Finite Group Databasebeta

← #20252910

Subgroups — #20252910

Order 6016.

490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094057C211yesmaximal, characteristic, complemented
2C22×#10625325C211yesmaximal, characteristic, complemented
3#15689692C211yesmaximal, characteristic
4#15689600C211yesmaximal, characteristic, complemented
5#15689346C214yesmaximal, complemented
6#15689324C214yesmaximal, complemented
7#15689129C211yesmaximal, characteristic, complemented
8#15689120C211yesmaximal, characteristic, complemented
9C47×#424C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12C22×D188C2211yescharacteristic
13#13094057—24no—
14C2×Dic188C2212yescomplemented
15C2×#10625325—24no—
16C2×#10625325C2214yes—
17C2×#10625325C2212yescomplemented
18#13094021C2212yes—
19#13094012C2212yes—
20#13093999—22no—
21#13093994—22no—
22C4×Dic94C2214yescomplemented
23#13093989—22no—
24#13093983C2211yescharacteristic
25#13093980—22no—
26#13093949C2212yescomplemented
27#13093946C2214yes—
28#13093946C2212yescomplemented
29C2×M16×C47C2211yescharacteristic
30C22×C8×C47C2211yescharacteristic
31#117×C47C2211yescharacteristic
32C4⋊C8×C47C2214yescomplemented
33C23×D47—21no—
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—21no—
36C22×Dic47—21no—
37#10625350—22no—
38#10625350—22no—
39C2×D188—22no—
40C2×D188—22no—
41C2×D188—21no—
42C2×D188—24no—
43C2×D188C2312yes—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94—21no—
47C2×Dic94—22no—
48C2×Dic94D414yescomplemented
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2312yes—
51M16×C47—22no—
52C2×C8×C47—22no—
53C2×C8×C47C2312yes—
54C2×C8×C47C2312yes—
55C4⋊C4×C47D412yes—
56C22⋊C4×C47D412yes—
57C42×C47C2312yes—
58C22⋊Dic47—21no—
59(C2×D47)⋊C4—24no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—24no—
62C4×Dic47—24no—
63C4×Dic47—21no—
64Dic188—24no—
65#10625325—28no—
66#10625325—24no—
67C23×C47C2×D411yescharacteristic
68C22×D47—22no—
69C22×D47—21no—
70C22×D47—42no—
71C22×D47—82no—
72C2×C4×C47C2×D414yes—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D412yes—
75C2×C4×C47#4112yes—
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—42no—
78C2×Dic47—24no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82D188—22no—
83D188—21no—
84D188—22no—
85D188—21no—
86D188—42no—
87D188—84no—
88C4×D47—42no—
89Dic94—24no—
90Dic94—22no—
91Dic94—21no—
92Dic94—21no—
93Dic94C2×D414yes—
94C8×C47—22no—
95C8×C47—22no—
96C22×C47—22no—
97C22×C47#12112yes—
98C22×C47C22×D411yescharacteristic
99C2×D47—41no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—44no—
103C2×D47—84no—
104C4×C47—24no—
105C4×C47#12112yes—
106C4×C47C22×D411yescharacteristic
107C4×C47C2×#4111yescharacteristic
108Dic47—24no—
109Dic47—41no—
110Dic47—42no—
111#3043—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47C2×#12111yescharacteristic
114C2×C47#57712yes—
115D47—81no—
116D47—82no—
117C2×#137—471no—
118C22×SD16—471no—
119#535—471no—
120#519—471no—
121#464—474no—
122#460—474no—
123#424D4711yescharacteristic, complemented
124#418—471no—
125#416—471no—
126C47#304311yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C22×Q8—471no—
129C22×D4—471no—
130#137—944no—
131C2×Q16—472no—
132C2×SD16—474no—
133C2×SD16—472no—
134C2×SD16—944no—
135C2×M16C2×D4711yescharacteristic
136C22×C8C2×D4711yescharacteristic
137#127—472no—
138#124—472no—
139#121—942no—
140#120—942no—
141C4×Q8—474no—
142C4×Q8—942no—
143#117—471no—
144#117—942no—
145#117C2×D4711yescharacteristic
146C4⋊C8C2×D4714yescomplemented
147#103—472no—
148#102—474no—
149#102—472no—
150C24—941no—
151#41—942no—
152#41—942no—
153C2×Q8—474no—
154C2×Q8—472no—
155C2×Q8—471no—
156C2×Q8—941no—
157C2×Q8—942no—
158C2×D4—472no—
159C2×D4—471no—
160C2×D4—941no—
161C2×D4—944no—
162C2×D4—941no—
163C2×D4—942no—
164C2×D4—942no—
165C22×C4—941no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168Q16—944no—
169SD16—948no—
170SD16—944no—
171M16—22no—
172C2×C8—22no—
173C2×C8C22×D4712yes—
174C2×C8C22×D4712yes—
175C4⋊C4—472no—
176C4⋊C4—944no—
177C4⋊C4D18812yes—
178C22⋊C4—941no—
179C22⋊C4—944no—
180C22⋊C4D18812yes—
181C42—941no—
182C42—944no—
183C42C22×D4712yes—
184C23—942no—
185C23—941no—
186C23—3762no—
187C23—1882no—
188C23C2×D18811yescharacteristic
189Q8—474no—
190Q8—944no—
191Q8—942no—
192Q8—941no—
193Q8—941no—
194D4—942no—
195D4—941no—
196D4—942no—
197D4—941no—
198D4—3764no—
199D4—1882no—
200D4—1882no—
201C2×C4—944no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4C2×D18814yes—
207C2×C4C2×D18811yescharacteristic
208C2×C4D4×D4712yes—
209C2×C4#1062535412yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—22no—
213C22—22no—
214C22—3764no—
215C22—1881no—
216C22—1882no—
217C22—1882no—
218C22—1884no—
219C22#1309399912yes—
220C22C22×D18811yescharacteristic
221C4—24no—
222C4—944no—
223C4—1881no—
224C4—1882no—
225C4#1309399912yes—
226C4C2×D4×D4711yescharacteristic
227C4C2×#1062535411yescharacteristic
228C2—22no—
229C2—3762no—
230C2—3761no—
231C2C2×#1309399911yescharacteristic
232C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#424C2
socleC22×C47C22×D4
hypercenter#424D47
hypocenterC47#3043
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C22×#10625325C2semidirect
4. #15689600C2semidirect
5. #15689346C2semidirect
6. #15689324C2semidirect
7. #15689129C2semidirect
8. #15689120C2semidirect
9. C47×#424C2semidirect
14. C2×Dic188C22semidirect
17. C2×#10625325C22semidirect
22. C4×Dic94C22semidirect
26. #13093949C22semidirect
28. #13093946C22semidirect
32. C4⋊C8×C47C22semidirect
48. C2×Dic94D4semidirect
123. #424D47semidirect
126. C47#3043semidirect
146. C4⋊C8C2×D47semidirect