Finite Group Databasebeta

← #20255054

Subgroups — #20255054

Order 6016.

482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094054C212yesmaximal, complemented
2D4×Dic94C211yesmaximal, characteristic, complemented
3#15689495C211yesmaximal, characteristic, complemented
4#15689367C212yesmaximal, complemented
5#15689333C211yesmaximal, characteristic, complemented
6#15689320C211yesmaximal, characteristic, complemented
7#15689285C212yesmaximal, complemented
8#15689261C212yesmaximal, complemented
9C4×#10625337C211yesmaximal, characteristic, complemented
10#15689201C211yesmaximal, characteristic, complemented
11C47×#550C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13#13094054—28no—
14C2×#10625337C2212yes—
15C2×#10625337C2211yescharacteristic
16C2×#10625335C2212yes—
17C2×#10625335C2212yes—
18C2×#10625335C2212yes—
19C2×#10625329C2212yes—
20#13094024C2211yescharacteristic
21#13094023—21no—
22#13094003C2212yes—
23#13094001—22no—
24C4×Dic94C2211yescharacteristic
25D4×Dic47—21no—
26#13093957C2211yescharacteristic
27C4⋊(C47⋊C8)C2211yescharacteristic
28#13093948C2211yescharacteristic
29#13093947C2211yescharacteristic
30#13093947C2212yes—
31#13093945C2212yes—
32C22⋊(C47⋊C8)C2212yes—
33C4×C47⋊C8C2211yescharacteristic
34C2×#41×C47C2212yes—
35#127×C47—21no—
36#127×C47C2211yescharacteristic
37#121×C47—22no—
38#121×C47C2212yes—
39C4×Q8×C47C2211yescharacteristic
40C4×D4×C47—21no—
41C4×D4×C47C2211yescharacteristic
42#41×C47—24no—
43#41×C47—42no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47—22no—
46C2×D4×C47—22no—
47C2×D4×C47—21no—
48C2×D4×C47—21no—
49C2×D4×C47D411yescharacteristic
50C2×D4×C47C2312yes—
51C22×C4×C47—22no—
52C22×C4×C47C2312yes—
53C22×Dic47—22no—
54C2×Dic94—24no—
55C2×Dic94—22no—
56C2×Dic94—42no—
57C2×Dic94C2312yes—
58C2×Dic94C2311yescharacteristic
59C4⋊C4×C47—21no—
60C4⋊C4×C47D411yescharacteristic
61C4⋊C4×C47C2311yescharacteristic
62C22⋊C4×C47—22no—
63C22⋊C4×C47D412yes—
64C42×C47—21no—
65C42×C47C2311yescharacteristic
66C22⋊Dic47—22no—
67#10625337—24no—
68#10625337D414yescomplemented
69#10625335—24no—
70#10625335—24no—
71#10625335—42no—
72C4⋊Dic47—21no—
73C4⋊Dic47—21no—
74C4⋊Dic47C2311yescharacteristic
75Dic47⋊C4—21no—
76Dic47⋊C4—22no—
77C4×Dic47—21no—
78#10625329—24no—
79C2×C47⋊C8C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81C2×C47⋊C8C2311yescharacteristic
82C23×C47—22no—
83C23×C47C2×D412yes—
84Q8×C47—21no—
85Q8×C47C2×D412yes—
86D4×C47—22no—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—44no—
90D4×C47—42no—
91D4×C47—81no—
92D4×C47—82no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—44no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2411yescharacteristic
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—44no—
106Dic94—21no—
107Dic94—22no—
108Dic94—22no—
109Dic94—44no—
110Dic94C2×D412yes—
111C47⋊C8—22no—
112C47⋊C8—21no—
113C47⋊C8C2×D412yes—
114C22×C47—22no—
115C22×C47—22no—
116C22×C47—22no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47—42no—
120C22×C47C22×D411yescharacteristic
121C4×C47—22no—
122C4×C47—22no—
123C4×C47—21no—
124C4×C47—41no—
125C4×C47#13712yescomplemented
126C4×C47C22×D411yescharacteristic
127C4×C47H(5,𝔽2)11yescharacteristic
128Dic47—22no—
129Dic47—42no—
130Dic47—41no—
131#3278—471nomaximal, Sylow
132C2×C47—42no—
133C2×C47—82no—
134C2×C47D4211yescharacteristic
135C2×C47C2×#13711yescharacteristic
136C2×C47#57711yescharacteristic
137C2×#137—472no—
138#550D4711yescharacteristic
139D4×Q8—471no—
140#492—471no—
141#468—472no—
142#462—471no—
143#460—471no—
144#452—472no—
145#448—472no—
146C4×Q16—471no—
147#436—471no—
148C47#327811yescharacteristic, complemented, Sylow
149C2×#41C2×D4712yes—
150C22×Q8—472no—
151#137—948no—
152C2×Q16—471no—
153C2×Q16—472no—
154C2×SD16—472no—
155C2×SD16—472no—
156C2×SD16—472no—
157C2×M16—472no—
158C4⋊Q8—471no—
159C4⋊Q8—941no—
160#127—21no—
161#127C2×D4711yescharacteristic
162C22⋊Q8—472no—
163C22⋊Q8—942no—
164#121—22no—
165#121C2×D4712yes—
166C4×Q8—471no—
167C4×Q8C2×D4711yescharacteristic
168C4×D4—21no—
169C4×D4—941no—
170C4×D4C2×D4711yescharacteristic
171#107—471no—
172C4⋊C8—471no—
173#103—471no—
174#103—471no—
175#103—472no—
176#102—472no—
177C22⋊C8—472no—
178C4×C8—471no—
179#41—24no—
180#41—42no—
181C2×Q8—471no—
182C2×Q8—472no—
183C2×Q8—944no—
184C2×Q8—942no—
185C2×Q8—1882no—
186C2×Q8C22×D4711yescharacteristic
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4C22⋊D4711yescharacteristic
192C2×D4C22×D4712yes—
193C22×C4—22no—
194C22×C4—942no—
195C22×C4C22×D4712yes—
196Q16—474no—
197Q16—944no—
198SD16—944no—
199SD16—944no—
200SD16—1882no—
201M16—944no—
202C2×C8—471no—
203C2×C8—471no—
204C2×C8—472no—
205C4⋊C4—21no—
206C4⋊C4—471no—
207C4⋊C4—941no—
208C4⋊C4—942no—
209C4⋊C4—941no—
210C4⋊C4—941no—
211C4⋊C4C22⋊D4711yescharacteristic
212C4⋊C4C22×D4711yescharacteristic
213C22⋊C4—22no—
214C22⋊C4—942no—
215C22⋊C4C22⋊D4712yes—
216C42—21no—
217C42—941no—
218C42C22×D4711yescharacteristic
219C23—22no—
220C23C2×C22⋊D4712yes—
221Q8—21no—
222Q8—472no—
223Q8—941no—
224Q8—942no—
225Q8—942no—
226Q8—1884no—
227Q8D4×D4712yes—
228D4—22no—
229D4—22no—
230D4—22no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—82no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—44no—
240C2×C4—941no—
241C2×C4—941no—
242C2×C4—942no—
243C2×C4—1884no—
244C2×C4C2×C22⋊D4711yescharacteristic
245C2×C4C2×C22⋊D4712yes—
246C2×C4C2×C22⋊D4711yescharacteristic
247C2×C4C23×D4711yescharacteristic
248C8—472no—
249C8—942no—
250C8—941no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—42no—
257C22C22×C22⋊D4711yescharacteristic
258C4—22no—
259C4—22no—
260C4—21no—
261C4—41no—
262C4—942no—
263C4—1882no—
264C4—1881no—
265C4#1309405412yescomplemented
266C4C2×D4×D4711yescharacteristic
267C4#1309406911yescharacteristic
268C2—42no—
269C2—82no—
270C2D4×C22⋊D4711yescharacteristic
271C2C2×#1309405411yescharacteristic
272C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#550C2
socleC22×C47C22×D4
hypercenter#550D47
hypocenterC47#3278
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. D4×Dic94C2semidirect
3. #15689495C2semidirect
4. #15689367C2semidirect
5. #15689333C2semidirect
6. #15689320C2semidirect
7. #15689285C2semidirect
8. #15689261C2semidirect
9. C4×#10625337C2semidirect
10. #15689201C2semidirect
68. #10625337D4semidirect
125. C4×C47#137semidirect
148. C47#3278semidirect
265. C4#13094054semidirect