Finite Group Databasebeta

← #20253247

Subgroups — #20253247

Order 6016.

376 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#15689750C211yesmaximal, characteristic, complemented
2#15689605C211yesmaximal, characteristic
3#15689432C211yesmaximal, characteristic, complemented
4#15689430C211yesmaximal, characteristic, complemented
5#15689424C211yesmaximal, characteristic, complemented
6#15689422C211yesmaximal, characteristic, complemented
7#15689412C211yesmaximal, characteristic, complemented
8#15689410C211yesmaximal, characteristic, complemented
9#15689406C211yesmaximal, characteristic, complemented
10#15689162C211yesmaximal, characteristic, complemented
11#106×D47C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic
14#15689118C211yesmaximal, characteristic
15C47×#475C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094022—21no—
21#13094016C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094002—21no—
25#13094000—21no—
26Q8×Dic47C2211yescharacteristic
27C4×D188—21no—
28C4×D188C2211yescharacteristic
29#13093986—21no—
30#13093986C2211yescharacteristic
31#13093982C2211yescharacteristic
32#13093981—21no—
33#13093981C2211yescharacteristic
34C4⋊C4×D47—21no—
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61#10625354—22no—
62#10625354Q814yescomplemented
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C42×C47—21no—
80C42×C47C2311yescharacteristic
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4D411yescharacteristic
85(C2×D47)⋊C4D411yescharacteristic
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C8×D47—22no—
106C22×D47—21no—
107C22×D47C2×D411yescharacteristic
108Q8×C47—21no—
109Q8×C47—81no—
110Q8×C47C2×Q812yes—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—24no—
125D188—21no—
126D188C2×Q812yes—
127C4×D47—24no—
128C4×D47—81no—
129C4×D47—81no—
130C4×D47—81no—
131C4×D47—81no—
132C4×D47C2×Q812yes—
133C4×D47#4112yes—
134Dic94—81no—
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—21no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47C22⋊Q812yes—
160#3084—471nomaximal, Sylow
161C2×C47C2×C22⋊Q811yescharacteristic
162C2×C47#57711yescharacteristic
163C2×C47#57711yescharacteristic
164D47—22no—
165D47—42no—
166#544—471no—
167#520—471no—
168#479—471no—
169#479—471no—
170#478—471no—
171#478—471no—
172#476—471no—
173#476—471no—
174#475—471no—
175#475D4711yescharacteristic, complemented
176#428—471no—
177C2×#106—471no—
178#424—471no—
179#417—471no—
180#416—471no—
181C47#308411yescharacteristic, complemented, Sylow
182C2×#41—471no—
183C2×M16—471no—
184C22×C8—471no—
185C4⋊Q8—471no—
186C4⋊Q8—941no—
187C4⋊Q8C2×D4711yescharacteristic
188#125—471no—
189#125—471no—
190#125—941no—
191C22⋊Q8—941no—
192C22⋊Q8—941no—
193C4×Q8—471no—
194C4×Q8C2×D4711yescharacteristic
195C4×D4—471no—
196C4×D4—471no—
197C4×D4—941no—
198C4×D4—941no—
199#117—471no—
200#117—471no—
201#117—941no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—941no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211#106C2×D4711yescharacteristic
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—21no—
228C2×Q8—941no—
229C2×Q8C22×D4711yescharacteristic
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
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⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C22⋊C4—471no—
263C22⋊C4—471no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C42—21no—
268C42—471no—
269C42—941no—
270C42—941no—
271C42C22×D4711yescharacteristic
272C23—471no—
273C23—941no—
274Q8—21no—
275Q8—81no—
276Q8—3761no—
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—472no—
287C2×C4—472no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—944no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4—3761no—
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—941no—
320C4—941no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4C2×Q8×D4711yescharacteristic
325C4#41×D4711yescharacteristic
326C2—942no—
327C2—1882no—
328C2C22⋊Q8×D4711yescharacteristic
329C2#1568992911yescharacteristic
330C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3084
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689432C2semidirect
4. #15689430C2semidirect
5. #15689424C2semidirect
6. #15689422C2semidirect
7. #15689412C2semidirect
8. #15689410C2semidirect
9. #15689406C2semidirect
10. #15689162C2semidirect
11. #106×D47C2semidirect
12. #15689148C2semidirect
15. C47×#475C2semidirect
62. #10625354Q8semidirect
175. #475D47semidirect
181. C47#3084semidirect