Finite Group Databasebeta

← #20253488

Subgroups — #20253488

Order 6016.

444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#15689680C211yesmaximal, characteristic, complemented
2C2×C4×D188C211yesmaximal, characteristic
3#15689459C212yesmaximal, complemented
4#15689404C212yesmaximal, complemented
5#15689329C212yesmaximal, complemented
6#15689276C212yesmaximal
7#15689225C214yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C4×D47—21no—
11C2×#10625325C2214yes—
12#13094024C2211yescharacteristic, complemented
13#13094024C2211yescharacteristic, complemented
14#13094016—21no—
15#13094003—21no—
16#13094003C2212yes—
17C4×Dic94—21no—
18C4×Dic94C2212yescomplemented
19C4×D188—21no—
20C4×D188—21no—
21C4×D188C2212yes—
22C4×D188C2212yes—
23#13093983—21no—
24C2×C4⋊Dic47C2211yescharacteristic
25C2×(C2×D47)⋊C4—21no—
26#13093958C2214yescomplemented
27#13093949C2214yescomplemented
28#13093946C2214yes—
29C2×C42×C47C2211yescharacteristic
30C4⋊C8×C47C2212yescomplemented
31C22⋊C8×C47C2212yes—
32#97×C47C2212yescomplemented
33C23×D47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C2×D188—21no—
39C2×D188—24no—
40C2×D188C2312yes—
41C2×C4×D47—22no—
42C2×C4×D47—22no—
43C2×C4×D47—44no—
44C2×Dic94—21no—
45C2×Dic94C2312yes—
46C2×C8×C47C2314yes—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2311yescharacteristic
50C42×C47C2311yescharacteristic
51C22⋊Dic47—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47C2312yes—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63#10625325—28no—
64C23×C47C2×D411yescharacteristic
65C22×D47—24no—
66C22×D47—22no—
67C22×D47—42no—
68C22×D47—42no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—42no—
82D188—24no—
83D188—22no—
84D188#4114yes—
85C4×D47—44no—
86C4×D47—44no—
87Dic94—24no—
88Dic94—42no—
89C8×C47—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#13712yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—24no—
95C2×D47—48no—
96C2×D47—42no—
97C2×D47—42no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47AGL(1,ℤ/8)12yes—
103C4×C47C2×#4112yes—
104Dic47—42no—
105Dic47—42no—
106Dic47—42no—
107#3110—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47#52511yescharacteristic
110C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—44no—
113#533—471no—
114C2×C4×D4—471no—
115#484—472no—
116#474—472no—
117#461—472no—
118#450—472no—
119#440—474no—
120#432D4711yescharacteristic, complemented
121C47#311011yescharacteristic, complemented, Sylow
122C22×D4—471no—
123C23×C4—941no—
124C2×SD16—474no—
125C4⋊Q8—471no—
126C4⋊Q8—471no—
127#125—941no—
128C22⋊Q8—472no—
129C22⋊Q8—941no—
130C4×Q8—472no—
131C4×Q8—941no—
132C4×D4—472no—
133C4×D4—472no—
134C4×D4—941no—
135C4×D4—941no—
136#117—941no—
137C2×C4⋊C4—471no—
138C2×C22⋊C4—941no—
139C2×C42C2×D4711yescharacteristic
140#107—474no—
141C4⋊C8C2×D4712yescomplemented
142#103—474no—
143#102—474no—
144C22⋊C8C2×D4712yes—
145#97C2×D4712yescomplemented
146C24—941no—
147C2×Q8—472no—
148C2×Q8—941no—
149C2×D4—472no—
150C2×D4—944no—
151C2×D4—941no—
152C22×C4—941no—
153C22×C4—942no—
154C22×C4—942no—
155C22×C4—1884no—
156C22×C4D18811yescharacteristic
157C22×C4D18811yescharacteristic
158C22×C4C22×D4711yescharacteristic
159SD16—948no—
160C2×C8C22×D4714yes—
161C4⋊C4—472no—
162C4⋊C4—472no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C42—942no—
173C42D18811yescharacteristic
174C42D18811yescharacteristic
175C42C22×D4711yescharacteristic
176C42C22×D4711yescharacteristic
177C23—944no—
178C23—942no—
179C23—1882no—
180C23—1882no—
181C23C2×D18811yescharacteristic
182Q8—944no—
183Q8—1882no—
184D4—474no—
185D4—944no—
186D4—942no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—1884no—
194C2×C4—1882no—
195C2×C4—1884no—
196C2×C4C2×D18811yescharacteristic
197C2×C4C2×D18811yescharacteristic
198C2×C4C2×D18811yescharacteristic
199C2×C4C2×D18811yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—944no—
206C22—1888no—
207C22—1882no—
208C22—1882no—
209C22#1309405712yes—
210C22C22×D18811yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—1882no—
216C4—1882no—
217C4—1882no—
218C4#1309405212yes—
219C4#41×D4712yes—
220C2—22no—
221C2—1884no—
222C2#1568963511yescharacteristic
223C2C2×#1309405211yescharacteristic
224C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3110
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689459C2semidirect
4. #15689404C2semidirect
5. #15689329C2semidirect
7. #15689225C2semidirect
8. C47×#432C2semidirect
12. #13094024C22semidirect
13. #13094024C22semidirect
18. C4×Dic94C22semidirect
26. #13093958C22semidirect
27. #13093949C22semidirect
30. C4⋊C8×C47C22semidirect
32. #97×C47C22semidirect
120. #432D47semidirect
121. C47#3110semidirect
141. C4⋊C8C2×D47semidirect
145. #97C2×D47semidirect