326C2—942no—
327C2—1882no—
328C2C22⋊Q8×D4711yescharacteristic
329C2#135×D4711yescharacteristic
330C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3076
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #15689679C2semidirect
3. #15689430C2semidirect
4. #15689424C2semidirect
5. #15689420C2semidirect
6. #15689416C2semidirect
7. #15689412C2semidirect
8. #15689406C2semidirect
9. #15689402C2semidirect
10. #15689160C2semidirect
11. #15689158C2semidirect
12. C4⋊C8×D47C2semidirect
15. C47×#479C2semidirect
61. #10625354Q8semidirect
169. #479D47semidirect
181. C47#3076semidirect