Finite Group Databasebeta

← #20256129

Subgroups — #20256129

Order 6016.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic94C211yesmaximal, characteristic, complemented
2#15689845C211yesmaximal, characteristic
3#15689484C211yesmaximal, characteristic
4#15689483C211yesmaximal, characteristic
5#15689472C211yesmaximal, characteristic, complemented
6#15689412C211yesmaximal, characteristic
7#15689408C211yesmaximal, characteristic, complemented
8#15689407C211yesmaximal, characteristic, complemented
9#15689347C211yesmaximal, characteristic
10#15689345C211yesmaximal, characteristic
11#15689331C211yesmaximal, characteristic, complemented
12#15689251C211yesmaximal, characteristic, complemented
13#15689227C211yesmaximal, characteristic, complemented
14#15689208C211yesmaximal, characteristic
15C47×#441C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18#13094024—21no—
19#13094024C2211yescharacteristic
20#13094023—21no—
21#13094023—21no—
22#13094023C2211yescharacteristic
23#13094023C2211yescharacteristic
24#13094022C2211yescharacteristic
25#13094019—21no—
26#13094018—21no—
27#13094013C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094002—21no—
30Q8×Dic47C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32C4×Dic94—21no—
33C4×Dic94C2211yescharacteristic
34#13093989C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093981—21no—
37#13093955C2211yescharacteristic
38#13093955C2211yescharacteristic
39C4⋊(C47⋊C8)C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×Dic94—21no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×Dic94D411yescharacteristic
67C2×Dic94C2311yescharacteristic
68Q16×C47—22no—
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C42×C47—21no—
76C42×C47—21no—
77C42×C47C2311yescharacteristic
78#10625337—22no—
79#10625336—22no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C22×D47—21no—
106Q8×C47—21no—
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47#4112yes—
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
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188—21no—
126C4×D47—42no—
127Dic94—22no—
128Dic94—21no—
129Dic94—21no—
130Dic94—81no—
131Dic94—81no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C22×C47C22×D411yescharacteristic
138C2×D47—41no—
139C2×D47—41no—
140C2×D47—41no—
141C4×C47—22no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47C2×#4111yescharacteristic
148C4×C472−1+411yescharacteristic
149Dic47—21no—
150Dic47—21no—
151Dic47—21no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47#13712yes—
156#3369—471nomaximal, Sylow
157C2×C47#54811yescharacteristic
158C2×C47C2×#13711yescharacteristic
159C2×C47#57711yescharacteristic
160D47—81no—
161Q82—471no—
162#556—471no—
163#489—471no—
164#489—471no—
165#487—471no—
166#476—471no—
167#475—471no—
168#475—471no—
169#464—471no—
170#464—471no—
171#462—471no—
172#446—471no—
173#441—471no—
174#441D4711yescharacteristic, complemented
175C4×SD16—471no—
176C47#336911yescharacteristic, complemented, Sylow
177C2×Q16—471no—
178C2×Q16C2×D4711yescharacteristic
179C2×SD16—471no—
180C4⋊Q8—471no—
181C4⋊Q8—471no—
182C4⋊Q8—471no—
183C4⋊Q8—471no—
184C4⋊Q8—941no—
185C4⋊Q8—941no—
186C4⋊Q8—941no—
187#126—941no—
188#126—941no—
189#124—471no—
190#124—471no—
191C22⋊Q8—941no—
192C4×Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—471no—
196C4×Q8—941no—
197C4×Q8C2×D4711yescharacteristic
198C4×Q8C2×D4711yescharacteristic
199C4×D4—471no—
200#117—941no—
201#106—471no—
202#106—471no—
203#106C2×D4711yescharacteristic
204C4⋊C8—471no—
205C4⋊C8—471no—
206C4⋊C8—471no—
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#103—471no—
212#103C2×D4711yescharacteristic
213#103C2×D4711yescharacteristic
214#102—471no—
215#102—471no—
216#102—471no—
217#97—471no—
218#97C2×D4711yescharacteristic
219C4×C8—471no—
220C2×Q8—471no—
221C2×Q8—471no—
222C2×Q8—941no—
223C2×Q8—941no—
224C2×Q8—941no—
225C2×Q8C22×D4711yescharacteristic
226C2×Q8C22×D4711yescharacteristic
227C2×D4—471no—
228C22×C4—941no—
229Q16—22no—
230Q16—942no—
231SD16—942no—
232C2×C8—471no—
233C2×C8—471no—
234C2×C8C22×D4711yescharacteristic
235C2×C8C22×D4711yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4C22×D4711yescharacteristic
252C4⋊C4C22×D4711yescharacteristic
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C42—21no—
259C42—21no—
260C42—471no—
261C42—471no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42C22×D4711yescharacteristic
266C23—941no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—942no—
271Q8—941no—
272Q8—941no—
273Q8—3761no—
274Q8—3761no—
275Q8—3761no—
276Q8#1062535012yes—
277D4—941no—
278D4—941no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—471no—
284C2×C4—471no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—1882no—
291C2×C4D4×D4711yescharacteristic
292C2×C4D4×D4711yescharacteristic
293C2×C4C23×D4711yescharacteristic
294C8—21no—
295C8—21no—
296C8—941no—
297C8—941no—
298C22—1881no—
299C22—1881no—
300C22—1881no—
301C22C2×D4×D4711yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—472no—
309C4—941no—
310C4—941no—
311C4—941no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4C2×#1062535011yescharacteristic
316C4#1309407111yescharacteristic
317C2—3761no—
318C2#1568978211yescharacteristic
319C2#137×D4711yescharacteristic
320C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3369
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
5. #15689472C2semidirect
7. #15689408C2semidirect
8. #15689407C2semidirect
11. #15689331C2semidirect
12. #15689251C2semidirect
13. #15689227C2semidirect
15. C47×#441C2semidirect
174. #441D47semidirect
176. C47#3369semidirect